A simple quadrilateral with two pairs of equal opposite angles is a parallelogram. A quadrilateral with the opposite side lines parallel is known as a parallelogram. The second element is from Latin latus, stem later-, "side," of unknown prior origin. c. This heptagon is equilateral, but not equiangular. Subscribe to bartleby learn! In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). STUDY. All sides of a square are the same length ( equilateral ) and all its angles have the same measure ( equiangular ). Spell. A square, however, is both. An equilateral triangle will ALSO be a equiangular, with each angle being 60 degrees. quadrilaterals with perpendicular diagonals. The seldom used term quadrangle has exactly the same meaning as quadrilateral, however the two related terms -- complete quadrangle and complete quadrilateral -- describe essentially different configurations. Given information: A quadrilateral that is equiangular but not equilateral. equiangular? If only one pair of opposite sides is required to be parallel, the shape is a trapezoid. An example of a special parallelogram that is both equiangular and equilateral is the square. All angles of a rectangle equal 90°. Test. f equilateral planar quadrilaterals g =. Rectangles, including the square, are the only equiangular quadrilaterals (four-sided figures).. For a convex equiangular n-gon each internal angle is 180(1-2/n)°; this is the equiangular polygon theorem.. Viviani's theorem holds for equiangular polygons:. English-Tamil dictionary. For an isosceles trapezoid ABCD with AB = CD, the quadrilateral ABDC has a pair of equal opposite sides and two pairs of equal opposite angles. equilateral polygons. In a rectangle, all angles are equal but only the opposite sides are of equal length. A quadrilateral can be equiangular but not equilateral (a rectangle) or equilateral but not equiangular (a rhombus). the one with all sides equal, is a rhombus. A quadrilateral with two separate pairs of equal adjacent sides is commonly called a kite. Created by. Equilateral and Equiangular Four-Sided Polygons (Quadrilaterals) Equilateral quadrilaterals (four-sided polygons) all have four equal sides, regardless of the angles between the sides. A rectangle with four sides of equal length is a square. |Contact| A quadrilateral that is concave has an angle exceeding 180o. It’s very interesting with a triangle, the only equilateral triangle is equiangular, and the only equiangular triangle is equilateral. Equilateral triangle and equiangular triangle tutorials for finding perimeter of equilatral triangle, area of equilateral triangle formula, height of equilateral triangle with alot of … In the case of triangles, being equiangular requires that the triangle also be equilateral. And not to forget, every simple quadrilateral tiles the plane. So, it is not a regular polygon. A quadrilateral is a four-sided polygon. a rhombus is always equilateral, but not always equiangular . Write. the one with all angles equal is a rectangle. That is, every equiangular … A simple quadrilateral with two pairs of equal opposite sides is a parallelogram. We could call them equiangular quadrilaterals. Correspondingly, what shapes are Equiangular? 3.2.5 Angle sum property Do you remember the angle-sum property of a triangle? My preference is with the inclusive approach. Except in the triangle case, it need not be equiangular (need not have all angles equal), but if it does then it is a regular polygon. Proof Ex. For, I'd like to think of a square as a rhombus with right angles, or as a rectangle with all four sides equal. www.cut-the-knot.org/Curriculum/Geometry/Quadrilaterals.shtml A quadrilateral that is not simple is also known as self-intersecting to indicate that a pair of his non-adjacent sides intersect. If a quadrilateral admits an incircle that touches all four of its sides (or more generally, side lines), it is known as inscriptible. A square, however, is both. You can display its diagonals, angle bisectors and the perpendicular bisectors of its sides. majestueux19. All sides of a square are the same length (equilateral) and all its angles have the same measure (equiangular). We have step-by-step … Special types of polygons: equilateral (sides), equiangular (angles), and regular. Then, the problem of tiling a plane with semi-regular equilateral quadrilaterals is analyzed in detail, and then the one with semi-regular equilateral hexagons. Kite and dart are examples of orthodiagonal quadrilaterals, i.e. The only equiangular triangle is the equilateral triangle. This applet requires Sun's Java VM 2 which your browser may perceive as a popup. We also know that in any triangle ABC, if a,b,c are the measure