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Jay: You know the difference between you and me? I make this look GOOD. 4.1 Congruent Figures Congruent Polygons Have the same size and shape. You can slide, flip, or turn the figure so that it fits exactly on the other one. You can determine whether two figures are congruent by comparing their corresponding parts. Order is very important! When you name congruent polygons, you must list corresponding parts in the same order. 4.1 Example 1 B F A E D C ABCD G H EFGH Complete each congruence statement. AB _____ EF A _____ E BC _____ FG B _____ F CD _____ GH C _____ G DA _____ HE D _____ H 4.1 Example 2 Suppose that ΔWYS ΔMKV. If m W=62 and m Y=35, what is m V? Explain. Y K 35° W 62° S 62 + 35 + m S = 180 m S = 83 m S = m V = 83 V M Triangle Angle-Sum Thm. Subtraction 4.1 Example 2 Suppose that ΔWYS ΔMKV. If m W=62 and m Y=35, what is m V? Explain. Y K 35° W 62° S W M Y S K V V M Corresponding parts of congruent triangles are congruent. (CPCTC) 4.1 Congruent Figures How many conditions must be proved to show that two triangles are congruent? The definition states that the figures must have congruent sides and angles. Since there are 3 sides and 3 angles in a triangle, we will need 6 congruence statements to prove two triangles congruent. 4.1 Example 3 D Is Δ ABD Δ CBD? A AD DC Given BD BD Reflexive Prop of B C Is this enough to conclude the triangles are congruent? NO. 4.1 Congruent Figures Theorem 4.1 Third Angles Theorem If two angles of one triangle are congruent to two angles of another triangle, then the third angles are congruent. D A B If A C D and B E F E, Then C F Note: This is the reason why we cannot use AAA to prove triangles congruent. Proof p. 220 4.1 Example 4 Given: A D, AE Prove: Δ AEB DC, EB CB, BA BD Δ DCB A B C D E A D, AE DC, EB CB, BA BD Given ABE DBC Vertical angles are AEB DCB Δ AEB Δ DCB Third Angle Thm. Def. of Δ’s Homework • pg. 222 #10-29 12 Iextraordinary need to believe, that something is possible. There has to be a mathematical explanation for how bad that tie is