Lesson 4-3 Congruent Triangles

Standardized Test Practice: Transparency 4-3 5-Minute Check on Lesson 4-2 Find the measure of each angle. 1. m1 2. m2 3. m3 4. m4 5. m5 6. Two angles of a triangle measure 46 and 65. What is the measure of the third angle? Standardized Test Practice: A 65 B 69 C 111 D 115

Standardized Test Practice: Transparency 4-3 5-Minute Check on Lesson 4-2 Find the measure of each angle. 1. m1 115 2. m2 72 3. m3 57 4. m4 18 5. m5 122 6. Two angles of a triangle measure 46 and 65. What is the measure of the third angle? Standardized Test Practice: A 65 B 69 C 111 D 115

Objectives Name and label corresponding parts of congruent triangles Identify congruence transformations

Vocabulary Congruent triangles – have the same size and shape (corresponding angles and sides ) Congruence Transformations: Slide (also known as a translation) Turn (also known as a rotation) Flip (also known as a reflection)

Properties of Triangle Congruence Reflexive – ∆JKL  ∆ JKL Symmetric – if ∆ JKL  ∆ PQR, then ∆ PQR  ∆ JKL Transitive – if ∆ JKL  ∆ PQR and ∆ PQR  ∆ XYZ, then ∆ JKL  ∆ XYZ

CPCTC – Corresponding Parts of Congruent Triangles are Congruent X A C Y B Z The vertices of the two triangles correspond in the same order as the letters naming the triangle ▲ABC  ▲XYZ A  X B  Y C  Z AB  XY BC  YZ CA  ZX CPCTC – 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. Answer: Since corresponding parts of congruent triangles are congruent, Name the congruent triangles. Answer: HIJ LIK

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: Answer: ABC DEF

COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST are R(3, 0), S(0, ─5), and T(─1, ─1). Verify that RST  RST. Use the Distance Formula to find the length of each side of the triangles.

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

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

COORDINATE GEOMETRY The vertices of RST are R(─3, 0), S(0, 5), and T(1, 1). The vertices of RST  are R(3, 0), S(0, ─5), and T(─1, ─1). Name the congruence transformation for RST and RST. Answer: RST 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 ABC are A(5, –5), B(0, –3), and C(4, –1). a. Verify that ABC ABC. Answer: Use a protractor to verify that corresponding angles are congruent. b. Name the congruence transformation for ABC and ABC. Answer: turn

Summary & Homework Summary: Homework: Two triangles are congruent when all of their corresponding parts are congruent. Order is important! Homework: pg 195-198: 9-12, 22-25, 40-42