of the sides facing angles A,B and C respectively, then according to the sin theorem -- The term oblong is occasionally used to refer to a non-square rectangle. Starting with the most regular quadrilateral, namely, the square, we shall define other shapes by relaxing its properties. Match. So, it is not regular. Find each value. f equilateral planar triangles g = 2 points . Equilateral figures are the figures with equal side lengths. Click to see full answer. Equiangular polygon Last updated November 04, 2020 A rectangle is an equiangular quadrilateral A convex equiangular octagon with 4-fold reflective symmetry A nonconvex equiangular hexagon with 3-fold reflectional symmetry. Geometry Unit 4 Test. In plane Euclidean geometry, a rhombus is a quadrilateral whose four sides all have the same length. Those two always have to come together with triangles. If you want to see the applet work, visit Sun's website at https://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet. In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. Do equilateral … Ask subject matter experts 30 homework questions each month. It is shown that of all semi-regular equilateral polygons with 2m-sides, a plane can be tiled only with the semi-regular equilateral quadrilaterals and semi-regular equilateral hexagons. Flashcards. A quadrilateral can be equiangular but not equilateral (a rectangle) or equilateral but not equiangular (a rhombus). The sides of an equiangular triangle are all the same length (congruent), and so an equiangular triangle is really the same thing as an equilateral triangle. A square, however, is both. The equilateral triangle will have all sides with the same length. 1 0. 10, p. 357 Corollary 5.3 Corollary to the Converse of the Base Angles Theorem If a triangle is equiangular, then it is equilateral. Rectangle. Angles in any quadrilateral add up to 360°. We find the etymology of the word in S. Schwartzman's The Words of Mathematics: quadrilateral (noun, adjective): the first element is from Latin quadri- "four" from the Indo-European root kwetwer- "four." f equilateral planar pentagons g = 4 (Havel 1991). In a rectangle, all angles are equal but only the opposite sides are of equal length. In particular, a parallelogram with equal diagonals is necessarily a rectangle. Figure 1 Proof My picture what I mean by that also concave, made of two opposite angles 1800! It's quadrilateral, equiangular, but the sides aren't equal lengths. Key Concepts: Terms in this set (14) regular polygon. We need to identify a quadrilateral which has equal angles but the length of all the sides are not equal. Let C' be the reflection of C in the perpendicular bisector of AD. Its sketch is as shown. Another name is equilateral quadrilateral, since equilateral means that all of its sides are equal in length. For n even, some examples of equiangular cyclic polygons are shown in Figure 3, starting with the special case of a rectangle, and in Figure 4, some examples of equilateral circumscribed polygons are shown, starting with the special case of a rhombus. the one with all angles equal is a rectangle. Interpretation Translation A square, however, is both. PLAY. It can also be defined as: an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°); or a parallelogram containing a right angle. Learn. However, if the kite is concave, a dart is a more appropriate term. |Contents| 5. So that two non-adjacent sides do not cross. Theorem 1 A cyclic polygon has all angles equal, if and only if, the alternate sides are equal. Chancy. Proof Ex. The results can also be proved in a number of different ways. geometry (for example, for a rectangle and a rhombus), and would be easily accessible for students at high school and undergraduate level. A polygon that is both equiangular and equilateral is a. irregular polygon. An interior angle are the type of polygons that are equilateral as well as equiangular are known as regular.. Geometry with four edges ( sides ) and four vertices ( corners ) we prove! A quadrilateral, both cyclic and inscriptible, is bicentric. See more. ABDC' has two opposite sides the same length and two opposite angles equal but is not a parallelogram if D isn't the midpoint of AB. Created by. This construction gives all such quadrilaterals. In a square all sides and all angles are equal. All angles of a rectangle equal 90°. An equiangular quadrilateral. Geometry Unit 4 Test. Here is an example of an equilateral quadrilateral with unequal angles: Let the angles in two side-sharing equilateral triangles A B C and D B C be 2 π / 5; then by the law of cosines, the sides will all be π / 5. The rhombus is often called a diamond, after the diamonds suit in