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4.3 Congruent Triangles Then: You identified and used congruent angles. Now: 1. Name and use corresponding parts of congruent triangles. 2. Prove triangles congruent using the definition of congruence.
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4.3 Congruent Triangles Corresponding parts- BCA EFD Corresponding angles: Corresponding sides: http://www.tutornext.com/system/files/u19/Congruent_triangles.gif
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Example 1: a. Identify all pairs of congruent corresponding parts. Write another congruence statement for the triangles. JKL NKM Corresponding angles: ___ ___
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Example 1 cont. Corresponding Sides: _____ _____ Congruence statement: ______ ______
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Example 1: Write a congruence statement for any figures that can be proved congruent. Explain your reasoning. b. c. _________________ ______________
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Example 2: In the diagram, ABC DEF a. Find the value of x. b. Find the value of y.
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Example 2: In the diagram, Δ FHJ Δ HFG. c. Find the value of x. d. Find the value of y.
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Theorem 4.3-Third Angles Theorem If two angles of one triangle are congruent to two angles of a second triangle, then the third angles are congruent. http://www.wyzant.com/Help/Images/congruent2.gif
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Example 3: a. TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If Δ KLM Δ NJL, KLM KML, and m KML = 47.5, find m LNJ.
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Example 3: Find the value of y. b. c.
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Example 4: Prove that triangles are congruent. a. Given: FH JH, FG JG, FHG JHG, FGH JGH Prove: FGH JGH Statements Reasons 1. FH JH, FG JG1. _________________ 2. HG HG2. _________________ 3. FHG JHG,3. _________________ FGH JGH 4. HFG HJG4. __________________ 5. FGH JGH5. __________________
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Theorem 4.4- Properties of Triangle Congruence Reflexive Property of Triangle Congruence: ABC ABC. Symmetric Property of Triangle Congruence : If ABC DEF, then DEF ABC. Transitive Property of Triangle Congruence : If ABC DEF and DEF JKL, then ABC JKL.
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Example 4: b. In the diagram, E is the midpoint of AC and BD. Show that ABE CDE.
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4.2 Assignment: p. 259-263 #10,11, 13-16, 18-20, 23, 24, 28, 30, 34, 35, 37, 43-46, 48-50, 55-57 #23 and 24 proofs on handout
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