Geometry 201 unit 4.4

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• UNIT 4.4 USING CORRESPONDING PARTS OF CONGRUENT TRIANGLES

• Warm Up

1. If ABC DEF, then A ? and BC ? .

2. What is the distance between (3, 4) and (1, 5)?

3. If 1 2, why is a||b?

4. List methods used to prove two triangles congruent. DConverse of Alternate Interior Angles TheoremSSS, SAS, ASA, AAS, HL

• Use CPCTC to prove parts of triangles are congruent. Objective

• CPCTCVocabulary

• 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.

• Example 1: Engineering ApplicationA 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.

• 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.

• Example 2: Proving Corresponding Parts Congruent Prove: XYW ZYW

• Example 2 Continued

• Check It Out! Example 2

• Check It Out! Example 2 Continued

• Example 3: Using CPCTC in a Proof

• 5. CPCTC5. NMO POM6. Conv. Of Alt. Int. s Thm.4. AAS4. MNO OPM3. Reflex. Prop. of 2. Alt. Int. s Thm.2. NOM PMO1. GivenReasonsStatementsExample 3 Continued

• Check It Out! Example 3

• Check It Out! Example 3 Continued5. CPCTC5. LKJ NMJ6. Conv. Of Alt. Int. s Thm.4. SAS Steps 2, 34. KJL MJN3. Vert. s Thm.3. KJL MJN2. Def. of mdpt.1. GivenReasonsStatements

• Example 4: Using CPCTC In the Coordinate PlaneGiven: 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.

• Step 2 Use the Distance Formula to find the lengths of the sides of each triangle.

• 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 RSTStep 1 Plot the points on a coordinate plane.

• Check It Out! Example 4 Step 2 Use the Distance Formula to find the lengths of the sides of each triangle.

• Lesson Quiz: Part I1. Given: Isosceles PQR, base QR, PA PB Prove: AR BQ

• Lesson Quiz: Part I Continued

• Lesson Quiz: Part II2. Given: X is the midpoint of AC . 1 2Prove: X is the midpoint of BD.

• Lesson Quiz: Part II Continued

• Lesson Quiz: Part III3. Use the given set of points to prove DEF GHJ: D(4, 4), E(2, 1), F(6, 1), G(3, 1), H(5, 2), J(1, 2).

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