Download 2-6 Proving Angles Congruent

Warm-up
2-4 Answers
1. a.
Add. Post.
b.Subst. Prop.
+5 c. Simplify.
d.Subtr. Prop. =
e. Div. Prop. of =
3. a. Mult. Prop. of =
+3 b. Distr. Prop.
c. Add. Prop. of =
5. Reflexive Prop. of
7. Div. Prop. of =
9. Mult. Prop. of =
11.Subtr. Prop. =
13. Subst. Prop.
15.Transitive Prop
17. 5x
19. K
21. 3
23. XYZ
WYT
25. Sample: LR and RL are
diff ways to name the same
segment & CBA and ABC
are diff ways to name the
same .
41 total -1 for < 25
27. a.Given
b.Def. of midpoint
+5 c. Subst. Prop. =
d.Subtr. Prop. =
e. Div. Prop. of =
29.a.
1. m GFE + m EFI = m GFI
+6 ( Addition Post.)
2. 9x – 2 + 4x = 128 (Subst.)
3. 13x – 2 = 128 (Simplify.)
4. 13x = 130 (Add. Prop. of =)
5. x = 10 (Div. Prop. of =)
b. 40
30. a. Given
b. Def. of Bisector
c. Subst. Prop.
+5 d. Subtr. Prop. Of =
e. Div. Prop. Of =
32. reflexive, symmetric, transitive
33. transitive
34. reflexive, symmetric, transitive
35. symmetric
43. Elena’s teacher is
concerned.
44. If a person has a job, then
that person can save money
each week.
2-5
Identifying Angle Pairs
I can identify angle pairs to prove and apply
theorems about them.
Vertical Angles: two angles whose sides
form two pairs of opposite rays.
4
1
3
2
Ex:
1&
2&
3
4
Adjacent Angles: two coplanar angles with
a common side, a common vertex, and no
common interior points.
Ex:
1&
A
1
B
2
C
2
Non-ex:
2 & ABC
Complementary Angles: two angles
whose measures have a sum of 90.
Supplementary Angles: two angles whose
measures have a sum of 180.
These angles may or may not be adjacent.
See p. 96.
See Ex. 1 on p. 97.
a. If m EFD = 27, find m AFD. 153
F
A
E
B
D
C
b. Is
AFB
EFD?
can’t tell
See p. 97 for the conclusions you can draw
from diagrams and those things you
cannot assume.
See Ex. 2 on p. 97.
Can you make each conclusion? Explain.
c.
TW
WV
T
Yes, tick
marks
No, no
marks
d.
W
P
PW WQ
e. TV
PQ No, no box
f.
PWT &
TWQ are adj.
V
s
Yes, they share a side
g. W is the midpoint of TV
Yes, TW & WV are congruent so
W is the midpoint.
Q
Thm 2-1: Vertical Angles Thm
Vertical angles are congruent.
2
1
4
3
Find the measure of each angle.
h. m 2 = 228 - 3x and m 4 = x
A is supplementary to
B is supplementary to
Write the conclusion.
A
B.
C.
C
Note: Neither the Law of Syllogism nor
the Trans Prop works for supplementary
Thm 2-2
Congruent Supplements Thm
If 2 angles are supplements of the same
angle (or of congruent angles), then the 2
angles are congruent.
Theorem 2-3
Congruent Complements Thm
p. 98
See the proof of Thm 2-2 p. 99.
Theorem 2-4
All right angles are congruent.
Theorem 2-5
If 2 angles are congruent and
supplementary, then each is a right angle.
2-5 p. 100-104
#10-21, 28, 32-34,
67-74