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5-Minute Check 1

BELLRINGER: 1)Find m 1. 2) Find m 2. 3) Find m 3. 5-Minute Check 1. Concept 1. Angles:. Sides:. Identify Corresponding Congruent Parts. Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement.

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5-Minute Check 1

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  1. BELLRINGER: 1)Find m1.2) Find m2.3) Find m3. 5-Minute Check 1

  2. Concept 1

  3. Angles: Sides: Identify Corresponding Congruent Parts Show that the polygons are congruent by identifying all of the congruent corresponding parts. Then write a congruence statement. Answer: All corresponding parts of the two polygons are congruent. Therefore, ABCDE RTPSQ. Example 1

  4. 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? Example 1

  5. 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

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

  7. 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

  8. Concept 2

  9. 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

  10. 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

  11. 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

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

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

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

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

  16. Concept 3

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