The document provides 4 examples proving properties of angles and triangles related to congruent complements and supplements. Each example gives angle or side relationships as given information, then uses properties of parallel lines, isosceles triangles, or angle relationships like complementary, supplementary and vertical angles to prove additional angle or side relationships and triangle congruence. The examples demonstrate theorems about congruent complements implying congruent angles and congruent supplements implying congruent angles.

1. M
Given: K is the midpoint of HM and AT
A
Prove: (a) ΔTMK ≅ ΔAHK
K
(b) <T ≅ <A
T (c) MT || AH
H
1.) Statement Reason
1) K is mdpt of HM & AT 1) Given
2) HK ≅ KM, AK ≅ KT 2) mdpt 2 ≅ segments
3) <1 ≅ <2 3) Vertical <s ≅ <s
4) ΔTMK ≅ ΔAHK 4) SAS
5) <T ≅ <A 5) ≅ Δs ≅ parts
6) MT || AH 6) || lines alt int <s ≅

2. B A
2.) 1
2
C D
1) AB ≅ CD 1) Given
2) <1 ≅ <2 2) Given
3) AC ≅ AC 3) Reflexive
4) ΔCAB ≅ ΔACD 4) SAS
5) <DAC ≅ <ACB 5) ≅ Δs ≅ parts
6) BC || DA 6) || lines alt int <s ≅
D
C E
3.)
A B
1) CA ≅ CB 1) Given
2) <CAB ≅ <ECB 2) Given
3) ΔACB isosceles 3) 2 ≅ sides isos Δ
4) <CAB ≅ <CBA 4) isos Δ ≅ base <s
5) <ECB ≅ <CBA 5) Transitive
6) CE || AB 6) || lines alt int <s ≅

3. B
4.)
D E
A C
Statements Reasons
1) BA ≅ BC 1) Given
2) <BDE ≅ <BCA 2) Given
3) ΔBAC isosceles 3) 2 ≅ sides isosceles
4) <BAC ≅ <BCA 4) isosceles ≅ base <s
5) <BDE ≅ <BAC 5) transitive
6) DE || AC 6) || lines corr <s ≅

4. Warmup:
1.) What are complementary angles?
Draw an example of a pair of adjacent complementary angles.
Draw an example of a pair of non­adjacent complmntry angles.
2.) What are supplementary angles?
Draw an example of a pair of adjacent supplementary angles.
Draw an example of a pair of non­adjacent supplmntry angles.

5. Theorem: congruent complements congruent angles
(≅ comps ≅ <'s)
E Given: <GOM is a right angle
G EO OY
1 M Prove: <1 ≅ <3
2
3
o Y
1.) <GOM is a right angle 1.) Given
2.) <1, <2 are comp <s 2.) Def of complementary
3.) EO OY 3.) Given
4.) <EOY is a rt < 4.) lines rt <s
5.) <2, <3 are comp <s 5.) Def of complementary
6.) <1 ≅ <3 6.) ≅ comps ≅ <'s

6. Complete in your notes:
R Given: RA bisector of HE
T W <2 ≅ <3
<H ≅ <E
2 3 Prove: ΔTHA ≅ ΔWEA
1 4
H A E

7. Theorem: congruent supplements congruent angles
(≅ sups ≅ <'s)
E Given: Line BOY, <2 ≅ <3
1 2
B 4 Y
o 3 Prove: <1 ≅ <4
M