Properties of Kites and Trapezoids
Properties of Kites and Trapezoids
Properties of Kites and Trapezoids
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LESSON<br />
6-6<br />
<strong>Properties</strong> <strong>of</strong> <strong>Kites</strong> <strong>and</strong> <strong>Trapezoids</strong><br />
Lesson Objectives (p. 427):<br />
______________________________________________________________<br />
______________________________________________________________<br />
Vocabulary<br />
1. Kite (p. 427): ___________________________________________________<br />
______________________________________________________________<br />
2. Trapezoid (p. 429): ______________________________________________<br />
______________________________________________________________<br />
3. Base <strong>of</strong> a trapezoid (p. 429): _______________________________________<br />
______________________________________________________________<br />
4. Leg <strong>of</strong> a trapezoid (p. 429): ________________________________________<br />
______________________________________________________________<br />
5. Base angle <strong>of</strong> a trapezoid (p. 429): __________________________________<br />
______________________________________________________________<br />
6. Isosceles trapezoid (p. 429): _______________________________________<br />
______________________________________________________________<br />
7. Midsegment <strong>of</strong> a trapezoid (p. 431): _________________________________<br />
______________________________________________________________<br />
Copyright © by Holt, Rinehart <strong>and</strong> Winston. 137 Geometry<br />
All rights reserved.
LESSON<br />
6-6<br />
<strong>Properties</strong> <strong>of</strong> <strong>Kites</strong> <strong>and</strong> <strong>Trapezoids</strong><br />
Lesson Objectives (p. 427):<br />
______________________________________________________________<br />
use properties <strong>of</strong> kites to solve problems; use properties <strong>of</strong> trapezoids to<br />
______________________________________________________________<br />
solve problems.<br />
Vocabulary<br />
1. Kite (p. 427): ___________________________________________________<br />
a quadrilateral with exactly two pairs <strong>of</strong> congruent sides.<br />
______________________________________________________________<br />
2. Trapezoid (p. 429): ______________________________________________<br />
a quadrilateral with exactly one pair <strong>of</strong> parallel sides.<br />
______________________________________________________________<br />
3. Base <strong>of</strong> a trapezoid (p. 429): one _______________________________________<br />
<strong>of</strong> the two parallel sides <strong>of</strong> the trapezoid.<br />
______________________________________________________________<br />
4. Leg <strong>of</strong> a trapezoid (p. 429): ________________________________________<br />
one <strong>of</strong> the two nonparallel sides <strong>of</strong> the trapezoid.<br />
______________________________________________________________<br />
5. Base angle <strong>of</strong> a trapezoid (p. 429): __________________________________<br />
one <strong>of</strong> a pair <strong>of</strong> consecutive angles whose<br />
______________________________________________________________<br />
common side is a base <strong>of</strong> the trapezoid.<br />
6. Isosceles trapezoid (p. 429): _______________________________________<br />
a trapezoid in which the legs are congruent.<br />
______________________________________________________________<br />
7. Midsegment <strong>of</strong> a trapezoid (p. 431): _________________________________<br />
the segment whose endpoints are the<br />
______________________________________________________________<br />
midpoints <strong>of</strong> the legs <strong>of</strong> the trapezoid.<br />
Copyright © by Holt, Rinehart <strong>and</strong> Winston. 137 Geometry<br />
All rights reserved.
LESSON 6-6 CONTINUED<br />
Key Concepts<br />
8. Theorems—<strong>Properties</strong> <strong>of</strong> <strong>Kites</strong> (p. 427):<br />
THEOREM HYPOTHESIS CONCLUSION<br />
6-6-1<br />
6-6-2<br />
9. Theorems—Isosceles <strong>Trapezoids</strong> (p. 429):<br />
THEOREM DIAGRAM EXAMPLE<br />
6-6-3<br />
6-6-4<br />
6-6-5<br />
Copyright © by Holt, Rinehart <strong>and</strong> Winston. 138 Geometry<br />
All rights reserved.
