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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, has two equal sides.  A line segment is drawn from upper vertex Q perpendicular to side P, R at point S forming a right triangles.

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



  • ( Reflexive helps)



  • ( Reflexive helps)

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

  1. Two lines W, T and X, Z intersect at point, Y, forming two triangles W, X, Y,  and T, Y, Z. Y is the midpoint of side W, T and side 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. Two triangles A, B, C and D, E, F.   Side A, B and E, D, are both 7.  Side B, C and side E, F are both, 6.  The length of F, C, is shared as part of the base for both triangles. The two bases are translated 3 units apart. Thus, A, F is 3 and C, D is 3.



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

  • you figure out why, add extra information.

  • you figure out why, add extra information.