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# 7.3: Properties of Rhombi, Kites and Trapezoids

Difficulty Level: At Grade Created by: CK-12

ID: 12093

Time Required: 45 minutes

## Activity Overview

In this activity, students will discover properties of the diagonals of rhombi and kites and properties of angles in rhombi, kites, and trapezoids.

• Rhombi
• Kites
• Trapezoids

Teacher Preparation and Notes

Associated Materials

• Student Worksheet: Properties of Rhombi, Kites and Trapezoids http://www.ck12.org/flexr/chapter/9691, scroll down to the third activity.
• Cabri Jr. Application
• KING1.8xv, KING2.8xv, KING3.8xv
• TRAP.8xv

## Problem 1 – Properties of Rhombi

Students will begin this activity by looking at angle properties of rhombi. They are asked several questions about the angles and diagonals of a rhombus.

An extension of this exercise would be to prove each of these using parallel lines and transversals. Students will need to know the properties of alternate interior angles, same-side interior angles, and corresponding angles.

## Problem 2 – Properties of Kites

In Problem 2, students will be asked to begin looking at angle properties of kites. They are asked several questions about the angles and diagonals of kites.

## Problem 3 – Properties of Trapezoids

In this problem, they will explore angle properties of trapezoids. Students are given trapezoid TRAP and the measure of angles \begin{align*}T\end{align*}, \begin{align*}R\end{align*}, \begin{align*}A\end{align*}, and \begin{align*}P\end{align*}. Students will move point \begin{align*}R\end{align*} to four different positions and collect the measures of angles \begin{align*}T\end{align*}, \begin{align*}R\end{align*}, \begin{align*}A\end{align*}, and \begin{align*}P\end{align*} onto their accompanying worksheet.

An extension of this exercise would be to prove leg angles are supplementary using parallel lines and transversals. Students will need to know the properties of alternate interior angles, same-side interior angles, and corresponding angles.

## Solutions

Position \begin{align*}\angle{R}\end{align*} \begin{align*}\angle{E}\end{align*} \begin{align*}\angle{A}\end{align*} \begin{align*}\angle{D}\end{align*}
1 76 104 76 104
2 51 129 51 128
3 95 85 95 85
4 64 116 64 116

2. supplementary

3. congruent

4. right angles

5. bisect

Position \begin{align*}\angle{K}\end{align*} \begin{align*}\angle{I}\end{align*} \begin{align*}\angle{N}\end{align*} \begin{align*}\angle{G}\end{align*}
1 69 130 32 130
2 71 116 58 116
3 61 123 53 123
4 37 142 38 142

7. One pair of opposite angles is congruent and one pair of opposite angles is not congruent.

8. right angles

9. One pair of opposite angles is bisected and one set of opposite angle is not. The pair that is not congruent is the one getting bisected.

Position \begin{align*}T\end{align*} \begin{align*}R\end{align*} \begin{align*}A\end{align*} \begin{align*}P\end{align*}
1 108 72 54 126
2 126 54 45 135
3 39 141 24 156
4 57 123 37 143

11. Leg angles are supplementary.

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