2.4 Congruent Supplements and Complements. If <1 is a supplement to < A, and <2 is a supplement to <A, what can you say about <s 1 and 2? Theorem 4: If.

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Presentation transcript:

2.4 Congruent Supplements and Complements

If <1 is a supplement to < A, and <2 is a supplement to <A, what can you say about <s 1 and 2? Theorem 4: If angles are supplementary to the same angle, then they are congruent.

Theorem 5: If angles are supplementary to congruent angles, then they are congruent.

Given:<F is supp to <G <H is supp to <J <G = <J Conclusion: <F = <H ~ ~ <F is supp to <G so <F + <G = 180 m<G = <Fm<F = <G <H is supp to <Jm<H = <J m<H = <G (substitution) <F = <H Both have the same measure. ~

Theorem 6: If angles are complementary to the same angle, then they are congruent. Theorem 7: If angles are complementary to congruent angles, then they are congruent.

However, for Theorems 4-7 need to be memorized in order to help remember concepts. Look for the double use of the word complementary or supplementary in a problem. When studying the definitions of such terms as right angle, bisector, midpoint and perpendicular, you will master the concepts more quickly if you try to understand the ideas involved without memorizing definitions word for word.

Given: <A is comp. to <C <DBC comp. <C Conclusion: C B A D StatementReason 1.<A comp <C1. Given 2.<DBC comp <C2. Given 3.<A = <DBC3. If angles are complementary to the same angle, then they are congruent. ~

ROSE Y Given:<6 = <7 Prove:<5 = <8 ~ ~ Statement Reason 1.<6 = <7 2.<ROS is a straight < 3.<6 is supp. to <5 4.<OSE is a straight <. 5.<7 is supp. to <8. 6.<5 = <8 1.Given 2.Assumed from diagram. 3.If 2 <‘s form a strt <, they are supplementary. 4.Same as #2. 5.Same as #3 6.Supplements of = <s are =. ~~ ~ ~