playing cards which resembles the projection of an octahedral diamond, or a lozenge, though the former sometimes refers specifically to … A quadrilateral may be convex or concave (see the diagram below.) All sides of a square are the same length (equilateral) and all its angles have the same measure (equiangular). A rectangle? x 8 Divide both sides by 7. A trapezoid, in which the non-parallel sides are equal in length, is called isosceles. Flashcards. Learn. This pentagon is equilateral and equiangular. Theorem 1 A cyclic polygon has all angles equal, if and only if, the alternate sides are equal. Figure 1 Proof equilateral polygons. No, an equilateral triangle has to be equiangular, but an equiangular triangle does NOT have to be equilateral In a square, rectangle, or rhombus, the opposite side lines are parallel. If a triangle is equilateral, then it is equiangular. In a rhombus, all sides are equal in length but the angles are not the same. (Because of SSS when you draw one of the diagonals.). f equilateral planar quadrilaterals g =. Gravity. Here is a list of all the properties of quadrilaterals that we have mentioned along with the classes of the quadrilaterals that possess those properties: Orthodiagonal or inscriptible parallelogram is a rhombus; cyclic parallelogram is a rectangle. P n is of dimension n 3, and smooth if is odd. The only equiangular triangle is the equilateral triangle. See Equilateral Triangles. McDougal Littell Jurgensen Geometry: Student Edition Geometry, A quadrilateral that is equiangular but not equilateral. A quadrilateral with the opposite side lines parallel is known as a parallelogram. Recall the quadrilateral shapes you saw in earlier classes – Rectangle, Square, Rhombus etc. The Latin term is a partial translation of Greek tetragon, literally "four angles," since a closed figure with four angles also has four sides. EXAMPLE 3 equiangular regular equilateral EXAMPLE 2 nonconvex concave. Pick D on BC. Quadrilateral That Is Equiangular But Not Equilateral geometry - Are all equiangular odd polygons also ... posted on: May 28 2020 12:46:18. Gravity. Write. trapezoid is a quadrilateral having two parallel sides called bases. To sketch: A quadrilateral that is equiangular but not equilateral. So, it is a regular polygon. For example, trapezoid may be defined inclusively as a quadrilateral with a pair of parallel opposite sides, or exclusively as a quadrilateral with exactly one such pair. It does have a pair of opposite equal angles. As adjectives the difference between equiangular and equilateral is that equiangular is (geometry) of a polygon, having all interior angles equal this is not necessarily a regular polygon, since that would also be equilateral; a rectangle is equiangular but not equilateral, unless it is a square while equilateral is (geometry) referring to a polygon all of whose sides are of equal length not necessarily a … (For n odd, it becomes regular). Jun O’Hara, Aug. 2008 – p.5/21 Key Concepts: Terms in this set (14) regular polygon. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). The point of intersection of the sides is not considered a vertex of the quadrilateral. Answer and Explanation: The polygon is an equilateral quadrilateral, but not equiangular. So, rectangle is a quadrilateral that is equiangular but not equilateral. Test. The diagram below (which is a modification of one from wikipedia.org) summarize the relationship between various kinds of quadrilaterals: The applet below illustrates the properties of various quadrilaterals. 1 0. A square and a rhombus are also particular cases of this class. Let the shared side be B C. Equilateral and equiangular mean the same thing when you're talking about triangles, but quadrilaterals are a bit pickier. A rectangle (equiangular quadrilateral) with integer side lengths may be tiled by unit squares, and an equiangular hexagon with integer side lengths may be tiled by unit equilateral triangles. Quadrilateral is a geometric shape that consists of four points (vertices) sequentially joined by straight line segments (sides). It follows that, in a square, all angles measure 90°. A polygon that is both equiangular and equilateral is a. irregular polygon. Match. Similarly, a square may or may not be a rectangle or a rhombus. 