LESSON 6-6 CONTINUED<br />
Key Concepts<br />
8. Theorems—<strong>Properties</strong> <strong>of</strong> <strong>Kites</strong> (p. 427):<br />
THEOREM HYPOTHESIS CONCLUSION<br />
6-6-1 If a quadrilateral is a kite,<br />
then its diagonals are<br />
perpendicular.<br />
(kite → diags. )<br />
6-6-2 If a quadrilateral is a kite,<br />
then exactly one pair <strong>of</strong><br />
opposite angles are<br />
congruent.<br />
(kite → one pair opp. )<br />
9. Theorems—Isosceles <strong>Trapezoids</strong> (p. 429):<br />
Copyright © by Holt, Rinehart <strong>and</strong> Winston. 138 Geometry<br />
All rights reserved.<br />
A<br />
A<br />
B<br />
D<br />
B<br />
D<br />
C<br />
C<br />
AC BD<br />
B D<br />
A C<br />
THEOREM DIAGRAM EXAMPLE<br />
6-6-3 If a quadrilateral is an<br />
isosceles trapezoid, then<br />
each pair <strong>of</strong> base angles<br />
are congruent.<br />
(isosc. trap. → base )<br />
6-6-4 If a trapezoid has one pair<br />
<strong>of</strong> congruent base angles,<br />
then the trapezoid is<br />
isosceles.<br />
(trap. with pair base<br />
→ isosc. trap.)<br />
6-6-5 A trapezoid is isosceles if<br />
<strong>and</strong> only if its diagonals<br />
are congruent.<br />
(isosc. trap. ↔ diags. )<br />
B<br />
C<br />
A D<br />
B<br />
C<br />
A D<br />
B<br />
C<br />
A D<br />
A D<br />
B C<br />
ABCD is<br />
isosceles.<br />
AC<br />
DB<br />
↔<br />
ABCD is<br />
isosceles.
LESSON 6-6 CONTINUED<br />
10. Theorem 6-6-6—Trapezoid Midsegment Theorem (p. 431):<br />
Theorem 6-6-6<br />
11. Get Organized Write the missing terms in the unlabeled sections. Then write<br />
the definition <strong>of</strong> each term. (p. 431)<br />
Parallelograms<br />
Quadrilaterals<br />
Rectangles Squares<br />
Rhombuses<br />
Copyright © by Holt, Rinehart <strong>and</strong> Winston. 139 Geometry<br />
All rights reserved.
LESSON 6-6 CONTINUED<br />
10. Theorem 6-6-6—Trapezoid Midsegment Theorem (p. 431):<br />
Theorem 6-6-6 The midsegment <strong>of</strong> a trapezoid<br />
is parallel to each base, <strong>and</strong><br />
its length is one half the sum<br />
<strong>of</strong> the lengths <strong>of</strong> the bases.<br />
XY BC , XY AD <br />
XY 1<br />
(BC AD)<br />
2<br />
B C<br />
X Y<br />
A D<br />
11. Get Organized Write the missing terms in the unlabeled sections. Then write<br />
the definition <strong>of</strong> each term. (p. 431)<br />
Rectangles<br />
quads with<br />
4 rt. <br />
Parallelograms<br />
quads<br />
with 2 pair <strong>of</strong> || sides<br />
Squares<br />
quads with 4 rt. <br />
<strong>and</strong> 4 ≅ sides<br />
Quadrilaterals<br />
Rhombuses<br />
quads with<br />
4 ≅ sides<br />
polygons<br />
with 4 sides<br />
<strong>Trapezoids</strong>:<br />
quads with exactly<br />
1 pair <strong>of</strong> || sides<br />
Isosceles<br />
trapezoid: traps.<br />
with ≅ legs<br />
<strong>Kites</strong>: quads<br />
with exactly 2<br />
pairs <strong>of</strong> congruent<br />
sides<br />
Copyright © by Holt, Rinehart <strong>and</strong> Winston. 139 Geometry<br />
All rights reserved.
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