4-3 Congruent triangles.

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4-4 Using Congruent Triangles: CPCTC

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Presentation transcript:

4-3 Congruent triangles

Congruent Polygons We will use: CPCTC for congruent triangles (A LOT!) Corresponding parts of congruent triangles are congruent CPCTC!!

Example Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Angles: Sides: Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE = RTPSQ.

TWAP The support beams on the fence form congruent triangles. In the figure ΔABC  ΔDEF, which of the following congruence statements correctly identifies corresponding angles or sides? A. B. C. D.

Example In the diagram, ΔITP  ΔNGO. Find the values of x and y. <O= <P CPCTC m<O = m<P 6y – 14 = 40 6y = 54 y = 9

Example 2 continued CPCTC NG = IT x – 2y = 7.5 x – 2(9) = 7.5 y = 9 Answer: x = 25.5, y = 9

TOO In the diagram, ΔFHJ = ΔHFG. Find the values of x and y. A. x = 4.5, y = 2.75 B. x = 2.75, y = 4.5 C. x = 1.8, y = 19 D. x = 4.5, y = 5.5

Third Angle Theorem

Example Write a two-column proof. Prove: ΔLMN  ΔPON

Example continued 1. Given 1. 2. LNM  PNO Proof: Statements Reasons 1. Given 1. 2. LNM  PNO 2. Vertical Angles Theorem 3. M  O 3. Third Angles Theorem 4. ΔLMN  ΔPON 4. CPCTC

Homework Pg. 259-262 #9, 11,13-16, 18-20, 37, 43