7.3: Properties of Rhombi, Kites and Trapezoids
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.
Topic: Quadrilaterals & General Polygons
- Rhombi
- Kites
- Trapezoids
Teacher Preparation and Notes
- This activity was written to be explored with the Cabri Jr. app on the TI-84.
- To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
- To download the calculator files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=12093 and select READ1, READ2, READ3, KING1, KING2, KING3, and TRAP.
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
- READ1.8xv, READ2.8xv, READ3.8xv
- 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
1. Sample answers:
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
6. Sample answers:
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.
10. Sample answers:
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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