Lesson 6-6
6. a. ∠P and ∠E, ∠O and ∠Z
(pp. 345–350)
b. ∠O and ∠P, ∠Z and ∠E
Mental Math
a. 104
R
7.
b. 156
T
c. 100
E
Guided Example 1
C
1. Linear Pair Theorem
8. a. Given
2. Corresponding Angles Postulate
c. definition of trapezoid
Questions
d. definition of isosceles trapezoid
1. trapezoids, parallelograms, isosceles trapezoids,
rhombuses, rectangles, and squares
2. m∠I = 96, m∠C = 86
___
___
3. a. AB and DC
b. ∠A and ∠B, or ∠D and ∠C
c. m∠D = 90, m∠B = 150
4. a.
b. Isosceles Triangle Base Angles Theorem
N
R
O
U
9. BC = 70
10. a. QRST
is ___
an isosceles trapezoid with bases
___
QR and ST is given. ∠Q ∠R, ∠T ∠S
by
definition of an isosceles trapezoid.
___the___
QT RS by the Isosceles Trapezoid Theorem.
___
Let m be the perpendicular bisector of ST.
m is the symmetry line of QRST by the
Isosceles Trapezoid Symmetry Theorem.
By the definition of
rm(S) = T and
___reflection,
___
=
rm(R) Q. Thus, QS RT by the Figure
Transformation Theorem. QS = RT by the
Segment Congruence Theorem.
b. The diagonals of an isosceles trapezoid are
congruent.
b.
11. a. true
b. true
c. true
C
R
O
N
U
c. One way to construct the center
___is to construct
the perpendicular bisector of RO and locate
where it intersects the symmetry line.
5. a. ∠P and ∠E, ∠O and ∠Z
b. There are not necessarily any congruent
angles.
A101
Geometry
12. a. Rectangle Symmetry Theorem
b. Answers vary. Sample: Tennis courts are likely
shaped this way for left-right symmetry and
to give an equal chance of winning to both
players or teams.
13. The symmetry lines are the lines that coincide
with the two diagonals and the two perpendicular
bisectors of the sides.
is the perpendicular bisector
14. It is
given that AB
___
of CD. By the Isosceles Triangle Symmetry
Theorem, ACD
BCD are
___and ___
___ isosceles
___
triangles. Then AC AD and BC BD by
the definition of an isosceles triangle. By the
definition of a kite, ACBD is a kite.
15. Suppose a kite has diagonals that are symmetry
lines. By the definition of kite and the Kite
Symmetry Theorem, the four sides of the kite are
congruent. Therefore, by definition of rhombus,
the kite is a rhombus.
b.
c.
16. true
17. m∠ABC = m∠AFC = 35
18.
d. no
e. yes
19. 540
20. a.
A102
Geometry