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4.1 Congruent Polygons Naming & Comparing Polygons ♥ List vertices in order, either clockwise or counterclockwise. ♥ When comparing 2 polygons, begin at corresponding vertices; name the vertices in order and; go in the same direction. ♥ By doing this you can identify corresponding parts. D E C A B DCBAE I H J P <D corresponds to < I AE corresponds to PH K IJKPH Name corresponding parts • Name all the angles that correspond: < D corresponds to < I < C corresponds to < J < B corresponds to < K < A corresponds to < P < E corresponds to < H I D H E C A B J P K DCBAE IJKPH • Name all the segments that correspond: DC corresponds to IJ CB corresponds to JK BA corresponds to KP AE corresponds to PH ED corresponds to HI How many corresponding angles are there? 5 How many corresponding sides are there? 5 D E C A • How many ways can you name pentagon DCBAE? 10 B Do it. Pick a vertex and go clockwise Pick a vertex and go counterclockwise DCBAE DEABC CBAED CDEAB BAEDC BCDEA AEDCB ABCDE EDCBA EABCD Polygon Congruence Postulate If each pair of corresponding angles is congruent, and each pair of corresponding sides is congruent, then the two polygons are congruent. Congruence Statements • Given: These polygons are congruent. A B • Remember, if they are congruent, they are EXACTLY the same. D E C H G ABCD ~ = EFGH F • That means that all of the corresponding angles are congruent and all of the corresponding sides are congruent. • DO NOT say that ‘all the sides are congruent” and “all the angles are congruent”, because they are not. Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent X A B Y C Z If <A = <X and <B = <Y, then <C = <Z X You are given this graphic and statement. Write a 2 column proof. Prove: ΔLXM ~ = ΔYXM Statements ~ XL XY = ~ LM = YM ~ XM = XM ~<Y <L= L M Y ~ < XMY = < XML Reasons Given Given Reflexive Property Given All right angles are congruent ~ <LXM = < YXM Third Angle Theorem ~ ΔYXM ΔLXM = Polygon Congruence Postulate Each pair of polygons is congruent. Find the measures of the numbered angles. m<1 = 110◦ m<2 = 120◦ m<5 = 140◦ m<6 = 90◦ m<8 = 90◦ m<7 = 40◦ A student says she can use the information in the figure to prove ACB ACD. Is she correct? Explain. Given: AD and BE bisect each other. AB DE A D Prove: ACB DCE Statements Reasons 1) AD and BE bisect 1) Given each other. AB DE, A D 2) AC CD , BC CE 2) 3) ACB DCE 3) Vertical angles are congruent 4) B E 4) 5) ACB DCE 5) Assignment 4.1 Reteach Worksheet 4.1 Practice Worksheet