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Home > GC > Chapter 7 > Lesson 7.2.5 > Problem 7-87

7-87.

For each pair of triangles below, determine if the triangles are congruent. If the triangles are congruent,

  • complete the correspondence statement,

  • state the congruence property,

  • and record any other ideas you use that make your conclusion true.

Otherwise, explain why you cannot conclude that the triangles are congruent. Note that the figures are not necessarily drawn to scale.  


  1. Quadrilateral A, B, C, D. Angle A is bisected by line A, C. Angle B is equal to angle D.



    ( Reflexive helps)

  1. Triangle, P Q R, with dashed segment from vertex Q, perpendicular to side, P R, at point, S, sides, Q P, & Q R, each have 1 tick mark.



    ( Reflexive helps)

  1. Two line segments, L, N and P, O intersect at point, M forming two triangles, L, M, P, and M, N, O, Angles, L, and N, each have 1 tick mark.

    No solution: and , but only enough information to prove similar by .
     

  1. Two line segments, W, T and X, Z intersect at point, Y, forming two triangles, W, X, Y, and T, Y, Z, arrow pointing at point Y, labeled, midpoint of segment, W, T and segment. X, Z.



    • ( & by definition of midpoint;  by vertical angles)

  1. Quadrilateral D, E, F, G where sides D, G and E, F have one arrow and sides D, E and G, F have two arrows. A dashed line, G, E, divides the shape in half.

    • you figure out why, add extra information.

  1. 2 connected triangles A, B, C and D, E, F, points, A, F, C, D, are on same segment, Side A, B, and side E, D, are each 7, Side B, C, and side E, F, are each 6, segment A, F, and segment C, D, are each 3.

    • you figure out why, add extra information.

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