1. 1-5-15 Unit 7 Congruency and Similarity 1 Congruent Figures and Triangles

2. 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.

3.  How many ways can you name pentagon DCBAE? A D C B E 10 Do it. DCBAE CBAED BAEDC AEDCB EDCBA Pick a vertex and go clockwisePick a vertex and go counterclockwise DEABC CDEAB BCDEA ABCDE EABCD

4. Name corresponding parts  Name all the angles that correspond: A D C B E P I J K H D corresponds to I C corresponds to J B corresponds to K A corresponds to P E corresponds to H DCBAEIJKPH 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? How many corresponding sides are there? 5 5

5. 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. A D C B E DCBAE P I J K H IJKPH  D corresponds to  I AE corresponds to PH

6. 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.

7. Congruence Statements  Given: These polygons are congruent.  Remember, if they are congruent, they are EXACTLY the same.  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”, unless it is given or marked.NOT because it “LOOKS like it. G H F E C D B A CONGRUENCE STATEMENT ABCD = EFGH ~

8.  LMC  BJK. Complete the following statements. 1.LC  _____ 2.KJ  _____ 3.JB  _____ 4.  L  _____ 5.  K  _____ 6.  M  _____ 7.  CML  _____ 8.  KBJ  _____ 9.  MLC  _____ 10.  JKB  _____ BK CM ML B C J KJB CLM JBK MCL Labeling an angle or a side in correct order is very important. Lets see if you can do it.

9. Lets label the congruent parts L NM P Q R  N  R  L  P  M  Q NL  RP LM  PQ NM  RQ  NLM   RPQ

10. AT S BC FNow it’s you turn to label all the congruent parts for the triangles.  A  C  S  F  T  B AS  CF ST  FB TA  BC  AST   CFB

11. Prove: ΔLXM = ΔYXM ~ X Y M L Statements Reasons XY = XLGiven LM = YMGiven XM = XMReflexive Property  LXM =  YXMGiven  L =  YGiven  XMY =  SMLRight angles ΔLXM = ΔYXMPolygon Congruence Postulate ~ ~ ~ ~ ~ ~ ~