LESSON 4 3 Congruent Triangles FiveMinute Check over

LESSON 4– 3 Congruent Triangles

Five-Minute Check (over Lesson 4– 2) TEKS 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 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 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 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

Targeted TEKS G. 6(D) Verify theorems about the relationships in triangles, including proof of the Pythagorean Theorem, the sum of interior angles, base angles of isosceles triangles, midsegments, and medians, and apply these relationships to solve problems. Mathematical Processes G. 1(F), G. 1(G)

You identified and used congruent angles. • Name and use corresponding parts of congruent polygons. • Prove triangles congruent using the definition of congruence.

• 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 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 6 y – 14 = 40 CPCTC Definition of congruence Substitution

Use Corresponding Parts of Congruent Triangles 6 y = 54 y= 9 Add 14 to each side. Divide each side by 6. CPCTC NG = IT x – 2 y = 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

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 JIK = 180 Substitution 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

Prove That Two Triangles are Congruent Write a two-column proof. Prove: ΔLMN ΔPON

Prove That Two Triangles are Congruent Proof: Statements Reasons 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. Given 2. Reflexive Property of Congruence 3. Q O, NPQ PNO 3. Given 4. _________ ? 4. QNP ONP 1. 2. 5. ΔQNP ΔOPN 5. Definition of Congruent Polygons

A. CPCTC B. Vertical Angles Theorem C. Third Angles Theorem D. Definition of Congruent Angles

LESSON 4– 3 Congruent Triangles