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 TI84.
 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, sameside 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
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, sameside interior angles, and corresponding angles.
Solutions
1. Sample answers:
Position 





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 





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 





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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