4.1 Congruent Polygons

Naming & Comparing Polygons D C B E 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. DCBAE P I J K H <D corresponds to < I AE corresponds to PH IJKPH

Name corresponding parts Name all the angles that correspond: P I J K H A D C B E < D corresponds to < I < C corresponds to < J < B corresponds to < K < A corresponds to < P < E corresponds to < H DCBAE IJKPH Name all the segments that correspond: How many corresponding sides are there? 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 5

How many ways can you name pentagon DCBAE? 10 Do it. Pick a vertex and go clockwise Pick a vertex and go counterclockwise DEABC CDEAB BCDEA ABCDE EABCD DCBAE CBAED BAEDC AEDCB EDCBA

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. 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”, because they are not. C D B A G H F E CONGRUENCE STATEMENT ABCD = EFGH ~

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 If <A = <X and <B = <Y, then <C = <Z Y B Z C

~ Prove: ΔLXM = ΔYXM You are given this graphic and statement. Write a 2 column proof. X ~ Prove: ΔLXM = ΔYXM Statements Reasons XY = XL LM = YM XM = XM < L = < Y < XMY = < XML <LXM = < YXM ΔLXM = ΔYXM ~ Given ~ Given ~ Reflexive Property ~ Given L Y ~ M All right angles are congruent ~ Third Angle Theorem Polygon Congruence Postulate ~

Each pair of polygons is congruent 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.

Definition of a bisector Given: bisect each other. and  A  D Prove: ACB  DCE Statements Reasons 1) AD and BE bisect each other. AB  DE, A  D 1) Given 2) AC  CD , BC  CE 2) 3) ACB  DCE 3) 4) B  E 4) 5) ACB  DCE 5) Definition of a bisector Vertical angles are congruent Third Angles Theorem Polygon Congruence Postulate

Assignment 4.1 Reteach Worksheet 4.1 Practice Worksheet