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4.2 Congruence and Triangles

4.2 Congruence and Triangles. Goal: Identify congruent figures and corresponding parts. Standards: 10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

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4.2 Congruence and Triangles

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  1. 4.2 Congruence and Triangles Goal: Identify congruent figures and corresponding parts. Standards: 10.0: Students compute areas of polygons, including rectangles, scalene triangles, equilateral triangles, rhombi, parallelograms, and trapezoids.

  2. When two figures are congruent, there is a correspondence between their angles and sides such that corresponding sides are congruent. For the triangles below, you can write ABC = PQR, which is read “triangle ABC is congruent to triangle PQR.” The notation shows the congruence and the correspondence. Corresponding angles corresponding sides <A<P ABPQ <B<Q BCQR <C<R CARP

  3. Solution • The diagram indicates that DEF RST. • The congruent angles and sides are as follows. • Angles:D, R, E, S, T • Sides:DE RS, EF ST, FD TR

  4. Theorem 4.3 Third Angle Theorem • If two angles of one triangle are congruent to two angles of another triangle, then the third angles are also congruent. • If <A=<D and <B = <E, then <C = <F

  5. Theorem 4.4 Properties of Congruent Triangles • Reflexive Property of Congruent Triangles Every triangle is congruent to itself. Symmetric Property of Congruent Triangles If ∆ABC≈∆DEF, then ∆DEF≈∆ABC. Transitive Property Of Congruent Triangles If ABC  DEF and DEF = JKL, then ABC JKL

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