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# 2.6 Proving Stmnts about angles - 5<1<3 Reasons 1...

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2.6 Proving Statements about Angles p. 109

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Theorem 2.2 – Properties of Angle Congruence Angle congruence is reflexive, symmetric, and transitive. A. A A, any For < 2245 < < A. B then B, A If 2245 < < 2245 < < C. A then C, B and B, A If 2245 < < 2245 < < 2245 < <
Proof of transitive part : Given: <A <B and <B <C Prove: <A <C Statements 1. <A <B; <B <C 2. m<A=m<B; m<B=m<C 3. m<A=m<C 4. <A <C * You will be proving the reflexive & symmetric parts for homework. Reasons 1. Given 2. Defn. of <s 3. Trans. Prop. Of = 4. Defn. of <s 2245 2245 2245 2245 2245 2245 2245 2245

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Thm 2.3 – Right Angle Congruence Thm. Statements 1. <A & <B are right <s. 2. m<A=90 o ; m<B=90 o 3. m<A=m<B 4. <A <B Reasons 1. Given 2. Defn. of rt. < 3. Subst. prop of = 4. Defn. of <s All right <s are . 2245 2245 2245
Thm 2.4 - supplements thm. If 2 <s are supplementary to the same < (or to <s), then they are . If <1 & <2 are suppl & <2 & <3 are suppl, then <1 <3. 2245 2245 2245 1 2 3 2245

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Proof of congruent suppl. Thm. Statements 1. <1 & <2 are suppl.; <2 & <3 are suppl. 2. m<1+m<2=180 o ; m<2+m<3=180 o 3. m<1+m<2=m<2+m<3 4. m<1=m<3 5. <1 <3 Reasons 1. Given

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Unformatted text preview: 5. <1 <3 Reasons 1. Given 1. defn,. of suppl <s 1. Subst. prop of = 2. - prop of = 3. Defn. of <s 2245 2245 Thm. 2.5 – Congruent complements thm • If 2 <s are complementary to the same < (or to <s), then they are . • If <1 & <2 are complementary, and <2 & <3 are complementary, then <1 <3. • Proof is almost identical to the last thm., just change suppl. to compl. 2245 2245 2245 1 2 3 Postulate 12 – Linear Pair Post. • If 2 <s form a linear pair, then they are supplementary. • <1 & <2 are a linear pair, therefore they are suppl. 1 2 Thm. 2.6 – Vertical <s Thm. • Vertical angles are . • <1 <3 & <2 <4. 2245 2245 2245 1 3 2 4 Proof of Vertical <s thm Statements 1. <1 & <3 are vert. <2 & <4 are vert. 2. <1 & <2 are a lin pr.; <3 & <2 are a lin. pr. 3. <1 & <2 are suppl; <3 & <2 are suppl. 4. <1 <3 Reasons 1. Given 1. Defn. of Lin. Pr. 1. Ln. Pr. Post. 1. Suppls. Thm. 2245 2245 Assignment Assignment...
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2.6 Proving Stmnts about angles - 5<1<3 Reasons 1...

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