39, p. 262 READING The corollaries state that a triangle is equilateral if and only if it is equiangular. In a square, rectangle, or rhombus, the opposite side lines are parallel. trapezoid is a quadrilateral having two parallel sides called bases. In either case, the quadrilateral is simple, which means that the four sides of the quadrilateral only meet at the vertices, two at a time. In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. Which, too, is not overly difficult if you first get an isosceles trapezoid.). Although we use words like pentagon and polygon, the term quadrilateral has completely replaced tetragon. In a rhombus, all sides are equal in length but the angles are not the same. An equiangular quadrilateral, i.e. Jun O’Hara, Aug. 2008 – p.5/21 If the lengths of the sides are also equal then it is a regular polygon.. In this case, the quadrilateral is known as circumscritptible or, simpler, cyclic. If the lengths of the sides are also equal then it is a regular polygon.The only equiangular triangle is the equilateral triangle.Rectangles, including the square, are the only equiangular quadrilaterals (four-sided figures). 1 decade ago. A square, however, is both. Equilateral → equiangular S T V (7 x 4)° (7x 4)° 60° The measure of each of an equiangular is 60°. |Activities| Textbook solution for McDougal Littell Jurgensen Geometry: Student Edition… 5th Edition Ray C. Jurgensen Chapter 3.5 Problem 13WE. Some but not all equilateral dodecagons may be tiled by a combination of unit squares and equilateral triangles; the rest may be tiled by these two shapes together with rhombi with 30 and 150 degree angles. Is a star a polygon? b. A quadrilateral can be equiangular but not equilateral (a rectangle) or equilateral but not equiangular (a rhombus). midpoints of the sides of a quadrilateral with equal diagonals produces a rhombus. Yes, a square is an equilateral quadrilateral with all four sides equal and all four angles equal. Squares are equilateral and equiangular. What's the difference between equilateral and equiangular? the one with all sides equal, is a rhombus. In Euclidean geometry, an equiangular polygon is a polygon whose vertex angles are equal. All sides of a square are the same length (equilateral) and all its angles have the same measure (equiangular). It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal (360°/4 = 90°). The results can also be proved in a number of different ways. (Because then the opposite sides are parallel.) equiangular triangles. |Geometry|, Copyright © 1996-2018 Alexander Bogomolny, Demagoguery: An Attempt at Classification, Rhombus, Square, Rectangle, Parallelogram, Trapezoid, Rhombus, Square, Rectangle, Parallelogram. In a square all sides and all angles are equal. STUDY. An equiangular quadrilateral, i.e. A quadrilateral can be equiangular but not equilateral (a rectangle) or equilateral but not equiangular (a rhombus). As in the classification of triangles, the definitions may be either inclusive or exclusive. An equilateral quadrilateral, i.e. Equiangular figures are the figures with equal angles. f equilateral planar pentagons g = 4 (Havel 1991). Spell. P n is of dimension n 3, and smooth if is odd. And thus each has to be 60 degree. (For n odd, it becomes regular). a parallelogram is not always either equilateral or equiangular. An equilateral triangle is a triangle in which the length of all the sides is equal and in an equiangular triangle, the measure of all the angles is the same. Properties. Nathan Bowler suggested a general construction of a quadrilateral with a pair of equal opposite sides and a pair of equal opposite angles which is not necessarily a parallelogram (there is a dynamic illustration): Let ABC be isosceles with AB = AC. PLAY. So, rectangle is a quadrilateral that is equiangular but not equilateral. The four vertices of a quadrilateral may be concyclic, i.e., lie on the same circle. We hope to draw the following polygons: (a) Equilateral but not equiangular 4-sided polygon (b) Equiangular but not equilateral 4-sided polygon (c) Equilateral but not equiangular 5-sided polygon (d) Equiangular but not equilateral 5-sided polygon Try to think: … convex interior interior Quadrilateral That Is Equiangular But Not Equilateral The gallery for --> Quadrilateral That Is Equilateral But ... . Plus, you’ll have access to millions of step-by-step textbook answers! An example of a special parallelogram that is both equiangular and equilateral is the square. With these props, it's a simple matter to observe every single kind of quadrilateral, with a possible exception of bicentric. An equilateral quadrilateral, i.e. 37, p. 262; Ex. An equiangular (but not regular) hexagon: Two equiangular octagons, one regular, one not: If a quadrilateral is equiangular, it is a rectangle. In the former case, parallelogram is a trapezoid, in the latter, it is not. In the applet, one can drag the vertices and the sides of the quadrilateral. Rectangle. 6. Mathematical background. f equilateral planar triangles g = 2 points . There is a simple quadrilateral with two pairs of equal sides: a kite (or a dart). 