2.8 Proving Angle Relaonships - Republic Middle School

Geo (H) 2.8 Proving Angle Relationships.notebook

2.8 Proving Angle RelaonshipsObjecves: 1. You will analyze given statements and diagrams to write proofs about angle addion and angle congruence.

Example 1:Given: ∠1 and ∠4 form a linear pair m∠3 +m ∠1 = 180Prove: ∠3 ≅ ∠4


Example 2:

If ∠1 and ∠2 are vercal angles and m∠1 = d – 32 and m∠2 = 175 – 2d, find m∠1 and m∠2. Jusfy each step.


Example 3:

In the figure, ∠NYR and ∠RYA form a linear pair, ∠AXY and ∠AXZ form a linear pair, and ∠RYA and ∠AXZ are congruent. Prove that ∠NYR and ∠AXY are congruent.


Example 4:Given: ∠1 and ∠3 are complementary ∠2 and ∠3 are complementaryProve: ∠1 ≅ ∠2


2.8 p.156

#1,6,8‐13,29,30,36‐39


Geo (H) 2.8 Proving Segment Relationships

1) 26 + <3=90 <3 = 64 Complement Theorem

6) 8) <5 + 90 + <5 = 180 2<5 = 90 <5 = 45

m<5 = m<6Congruent Supplements Theorem

9) <2 + <3 = 90 28 + <3 = 90 m<3 = 62<1 + <2 + <3 + <4 = 180 <1 + 90 + <4 = 180 <1 + <4 = 90 <1 + <1 = 90 2<1 = 90 <1 = 45m<1 = m<4 = 45Congruent Complements& Congruent Supplements Theorems.

10) <2 + <4 = 180 <4 + <5 = 180 ∴<2 = <5 <2 + 105 = 180 <2 = 75 ∴<5 = <75 <2 + <3 = 180 75 + <3 = 180

<3 = 105Congruent SupplementsTheorem

11) <9 + <10 = 180 3x + 12 + x 14 = 180 4x = 192 x = 48 <9=156, <10=24 Supplement Theorem

12) <3=<4 by Vertical Angles Theorem 2x + 23 = 5x 112 3x = 135 x = 45 <3 = <4 = 113

13) <6 + <7 = 180 by Supp. Thm. 2x 21 + 3x 34 = 180 5x = 235 x = 47 <6 = 73 , <7 = 103 by Vertical Angle Thm < 8 = 73

29)

30)

36) 4

37) B

38) H

39) B

2.8 p.156 #1,6,8‐13,29,30,36‐39

2.8 Proving Angle Relaonships - Republic Middle School

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