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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.

  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.

  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.
     



  • ( Reflexive helps)



  • ( Reflexive helps)

  • 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.

  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.

  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.



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

  • you figure out why, add extra information.

  • you figure out why, add extra information.