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4.3 Congruent Triangles

4.3 Congruent Triangles. We will… …name and label corresponding parts of congruent triangles. …identify congruence transformations. Corresponding parts of congruent triangles. Triangles that are the same size and shape are congruent triangles .

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4.3 Congruent Triangles

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  1. 4.3 Congruent Triangles We will… …name and label corresponding parts of congruent triangles. …identify congruence transformations.

  2. Corresponding parts of congruent triangles Triangles that are the same size and shape are congruent triangles. Each triangle has three angles and three sides. If all six corresponding parts are congruent, then the triangles are congruent.

  3. B Y Z C X A ~ ΔABC=ΔXYZ Corresponding parts of congruent triangles If ΔABC is congruent to ΔXYZ , then vertices of the two triangles correspond in the same order as the letter naming the triangles.

  4. B Y Z C X A ~ ΔABC=ΔXYZ Corresponding parts of congruent triangles This correspondence of vertices can be used to name the corresponding congruent sides and angles of the two triangles.

  5. Definition of Congruent Triangles (CPCTC) Two triangles are congruent if and only if their corresponding parts are congruent. CPCTC Corresponding Parts of Congruent Triangles are Congruent

  6. Answer:Since corresponding parts of congruent triangles are congruent, Example 3-1a ARCHITECTUREA tower roof is composed of congruent triangles all converging toward a point at the top. Name the corresponding congruent angles and sides of HIJ and LIK.

  7. The support beams on the fence form congruent triangles. a.Name the corresponding congruent angles and sides of ABC and DEF. b.Name the congruent triangles. Answer:ABC DEF Example 3-1c Answer:

  8. Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive. REFLEXIVE ΔJKL = ΔJKL K K ~ L L J J

  9. Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive. SYMMETRIC ~ If ΔJKL = ΔPQR, then ΔPQR =ΔJKL. K Q L ~ R J P

  10. Properties of Triangle Congruence Congruence of triangles is reflexive, symmetric, and transitive. TRANSITIVE ~ If ΔJKL = ΔPQR, and ΔPQR = ΔXYZ, then ΔJKL =ΔXYZ. ~ K Q ~ L R J Y P Z X

  11. B E C F A D IDENTIFY CONGRUENCE TRANSFORMATIONS If you slide ΔABC down and to the right, it is still congruent to ΔDEF. B C A

  12. B E C F A D IDENTIFY CONGRUENCE TRANSFORMATIONS If you turn ΔABC, it is still congruent to ΔDEF. A B C

  13. B E C F A D IDENTIFY CONGRUENCE TRANSFORMATIONS If you flip ΔABC, it is still congruent to ΔDEF. A C B

  14. COORDINATE GEOMETRYThe vertices of RSTare R(─3, 0), S(0, 5), and T(1, 1). The vertices of RSTare R(3, 0), S(0, ─5), and T(─1, ─1).How would you verify RST RST. Example 3-2a

  15. Example 3-2g b.Name the congruence transformation for ABC and ABC. Answer:turn

  16. Classwork/Homework

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