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1-5-15 Unit 7 Congruency and Similarity Congruent Figures and Triangles 1 First, we need to look at some things. What makes two figures congruent? All the corresponding sides are congruent. All the corresponding angles are congruent. 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 Name corresponding parts Name all the angles that correspond: D corresponds to C corresponds to B corresponds to A corresponds to E corresponds to I J K P H I D H E C A B DCBAE J P K 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 Naming & Comparing Polygons D ♥ 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 corresponds to I AE corresponds to PH E C A B DCBAE I H J P K IJKPH Polygon Congruence Rule If each pair of corresponding angles is congruent, and each pair of corresponding sides is congruent, then the two polygons are congruent. What makes two figures congruent? All the corresponding sides are congruent. All the corresponding angles are congruent. Congruence Statements A B Given: These polygons are congruent. Remember, if they are congruent, they are EXACTLY the same. D E C H G ABCD ~ = EFGH That means that all of the corresponding angles are F congruent and all of the corresponding sides are congruent. DO NOT say that ‘all the sides are congruent” and “all the angles are congruent”, unless it is given or marked.NOT because it “LOOKS like it. LMCBJK. Complete the following statements. BK 1. LC_____ Labeling an angle or a side in correct order is very important. CM 2. KJ_____ ML 3. JB_____ B 4. L_____ C 5. K_____ J 6. M_____ KJB 7. CML_____ CLM 8. KBJ_____ JBK 9. MLC_____ MCL 10. JKB_____ Lets see if you can do it. Lets label the congruent parts L P N M Q R N R NL RP L P LM PQ M Q NM RQ NLM RPQ Now it’s you turn to label all the congruent parts for the triangles. S F A T B C A C AS CF S F ST FB T B TA BC AST CFB