Download “Congru-Ment” Angles Given: ∠1 is complementary to ∠2 ∠3 is

“Congru-Ment” Angles
GEOMETRY
NAME______________________________
Per._______ DATE ___________________
Proofs
Fill in the missing Statements and Justifucations to prove each theorem.
Congruent Complements Theorem
Congruent Supplements Theorem
If two angles are complementary to the same
angle (or congruent angles), then the two angles
are congruent.
1
2
3
Given:
∠1 is complementary to ∠2
∠3 is complementary to ∠2
If two angles are supplementary to the same
angle (or congruent angles), then the two angles
are congruent.
1
2
3
Prove: Given:
∠1 ≅ ∠3 ∠1 is supplementary to ∠2
∠3 is supplementary to ∠2
Prove:
∠1 ≅ ∠3
STATEMENTS
JUSTIFICATIONS
STATEMENTS
JUSTIFICATIONS
GIVEN
__________
1) ______ are complementary
1) ∠1 & ∠2 are supplementary
2) ∠3 & ∠2 are ___________
3) m∠1 + m∠2 = 90°
___________
Definition of
________________ ______________
4) m∠1 = _________
5) _________________
6) m∠3 = 90° - m∠2
7) __________________
8) ∠3 ≅ ∠1
9) ∠1 ≅ ∠3
2) ________________________
3) m∠1 + m∠2 = _____
GIVEN
Definition of
SUPPLEMENTARY ANGLES
SUBTRACTION
Property of Equality
4) _____ = 180° - m∠2
_____________________
Property of Equality
Definition of
COMPLEMENTARY ANGLES
5) _________________
Definition of
________________ ______________
_____________________
Property of Equality
TRANSITIVE
Property of Equality
Definition of
____________ ____________
____________________
Property of Congruence
6) m∠3 = 180° - _____
7) m∠3 = m∠1
8) m∠1 = m∠3
9) ___________
SUBTRACTION
Property of Equality
___________________
Property of Equality
____________________
Property of Equality
Definition of
CONGRUENT ANGLES