Lesson 4-3 Congruent Triangles Congruent triangles- triangles that are the same size and shape Definition of Congruent Triangles (CPCTC) Two triangles.

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Presentation transcript:

Lesson 4-3 Congruent Triangles Congruent triangles- triangles that are the same size and shape Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding sides are congruent. Congruence transformations- when you slide, flip, or turn a triangle, the size and shapes do not change.

Lesson 4-3 Congruent Triangles Theorem 4.4 Properties of Triangle Congruence Reflexive Symmetric Transitive

Answer: Since corresponding parts of congruent triangles are congruent, ARCHITECTURE A tower roof is composed of congruent triangles all converging toward a point at the top. Name the corresponding congruent angles and sides of  HIJ and  LIK.

Name the congruent triangles. ARCHITECTURE A tower roof is composed of congruent triangles all converging toward a point at the top. Answer:  HIJ  LIK

Answer: The support beams on the fence form congruent triangles. b. Name the congruent triangles. a. Name the corresponding congruent angles and sides of  ABC and  DEF. Answer:  ABC  DEF

COORDINATE GEOMETRY The vertices of  RST are R (─3, 0), S (0, 5), and T (1, 1). The vertices of  RST are R (3, 0), S (0, ─5), and T (─1, ─1). Verify that  RST  RST.

Use the Distance Formula to find the length of each side of the triangles.

Use a protractor to measure the angles of the triangles. You will find that the measures are the same. Answer: The lengths of the corresponding sides of two triangles are equal. Therefore, by the definition of congruence, TempCopy In conclusion, because,

COORDINATE GEOMETRY The vertices of  RST are R (─3, 0), S (0, 5), and T (1, 1). The vertices of  RST are R (3, 0), S (0, ─5), and T (─1, ─1). Name the congruence transformation for  RST and  RST. Answer:  RST is a turn of  RST.

COORDINATE GEOMETRY The vertices of  ABC are A (–5, 5), B (0, 3), and C (–4, 1). The vertices of  ABC are A (5, –5), B (0, –3), and C (4, –1). Answer: Use a protractor to verify that corresponding angles are congruent. a. Verify that  ABC  ABC.

Answer: turn b. Name the congruence transformation for  ABC and  ABC.