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Over Lesson 4–2 Find m∠1. A. 115 B. 105 C. 75 D. 65 Over Lesson 4–2 Find m∠1. A. 115 B. 105 C. 75 D. 65 Over Lesson 4–2 Find m∠2. A. 75 B. 72 C. 57 D. 40 Over Lesson 4–2 Find m∠2. A. 75 B. 72 C. 57 D. 40 Over Lesson 4–2 Find m∠3. A. 75 B. 72 C. 57 D. 40 Over Lesson 4–2 Find m∠3. A. 75 B. 72 C. 57 D. 40 Over Lesson 4–2 Find m∠4. A. 18 B. 28 C. 50 D. 75 Over Lesson 4–2 Find m∠4. A. 18 B. 28 C. 50 D. 75 Over Lesson 4–2 Find m∠5. A. 70 B. 90 C. 122 D. 140 Over Lesson 4–2 Find m∠5. A. 70 B. 90 C. 122 D. 140 Over Lesson 4–2 One angle in an isosceles triangle has a measure of 80°. What is the measure of one of the other two angles? A. 35 B. 40 C. 50 D. 100 Over Lesson 4–2 One angle in an isosceles triangle has a measure of 80°. What is the measure of one of the other two angles? A. 35 B. 40 C. 50 D. 100 Content Standards G.CO.7 Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G.SRT.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. Mathematical Practices 6 Attend to precision. 3 Construct viable arguments and critique the reasoning of others. You identified and used congruent angles. • Name and use corresponding parts of congruent polygons. • Prove triangles congruent using the definition of congruence. • congruent • congruent polygons • corresponding parts Identify Corresponding Congruent Parts Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Angles: Sides: Answer: Identify Corresponding Congruent Parts 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. 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. 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. Use Corresponding Parts of Congruent Triangles In the diagram, ΔITP ≅ ΔNGO. Find the values of x and y. ∠O ≅ ∠P m∠O = m∠P 6y – 14 = 40 CPCTC Definition of congruence Substitution Use Corresponding Parts of Congruent Triangles 6y = 54 y= 9 Add 14 to each side. Divide each side by 6. CPCTC NG = IT x – 2y = 7.5 x – 2(9) = 7.5 x – 18 = 7.5 x = 25.5 Answer: Definition of congruence Substitution y=9 Simplify. Add 18 to each side. Use Corresponding Parts of Congruent Triangles 6y = 54 y= 9 Add 14 to each side. Divide each side by 6. CPCTC NG = IT x – 2y = 7.5 x – 2(9) = 7.5 x – 18 = 7.5 x = 25.5 Answer: x = 25.5, y = 9 Definition of congruence Substitution y=9 Simplify. Add 18 to each side. 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 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 Use the Third Angles Theorem ARCHITECTURE A drawing of a tower’s roof is composed of congruent triangles all converging at a point at the top. If ∠IJK ≅∠IKJ and m∠IJK = 72, find m∠JIH. ΔJIK ≅ ΔJIH Congruent Triangles m∠IJK + m∠IKJ + m∠JIK =180 Triangle Angle-Sum Theorem Use the Third Angles Theorem m∠IJK + m∠IJK + m∠JIK = 180 Substitution 72 + 72 + m∠JIK = 180 Substitution 144 + m∠JIK = 180 Answer: Simplify. m∠JIK = 36 Subtract 144 from each side. m∠JIH = 36 Third Angles Theorem Use the Third Angles Theorem m∠IJK + m∠IJK + m∠JIK = 180 Substitution 72 + 72 + m∠JIK = 180 Substitution 144 + m∠JIK = 180 Simplify. m∠JIK = 36 Subtract 144 from each side. m∠JIH = 36 Third Angles Theorem Answer: m∠JIH = 36 TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM ≅ ΔNJL, ∠KLM ≅∠KML, and m∠KML = 47.5, find m∠LNJ. A. 85 B. 45 C. 47.5 D. 95 TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ΔKLM ≅ ΔNJL, ∠KLM ≅∠KML, and m∠KML = 47.5, find m∠LNJ. A. 85 B. 45 C. 47.5 D. 95 Prove That Two Triangles are Congruent Write a two-column proof. Prove: ΔLMN ≅ ΔPON To be completed in class…...