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

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Presentation transcript:

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

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. Vocabulary

The Right Match CongruentNot congruent A B C D E F

Corresponding sides and angles Corresponding AnglesCorresponding sides AB C R S T AB RS BC ST AC RT

A B C H J K

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. Sides: Angles:

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.

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. CP CTC

 O  PCPCTC m  O=m  PDefinition of congruence 6y – 14=40Substitution In the diagram, ΔITP  ΔNGO. Find the values of x and y. 6y=54Add 14 to each side. y=9Divide each side by 6. NG=ITDefinition of congruence x – 2y=7.5Substitution y = 9 x – 18=7.5x = 25.5, y = 9 CPCTC

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 In the diagram, ΔFHJ  ΔHFG. Find the values of x and y.

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.

m  IJK + m  IJK + m  JIK =180Substitution m  JIK =180Substitution m  JIK =180Simplify. m  JIK =36Subtract 144 from each side. m  JIH =36Third Angles Theorem Answer: m  JIH = 36 m  IJK + m  IKJ + m  JIK = 180 Triangle Angle-Sum Theorem ΔJIK  ΔJIH Congruent Triangles

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

Find the missing information in the following proof. Prove:ΔQNP  ΔOPN ReasonsStatements 3.  Q   O,  NPQ   PNO 3. Given 5. Definition of Congruent Polygons 5. ΔQNP  ΔOPN 4. _________________ 4.  QNP   ONP ? Reflexive Property of Congruence Given Third angle theorem

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

4-3 Assignment Page 259, 10, 12, 13-16, 18-20