Download Chapter 5 - Frost Middle School

Chapter 5
EA = HG, HOG EXA. Because
corresponding angles of congruent figures are
congruent, HOG EXA.
Proofs Using Congruence
Self-Test
(pp. 300–301)
1. ∠L, because corresponding parts of congruent
figures are congruent.
12.
F
___
2. RB, because corresponding parts of congruent
figures are congruent.
3. m∠2 = 143. m∠5 = m∠3 by the Vertical Angles
Theorem, and m∠2 + m∠3 = 180 by the Interior
Angles Theorem.
T
S
4.
4 cm
4 cm
4 cm
5. a. AE = EB and AC = BC by the Perpendicular
Bisector Theorem. Therefore, by the
definition of congruence AEC BEC,
and thus ∠ECA ∠ECB since corresponding
angles of congruent figures are congruent.
13. I, O, and E are not necessarily collinear, as
collinearity cannot be assumed from a picture.
14. The road goes in an east-west direction and is the
perpendicular bisector of the segment with
endpoints at Smallville and Littleville.
Smallville
b. 2x - 20 = x + 15; x = 35
6. By the definition of midpoint, MN = NB. Since
it is given that AM = MN, by transitivity, AM =
NB. By___
the Segment Congruence Theorem,
____
AM NB.
7. x + x + 2x = 180, so 4x = 180 and x = 45; the
measure of the third angle is 90.
8. a. Given
Littleville
15. By the Alternate Interior Angles Theorem, he
should make sure that he draws a line such that
the alternate interior angle of the given figure is
also 40.
16. Answers vary. Sample:
C
B
D
A
b. Vertical Angles Theorem
c. Given
d. Transitive Property
e. Corresponding Angles Theorem
9. (10 – 2) · 180 = 1,440, and there are 10 angles, so
each angle is 144°.
10. 2x. Because ∠EAB is an exterior angle, its
measure is the sum of the measures of the two
interior angles not adjacent to it.
11. Answers vary. Sample: Draw auxiliary lines from
E to A and from H to G. Then FEAT FHGT,
since both have four right angles and equivalent
sides. Now HO = EX by the definition of
reflection, as OG = XA. Therefore, since
A88
Geometry
17. a.
30°
30°
b. She turned 30° to the left. Because the lines
of travel west are parallel, the corresponding
angles must be congruent, so she turned the
same amount to the left.