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4-7 Triangle Congruence: CPCTC Materials:NEW WARM UP SHEET, Pencil/Pen, NOTES SHEET WITH THEOREMS GEL 12/5 G: I CAN USE CPCTC TO PROVE PARTS OF TRIANGLES ARE CONGRUENT. E: REAL-WORLD PROBLEMS Warm Up 12/5 1. If ∆ABC ∆DEF, then A ? and BC ? . 2. List methods used to prove two triangles congruent L: PROBLEM SOLVING HOMEWORK: FINISH PROBLEM SOLVING IF NOT DONE IN CLASS… DUE TOMORROW Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC CPCTC is an abbreviation for the phrase “Corresponding Parts of Congruent Triangles are Congruent.” It can be used as a justification in a proof after you have proven two triangles congruent. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Remember! SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Example 1: Engineering Application A and B are on the edges of a ravine. What is AB? One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal. Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so AB = 18 mi. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Check It Out! Example 1 A landscape architect sets up the triangles shown in the figure to find the distance JK across a pond. What is JK? One angle pair is congruent, because they are vertical angles. Two pairs of sides are congruent, because their lengths are equal. Therefore the two triangles are congruent by SAS. By CPCTC, the third side pair is congruent, so JK = 41 ft. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Example 4: Using CPCTC In the Coordinate Plane Given: D(–5, –5), E(–3, –1), F(–2, –3), G(–2, 1), H(0, 5), and I(1, 3) Prove: DEF GHI Step 1 Plot the points on a coordinate plane. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Step 2 Use the Distance Formula to find the lengths of the sides of each triangle. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC So DE GH, EF HI, and DF GI. Therefore ∆DEF ∆GHI by SSS, and DEF GHI by CPCTC. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Check It Out! Example 4 Given: J(–1, –2), K(2, –1), L(–2, 0), R(2, 3), S(5, 2), T(1, 1) Prove: JKL RST Step 1 Plot the points on a coordinate plane. Holt McDougal Geometry 4-7 Triangle Congruence: CPCTC Check It Out! Example 4 Step 2 Use the Distance Formula to find the lengths of the sides of each triangle. RT = JL = √5, RS = JK = √10, and ST = KL = √17. So ∆JKL ∆RST by SSS. JKL RST by CPCTC. Holt McDougal Geometry