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4-3 Congruent Triangles

You identified and used congruent angles. 4-3 Congruent Triangles. Name and use corresponding parts of congruent polygons. Prove triangles congruent using the definition of congruence. Vocabulary. If two geometric figures have exactly the same shape and size, they are congruent .

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4-3 Congruent Triangles

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  1. You identified and used congruent angles. 4-3 Congruent Triangles • Name and use corresponding parts of congruent polygons. • Prove triangles congruent using the definition of congruence.

  2. Vocabulary • If two geometric figures have exactly the same shape and size, they are congruent. • Un two congruent polygons, all of the parts of one polygon are congruent to the corresponding parts or matching parts of the other polygon. These corresponding parts include corresponding angles and corresponding sides.

  3. The Right Match Congruent Not congruent A D F E C B

  4. Corresponding sides and angles C T Corresponding Angles A B S R Corresponding sides AB RS BC ST AC RT

  5. Angles: Sides: 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.

  6. 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?

  7. The phrase “if and only if” in the congruent polygon definition means that both the conditional and its converse are true. So, if two polygons are congruent, then their corresponding parts are congruent. For triangles, Corresponding parts of congruent triangles are congruent, or CPCTC. C T C C P

  8. CPCTC 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 6y = 54Add 14 to each side. y= 9Divide each side by 6. NG= ITDefinition of congruence x – 2y = 7.5 Substitution y = 9 x – 18 = 7.5x = 25.5, y = 9

  9. 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

  10. 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.

  11. ΔJIK  ΔJIH Congruent Triangles mIJK + mIKJ + mJIK = 180 Triangle Angle-Sum 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

  12. Statements Reasons 1. Given 1. 2. LNM  PNO 2. Vertical Angles Theorem 3. M  O 3. Third Angles Theorem 4. ΔLMNΔPON 4. CPCTC Write a two-column proof. Prove:ΔLMNΔPON

  13. 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 Third angle theorem

  14. Like congruence of segments and angles, congruence of triangles is reflexive, symmetric, and transitive.

  15. 4-4 Assignment

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