3 2 Corresponding Parts of Congruent Triangles CPCTC

3. 2 Corresponding Parts of Congruent Triangles CPCTC: Corresponding parts of congruent triangles are congruent. Using CPCTC to prove parts of congruent triangles are congruent. Ex 1 p. 138 ▬ W Given: ▬ WZ bisects TWV ▬ WT WV ▬ ▬ Prove: TZ VZ PROOF Statements ___ 1. WZ bisects TWV 2. TWZ VWZ __ ___ 3. WT WV 4. WZ 5. Δ TWZ Δ VWZ 6. TZ TZ 2/27/2021 Reasons T Z V 1. Given 2. The bisector of an angle separates it into two ’s 3. Given 4. Identity 5. SAS 6. CPCTC Section 3. 2 Nack 1

Three Types of Conclusions Involving Triangles 1. Proving triangles congruent. 2. Proving corresponding pairs of congruent triangles. Note that the two triangles have to be proven congruent before you use CPCTC. 3. Establishing a further relationship. Note that the two triangles have to be proven congruent and also apply CPCTC first. 2/27/2021 Section 3. 2 Nack 2

Example 2 p. 139 __ __ Given: ZW YX ZY WX Prove: ZY || WX Z Y 2 1 W X Plan for Proof: Show that ΔZWX ΔXYZ ; then we can say that 1 2 by CPCTC. Since these are alt. int angles for ZY and WX, these lines must be parallel. Statements Reasons ___ __ 1. ZW YX; ZY WX 1. Given 2. ZX 2. Identity 3. ΔZWX ΔXYZ 3. SSS 4. 1 2 4. CPCTC 5. ZY || WX 5. If two lines are cut by a transversal so that the alt. Int. s are , these lines are parallel. 2/27/2021 Section 3. 2 Nack 3

Suggestions for Proving Triangles Congruent 1. Mark the figures systematically, using: a. A square in the opening of each right angle. b. The same number of dashes on congruent sides. c. The same number of arcs on congruent angles. 2. Trace the triangles to be proved congruent in different colors. 3. If the triangles overlap, draw them separately. 2/27/2021 Section 3. 2 Nack 4

Right Triangles and the HL method for proving Right Triangles Congruent. Hypotenuse Leg Theorem 3. 2. 1: If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of a second right triangle then the triangles are congruent. (HL) This theorem is illustrated in the construction on p. 141, Example 3, Fig. 3. 20 Ex. 4 p. 141 Pythagorean Theorem: The square of the length (c) of the hypotenuse of a right triangle equals the sum of the squares of the lengths (a and b) of the legs of the right triangle. a² + b² = c² Ex. 5 p. 142 2/27/2021 Section 3. 2 Nack 5