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Advanced Geometry
Topic 2 – Reasoning and Proof
Proving Angles Congruent (2-6 Day 2)
Name: _________________________________________________
Date: ______________________________ Period: ___________
Complete the proofs by filling in the blanks.
1.
Given: ∠1 and ∠2 are supplementary
∠3 and ∠4 are supplementary
∠2 ≅ ∠3
Prove: ∠1 ≅ ∠4
STATEMENTS
REASONS
1)
2) 𝑚∠1 + 𝑚∠2 = 180
3) ∠3 and ∠4 are supplementary
4)
Definition of supplementary angles
5) 𝑚∠1 + 𝑚∠2 = 𝑚∠3 + 𝑚∠4
6)
Given
7) 𝑚∠2 = 𝑚∠3
8)
Substitution property (steps 5 & 7)
9)
10)
2.
Given: 𝑚∠2 = 2(𝑚∠1)
Prove: 𝑚∠1 = 60
STATEMENTS
REASONS
1)
2)
3)
4) 3(𝑚∠1) = 180
5)
Definition of linear pair
3.
Given: ∠𝐵𝐴𝐶 is a right angle
∠2 ≅ ∠3
Prove: ∠1 and ∠3 are complementary
STATEMENTS
REASONS
1)
2)
Definition of right angle
3) 𝑚∠1 + 𝑚∠2 = 𝑚∠𝐵𝐴𝐶
4)
Substitution property (steps __ & __ )
5)
Given
6)
Definition of ≅
7)
Substitution property (steps __ & __ )
8)
4.
Given: 𝑚∠1 = 𝑚∠3
Prove: 𝑚∠𝐽𝑂𝐿 = 𝑚∠𝐾𝑂𝑀
STATEMENTS
REASONS
1)
2)
Reflexive property
3)
Addition postulate
4)
Angle addition postulate
5)
6)
5.
̅̅̅̅ bisects ∠𝐵𝐴𝐶
Given: 𝐴𝐷
∠1 ≅ ∠3
Prove: ∠2 ≅ ∠3
STATEMENTS
REASONS
1)
2)
Definition of angle bisector
3)
Given
4)