2.6 Proving Stmnts about angles

2.6 Proving Stmnts about angles - 5. <1...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
2.6 Proving Statements about Angles p. 109
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
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 < <
Background image of page 2
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
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Thm 2.3 – Right Angle Congruence Thm. Statements 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
Background image of page 4
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
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Proof of congruent suppl. Thm. Statements 1. <1 & <2 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
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 10
Background image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: 5. &lt;1 &lt;3 Reasons 1. Given 1. defn,. of suppl &lt;s 1. Subst. prop of = 2. - prop of = 3. Defn. of &lt;s 2245 2245 Thm. 2.5 Congruent complements thm If 2 &lt;s are complementary to the same &lt; (or to &lt;s), then they are . If &lt;1 &amp; &lt;2 are complementary, and &lt;2 &amp; &lt;3 are complementary, then &lt;1 &lt;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 &lt;s form a linear pair, then they are supplementary. &lt;1 &amp; &lt;2 are a linear pair, therefore they are suppl. 1 2 Thm. 2.6 Vertical &lt;s Thm. Vertical angles are . &lt;1 &lt;3 &amp; &lt;2 &lt;4. 2245 2245 2245 1 3 2 4 Proof of Vertical &lt;s thm Statements 1. &lt;1 &amp; &lt;3 are vert. &lt;2 &amp; &lt;4 are vert. 2. &lt;1 &amp; &lt;2 are a lin pr.; &lt;3 &amp; &lt;2 are a lin. pr. 3. &lt;1 &amp; &lt;2 are suppl; &lt;3 &amp; &lt;2 are suppl. 4. &lt;1 &lt;3 Reasons 1. Given 1. Defn. of Lin. Pr. 1. Ln. Pr. Post. 1. Suppls. Thm. 2245 2245 Assignment Assignment...
View Full Document

This note was uploaded on 02/12/2011 for the course MTG 3212 taught by Professor Jackson during the Spring '11 term at University of Florida.

Page1 / 11

2.6 Proving Stmnts about angles - 5. &amp;amp;lt;1...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online