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Published byMarion Dorsey Modified over 9 years ago
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________________ 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.
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SSS, SAS, ASA, AAS, and HL use corresponding parts to prove triangles congruent. CPCTC uses congruent triangles to prove corresponding parts congruent. Remember!
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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 ______________________. Two pairs of sides are congruent, because their ______________________.
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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?
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Example 2: Proving Corresponding Parts Congruent Prove: XYW ZYW Given: YW bisects XZ, XY YZ. Z
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Check It Out! Example 2 Prove: PQ PS Given: PR bisects QPS and QRS.
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Work backward when planning a proof. To show that ED || GF, look for a pair of angles that are congruent. Then look for triangles that contain these angles. Helpful Hint
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Example 3: Using CPCTC in a Proof Prove: MN || OP Given: NO || MP, N P
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Check It Out! Example 3 Prove: KL || MN Given: J is the midpoint of KM and NL.
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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.
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Step 2 Use the Distance Formula to find the lengths of the sides of each triangle.
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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.
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Check It Out! Example 4 Step 2 Use the Distance Formula to find the lengths of the sides of each triangle.
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Lesson Quiz: Part I 1. Given: Isosceles ∆PQR, base QR, PA PB Prove: AR BQ
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Lesson Quiz: Part II 2. Given: X is the midpoint of AC. 1 2 Prove: X is the midpoint of BD.
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