Splash Screen

Find m1. A. 115 B. 105 C. 75 D. 65 5-Minute Check 1

Find m2. A. 75 B. 72 C. 57 D. 40 5-Minute Check 2

Find m3. A. 75 B. 72 C. 57 D. 40 5-Minute Check 3

Find m4. A. 18 B. 28 C. 50 D. 75 5-Minute Check 4

Find m5. A. 70 B. 90 C. 122 D. 140 5-Minute Check 5

One angle in an isosceles triangle has a measure of 80° 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 5-Minute Check 6

congruent congruent polygons corresponding parts Vocabulary

Concept 1

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. Example 1

The support beams on the fence form congruent triangles 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. Example 1

In the diagram, ΔITP  ΔNGO. Find the values of x and y. Use Corresponding Parts of Congruent Triangles In the diagram, ΔITP  ΔNGO. Find the values of x and y. O  P CPCTC mO = mP Definition of congruence 6y – 14 = 40 Substitution Example 2

NG = IT Definition of congruence x – 2y = 7.5 Substitution Use Corresponding Parts of Congruent Triangles 6y = 54 Add 14 to each side. y = 9 Divide each side by 6. CPCTC NG = IT Definition of congruence x – 2y = 7.5 Substitution x – 2(9) = 7.5 y = 9 x – 18 = 7.5 Simplify. x = 25.5 Add 18 to each side. Answer: x = 25.5, y = 9 Example 2

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 Example 2

Concept 2

ΔJIK  ΔJIH Congruent Triangles 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 Example 3

mIJK + mIJK + mJIK = 180 Substitution 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 Example 3

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 Example 3

Write a two-column proof. Prove That Two Triangles are Congruent Write a two-column proof. Prove: ΔLMN  ΔPON Example 4

2. Vertical Angles Theorem Prove That Two Triangles are Congruent Proof: Statements Reasons 1. Given 1. 2. LNM  PNO 2. Vertical Angles Theorem 3. M  O 3. Third Angles Theorem 4. ΔLMN  ΔPON 4. CPCTC Example 4

Find the missing information in the following proof. Prove: ΔQNP  ΔOPN Proof: Reasons Statements 1. 1. Given 2. 2. Reflexive Property of Congruence 3. Q  O, NPQ  PNO 3. Given 4. _________________ 4. QNP  ONP ? 5. Definition of Congruent Polygons 5. ΔQNP  ΔOPN Example 4

B. Vertical Angles Theorem A. CPCTC B. Vertical Angles Theorem C. Third Angles Theorem D. Definition of Congruent Angles Example 4

Concept 3