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# 7.3: Properties of Rhombi, Kites, and Trapezoids

Difficulty Level: At Grade Created by: CK-12

This activity is intended to supplement Geometry, Chapter 6, Lesson 5.

## Problem 1 – Properties of Rhombi

You will begin this activity by looking at angle properties of rhombi. Open the Cabri Jr. application by pressing APPS and selecting CabriJr. Open the file READ1 by pressing Y=\begin{align*}Y=\end{align*}, selecting Open..., and selecting the file. You are given rhombus READ and the measure of angles R\begin{align*}R\end{align*}, E\begin{align*}E\end{align*}, A\begin{align*}A\end{align*}, and D\begin{align*}D\end{align*}.

1. Move point E\begin{align*}E\end{align*} to four different positions. Record the measures of angles R\begin{align*}R\end{align*}, E\begin{align*}E\end{align*}, A\begin{align*}A\end{align*}, and D\begin{align*}D\end{align*} in the table below.

Position R\begin{align*}\angle{R}\end{align*} E\begin{align*}\angle{E}\end{align*} A\begin{align*}\angle{A}\end{align*} D\begin{align*}\angle{D}\end{align*}
1
2
3
4

2. Consecutive angles of a rhombus are ___________________.

3. Opposite angles of a rhombus are ___________________.

Next, you will look at the properties of the angles created by the diagonals of a rhombus. Open the file READ2. You are given rhombus READ and the measure of angles ESR\begin{align*}ESR\end{align*}, ASE\begin{align*}ASE\end{align*}, RSD\begin{align*}RSD\end{align*}, and ASD\begin{align*}ASD\end{align*}.

4. Move point E\begin{align*}E\end{align*} to four different positions. Angles formed by the intersection of the two diagonals of a rhombus are ___________________.

Open the file READ3. You are given rhombus READ and the measure of all angles created by the diagonals of the rhombus.

5. Move point E\begin{align*}E\end{align*} to four different positions. The diagonals of a rhombus _________ the vertices of the rhombus.

## Problem 2 – Properties of Kites

You will begin this problem by looking at angle properties of kites. Open the file KING1. You are given kite KING and the measure of angles K\begin{align*}K\end{align*}, I\begin{align*}I\end{align*}, N\begin{align*}N\end{align*}, and G\begin{align*}G\end{align*}.

6. Move point I\begin{align*}I\end{align*} to two different positions and point K\begin{align*}K\end{align*} to two different positions. Record the measures of angles K\begin{align*}K\end{align*}, I\begin{align*}I\end{align*}, N\begin{align*}N\end{align*}, and G\begin{align*}G\end{align*} in the table below.

Position K\begin{align*}\angle{K}\end{align*} I\begin{align*}\angle{I}\end{align*} N\begin{align*}\angle{N}\end{align*} G\begin{align*}\angle{G}\end{align*}
1
2
3
4

7. What do you notice about the opposite angles of a kite?

Next, you will look at the properties of the angles created by the diagonals of a kite. Open the file KING2. You are given kite KING and the measure of angles ISK\begin{align*}ISK\end{align*}, GSN\begin{align*}GSN\end{align*}, ISN\begin{align*}ISN\end{align*}, and GSK\begin{align*}GSK\end{align*}.

8. Move point I\begin{align*}I\end{align*} to four different positions. Angles formed by the intersection of the two diagonals of a kite are ___________________.

Open the file KING3. You are given kite KING and the measure of all angles created by the diagonals of the kite.

9. Move point I\begin{align*}I\end{align*} to four different positions. What do you notice about the angles created by the diagonals of a kite?

## Problem 3 – Properties of Trapezoids

In this problem, you will look at angle properties of trapezoids. Open the file TRAP. You are given trapezoid TRAP and the measure of angles T\begin{align*}T\end{align*}, R\begin{align*}R\end{align*}, A\begin{align*}A\end{align*}, and P\begin{align*}P\end{align*}.

10. Move point R\begin{align*}R\end{align*} to four different positions. Record the measures of angles T\begin{align*}T\end{align*}, R\begin{align*}R\end{align*}, A\begin{align*}A\end{align*}, and P\begin{align*}P\end{align*} in the table below.

Position T\begin{align*}\angle{T}\end{align*} R\begin{align*}\angle{R}\end{align*} A\begin{align*}\angle{A}\end{align*} P\begin{align*}\angle{P}\end{align*}
1
2
3
4

11. What do you notice about the angles of a trapezoid?

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