Over Lesson 42 5-Minute Check 1 BELLRINGER: 1)Find m 1. 2) Find m 2. 3) Find m 3. Concept 1 Example 1 Identify Corresponding Congruent Parts Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ. Sides: Angles: Example 1 The support beams on the fence form congruent triangles. In the figure ABC DEF, which of the following congruence statements correctly identifies corresponding angles or sides? A. B. C. D. Example 2 Use Corresponding Parts of Congruent Triangles O PCPCTC m O=m PDefinition of congruence 6y 14=40Substitution In the diagram, ITP NGO. Find the values of x and y. Example 2 Use Corresponding Parts of Congruent Triangles 6y=54Add 14 to each side. y=9Divide each side by 6. NG=ITDefinition of congruence x 2y=7.5Substitution x 2(9)=7.5y = 9 x 18=7.5Simplify. x=25.5Add 18 to each side. CPCTC Answer: x = 25.5, y = 9 Example 2 A.x = 4.5, y = 2.75 B.x = 2.75, y = 4.5 C.x = 1.8, y = 19 D.x = 4.5, y = 5.5 In the diagram, FHJ HFG. Find the values of x and y. Concept 2 Example 3 Use the Third Angles Theorem ARCHITECTURE A drawing of a towers roof is composed of congruent triangles all converging at a point at the top. If IJK IKJ and m IJK = 72, find m JIH. m IJK + m IKJ + m JIK=180Triangle Angle-Sum Theorem JIK JIH Congruent Triangles Example 3 Use the Third Angles Theorem m IJK + m IJK + m JIK =180Substitution m JIK =180Substitution m JIK =180Simplify. m JIK =36Subtract 144 from each side. m JIH =36Third Angles Theorem Answer: m JIH = 36 Example 3 A.85 B.45 C.47.5 D.95 TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If KLM NJL, KLM KML, and m KML = 47.5, find m LNJ. Example 4 Prove That Two Triangles are Congruent Write a two-column proof. Prove:LMN PON Example 4 Prove That Two Triangles are Congruent 2. LNM PNO 2. Vertical Angles Theorem Proof: StatementsReasons 3. M O 3. Third Angles Theorem 4.LMN PON 4. CPCTC 1. Given 1. Example 4 Find the missing information in the following proof. Prove:QNP OPN Proof: ReasonsStatements 3. Q O, NPQ PNO 3. Given 5. Definition of Congruent Polygons 5. QNP OPN 4. _________________ 4. QNP ONP ? Reflexive Property of Congruence Given Example 4 A.CPCTC B.Vertical Angles Theorem C.Third Angles Theorem D.Definition of Congruent Angles Concept 3