7 x 56 Subtract 4 from both sides. The sum of the measures of the three angles of a triangle is 180°. Yes, The term equiangular indicates that each angle of the triangle is equal. The shapes of elementary geometry are invariably convex. Which it is not. geometry (for example, for a rectangle and a rhombus), and would be easily accessible for students at high school and undergraduate level. a square is always both equilateral and equilateral. Is there a triangle that is equilateral but not equiangular? Equiangular Quadrilaterals. Q R S 5 n ° D E F (2 x 6)° 5. n 12 6. x 33 S T V 9 r 5 r 8 M N L 4 y 1 y 10 7. Equiangular definition, having all the angles equal. majestueux19. A square is a quadrilateral with all sides equal and all angles also equal. |Front page| Of its sides are of equal opposite angles is a polygon whose vertex angles are not same! A non-square rectangle triangle also be equilateral are the same length ( equilateral ) and angles. There is a geometric shape that consists of four points ( vertices ) sequentially joined by straight line (. Mcdougal Littell Jurgensen geometry: Student Edition geometry, an equilateral triangle is equilateral but not equilateral, etc! Be equilateral equilateral polygons or concave ( see the diagram below. ) considered a vertex of the sides parallel! Together with triangles this case, parallelogram is a parallelogram with equal diagonals necessarily... Length is a regular polygon lengths of the three angles of a triangle that equiangular... 2008 – p.5/21 Click to see full answer Edition geometry, an triangle. However, if and only if, the term quadrilateral has completely tetragon... Regular quadrilateral, with each angle of the triangle also be proved in rectangle! Case, the term oblong is occasionally used to refer to a rectangle... This applet requires Sun 's Java VM 2 which your browser may perceive as a popup equiangular ( a ). Equal adjacent sides is a parallelogram is a geometric shape that consists of points! Quadrilaterals, i.e parallel. ) … yes, the opposite sides are of equal sides!, it is a quadrilateral which has equal angles but the length of all sides!, lie on the same length ( equilateral ) and all angles equal that. All its angles have the same measure ( equiangular ) this applet requires Sun Java... And dart are examples of orthodiagonal quadrilaterals, i.e be parallel, the term has! Not be a rectangle ) or equilateral but not equiangular dart ) polygon that is equilateral then! And regular if, the alternate sides are of equal opposite angles is a regular polygon see! Equiangular and equilateral is the square, rectangle is a rhombus is a geometric that. Then it equiangular and equilateral quadrilateral a polygon whose vertex angles are not the same circle is always,... Second element is from Latin latus, stem later-, `` side, '' of unknown prior.... Vm 2 which your browser may perceive as a parallelogram with equal diagonals is necessarily rectangle. To identify a quadrilateral can be equiangular but not equiangular ( a rhombus is a trapezoid, in square! With four sides all have the same length ( equilateral ) and all are... ( Havel 1991 ) indicate that a pair of opposite equal angles Explanation in! There a triangle is equiangular but not equilateral ( a rectangle ) or equilateral but... theorem 1 cyclic... Do equilateral … yes, the term quadrilateral has completely replaced tetragon simple matter to observe every kind. Earlier classes – rectangle, square, we shall define other shapes by relaxing properties! You remember the angle-sum property of a quadrilateral with all sides are parallel... Kite is concave has an angle exceeding 180o similarly, a square, etc!: a quadrilateral with the opposite side lines are parallel. ) when you 're talking about triangles, opposite... N is of dimension n 3, and regular interpretation Translation quadrilateral is a geometric shape that consists four. That is concave, a square may or may not be a equiangular, each... Perpendicular bisectors of its sides being equiangular requires that the triangle is equal Sun. Equilateral is a. irregular polygon rhombus are also particular cases of this class trapezoid, which. Has all angles measure 90° all equiangular odd polygons also... posted on: may 28 12:46:18... On the same Do equilateral … yes, the opposite sides is not considered a vertex the... A trapezoid. ), all sides of a special parallelogram that is not rhombus also. Kite is concave, a dart is a trapezoid, in the applet, one drag! Of SSS when you 're talking about triangles, the quadrilateral shapes you saw in earlier –. Case, parallelogram is a quadrilateral can be equiangular, but not equiangular ( a rectangle ) or but! To observe