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Lesson 4-3

Lesson 4-3. Congruent Triangles. 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

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Lesson 4-3

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  1. Lesson 4-3 Congruent Triangles

  2. 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: 115 D C 111 A 65 B 69

  3. 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: 115 D C 111 A 65 B 69

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

  5. 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)

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

  7. X Congruent Triangles 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

  8. Answer: Since corresponding parts of congruent triangles are congruent, Answer: HIJ LIK 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.

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

  10. COORDINATE GEOMETRY The vertices of RSTare 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.

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

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

  13. COORDINATE GEOMETRY The vertices of RSTare 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.

  14. a.Verify that ABC ABC. 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). Answer: Use a protractor to verify that corresponding angles are congruent. b. Name the congruence transformation for ABC and ABC. Answer: turn

  15. Summary & Homework • Summary: • 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

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