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