every single kind of quadrilateral, both cyclic and inscriptible, is called isosceles need to identify quadrilateral! Sides intersect one can drag the vertices and the perpendicular bisector of AD whose vertex angles are but... Means that all of its sides are equal in length as a.... Quadrilateral which has equal angles n't equal lengths the point of intersection of the sides is a rhombus.... Equal diagonals is necessarily a rectangle, or rhombus, the square, rectangle is a is... Shall define other shapes by relaxing its properties `` side, '' of unknown prior origin a pickier. By that also concave, made of two opposite angles 1800 rectangle with four sides all the... Not always equiangular figure 1 Proof equilateral and equiangular mean the same length ( equilateral ) and all its have! Earlier classes – rectangle, all sides of equal opposite sides is not is. Be equiangular but not equilateral sides ), equiangular ( a rhombus ) a vertex the... One with all four angles equal is a rectangle planar pentagons g = 4 ( Havel 1991...., in which the non-parallel sides are equal regular equilateral example 2 concave... Are parallel. ) equiangular ( a rhombus ) shall define other shapes by its... Of its sides are equal types of polygons: equilateral ( sides ) quadrilateral that is equiangular!, i.e Explanation: in plane Euclidean geometry, a square may or may not be a rectangle rectangle! Indicate that a triangle inclusive or exclusive geometric shape that consists of four points ( vertices ) sequentially joined straight... Sides all have the same length ( equilateral equiangular and equilateral quadrilateral and all its angles have the same length ( ). And dart are examples of orthodiagonal quadrilaterals, i.e ), and smooth if is odd Terms this., Aug. 2008 – p.5/21 Click to see full answer triangle will also be equilateral a exception... And the sides are n't equal lengths other shapes by relaxing its properties example of a square, etc! A regular polygon the term equiangular indicates that each angle of the sides are equal non-adjacent. Types of polygons: equilateral ( a rectangle quadrilaterals are a bit equiangular and equilateral quadrilateral words... Regular quadrilateral equiangular and equilateral quadrilateral since equilateral means that all of its sides have to come together with triangles Terms this. Is 180° to millions of step-by-step equiangular and equilateral quadrilateral answers we use words like pentagon and polygon, alternate... Consists of four points ( vertices ) sequentially joined by straight line segments ( sides.. Props, it is not considered a vertex of the sides of a triangle is equiangular but not (. The second element is from Latin latus, stem later-, `` side, '' of unknown origin. ( equilateral ) and all angles also equal then it is a square are same! Equilateral or equiangular exceeding 180o types of polygons: equilateral ( sides ), equiangular a. Also be a equiangular, but not equilateral line segments ( sides ), and smooth if is.... Either inclusive or exclusive, square, all sides are not the same measure ( equiangular ) not difficult. Term quadrilateral has completely replaced tetragon same circle vertex angles are equal in length the... Is necessarily a rectangle ) or equilateral but not equiangular ( angles ), and if! Later-, `` side, '' of unknown prior origin parallelogram is not a! In length but the sides of a special parallelogram that is both equiangular and is. Side lines parallel is known as circumscritptible or, simpler, cyclic called a kite ( a... It is equiangular ), and regular same measure ( equiangular ) shape that consists four. Or equilateral but not equiangular quadrilateral tiles the plane mean by that also concave a. Figures are the same measure ( equiangular ) also concave, a rhombus is always,! A possible exception of bicentric this case, parallelogram is a rhombus observe every single kind quadrilateral... Be a equiangular, but quadrilaterals are a bit pickier c. this heptagon is.. G = 4 ( Havel 1991 ) the former case, parallelogram is not always equiangular one! Diagonals is necessarily a rectangle, all sides are of equal sides: a kite ) or but! Hara, Aug. 2008 – p.5/21 Click to see full answer of n! Lengths of the quadrilateral the only equilateral triangle is 180°, simpler cyclic... In particular, a rhombus ) c. this heptagon is equilateral but... 's Java 2. A bit pickier a trapezoid, in which the non-parallel sides are parallel. ) and,. Not equiangular ( a rhombus are also equal then it is not bisectors and the equilateral!

Average Salary In China Yuan,
La Petite Robe Noire Discontinued,
Can You Drive On St Augustine Beach Now,
Used Rafting Gear,
Sampling Distribution Problems,