Chapter 2 Section 2.6-Part 2
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Transcript of Chapter 2 Section 2.6-Part 2
Chapter 2Section 2.6-Part 2
Proving things about Angles
Properties of Angle Congruence
• Angle congruence is reflexive, symmetric, and transitive
Reflexive: AAAangleanyFor ,
Symmetric: ABthenBAIf ,
Transitive: CAthenCBandBAIf
More Theorems and Postulates
• Theorem 2.3 Right Angle Congruence Theorem– All right angles are congruent
A
B
A and B are both right angles. Thus, A B
More Theorems and Postulates• Theorem 2.4 Congruent supplements theorem
– If two angles are supplementary to the same angle, then they are congruent to each other
H42°
PG138°
G and P are supplementary.
H and P are supplementary.
Thus, G H
More Theorems and Postulates• Theorem 2.5 Congruent complements theorem
– If two angles are complementary to the same angle, then they are congruent to each other
60°
M30°
NQ
N and M are complementary.
Q and M are complementary.
Thus, N Q
More Theorems and Postulates
• Postulate 12 Linear Pair Postulate– If two angles form a linear pair, then they are
supplementary
• Theorem 2.6 Vertical Angle Theorem– Vertical Angles are congruent
Complete the statement given that mBHD = mCHE = mEHF = 90°
•If m3 = 42, then m6 = _____
•If mBHE = 142, then m1 = _____
•If m1 = 37, then m6 = _____
•If mEHG = 132, then m7 = _____
•If m7 = 51, then m3 = _____
•If mEHB = 153, then m2 = _____
12 3
4
56
7
• A• B
• C
• D• E
• F
H
• G
Write a Two Column Proof
Statements Reasons
1. 1 and 2 are Supplementary
3 and 2 are Supplementary
2. m1 + m2 = 180 m3 + m2 = 180 3. m1 + m2 = m3 + m2
4. m1 = m3
Given: 1 and 2 are Supplementary
3 and 2 are Supplementary
Prove: 1 3
5. 1 3
Given: 1 and 2 are complementary
1 3 and 2 4
Prove: 3 and 4 are complementary 1
23
4
Statements Reasons
1. 1 and 2 are complementary
1 3 and 2 42. m1 + m2 = 903. m1 = m3, m2 = m44. m3 + m2 = 905. m3 + m4 = 906. 3 and 4 are complementary