#### Transcript lesson 4.3

Five-Minute Check (over Lesson 4–2) NGSSS Then/Now New Vocabulary Key Concept: Definition of Congruent Polygons Example 1: Identify Corresponding Congruent Parts Example 2: Use Corresponding Parts of Congruent Triangles Theorem 4.3: Third Angles Theorem Example 3: Real-World Example: Use the Third Angles Theorem Example 4: Prove that Two Triangles are Congruent Theorem 4.4: Properties of Triangle Congruence Over Lesson 4–2 Find m1. A. 115 B. 105 C. 75 D. 65 0% D 0% C 0% B A 0% A. B. C. D. A B C D Over Lesson 4–2 Find m2. A. 75 B. 72 C. 57 D. 40 0% D 0% C 0% B A 0% A. B. C. D. A B C D Over Lesson 4–2 Find m3. A. 75 B. 72 C. 57 D. 40 0% D 0% C 0% B A 0% A. B. C. D. A B C D Over Lesson 4–2 Find m4. A. 18 B. 28 C. 50 D. 75 0% D 0% C 0% B A 0% A. B. C. D. A B C D Over Lesson 4–2 Find m5. A. 70 B. 90 C. 122 D. 140 0% D 0% C 0% B A 0% A. B. C. D. A B C D 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 0% B D. 100 A 0% A B C 0% D D C. 50 A. B. C. 0% D. C B. 40 MA.912.G.4.4 Use properties of congruent and similar triangles to solve problems involving lengths and areas. MA.912.G.4.6 Prove that triangles are congruent or similar and use the concept of corresponding parts of congruent triangles. You identified and used congruent angles. (Lesson 1–4) • 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: 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 directly matches corresponding angles or sides? A. A. B. C. D. B. C. D. 0% D 0% C 0% B A 0% A B C D Use Corresponding Parts of Congruent Triangles In the diagram, ΔITP ΔNGO. Find the values of x and y. O P mO = mP 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: 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 0% B A 0% A B C 0% D D D. x = 4.5, y = 5.5 C C. x = 1.8, y = 19 A. B. C. 0% D. 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 J K and mJ = 72, find mJIH. ∆JIK ∆JIH mKJI + mIKJ + mJIK = 180 H K, I I, and J J Congruent Triangles Triangle Angle Sum Theorem CPCTC Use the Third Angles Theorem 72 + 72 + mJIK = 180 144 + mJIK = 180 Substitution Simplify. mJIK = 36 Subtract 144 from each side. mJIH = 36 Third Angles Theorem Answer: mJIH = 36 TILES A drawing of a tile contains a series of triangles, rectangles, squares, and a circle. If ∆KLM ∆NJL, KLM KML and mKML = 47.5, find mLNJ. A. 85 B. 45 C. 47.5 0% D 0% C A 0% B 0% D. 95 A. B. C. D. A B C D Prove That Two Triangles are Congruent Write a two-column proof. Prove: ΔLMN ΔPON Prove That Two Triangles are Congruent Proof: Statements Reasons 1. 1. Given 2. LNM PNO 2. Vertical Angles Theorem 3. M O 3. Third Angles Theorem 4. ΔLMN ΔPON 4. CPCTC Find the missing information in the following proof. Prove: ΔQNP ΔOPN Proof: Statements Reasons 1. 1. Given 2. 3.Q O, NPQ PNO 4. QNP ONP 2. Reflexive Property of Congruence 3. Given 4. _________________ ? 5. ΔQNP ΔOPN 5. Definition of Congruent Polygons A. CPCTC B. Vertical Angles Theorem C. Third Angle Theorem A B C 0% D D 0% B A 0% C D. Definition of Congruent Angles A. B. C. 0% D.