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

  • Complete the congruence statement

  • State the congruence property

  • Determine a sequence of rigid transformations that maps one triangle onto the other

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.

    ; (Remember that  by the  reflexive property.)

  1. Line Segments L,N, & P,O, intersect at point, M, with line segments connecting L to P, & O to N, creating 2 triangles: L,M,P, & M,N,O, labeled as follows: angle L & angle N, each have 1 tick mark, angle O,M,N, & angle L,M,P, each have 2 tick marks.

    No solution; only the angles are congruent. These triangles can only be proved to be similar by but not congruent.

  1. Line Segments W,T, & Z,X, intersect at point, Y, with line segments connecting W to X, & Z to T, creating 2 triangles: X,Y,W, & T,Y,Z, labeled as follows: side W,Y, & side T,Y, each have 1 tick mark, side Y,X, & side Y,Z, each have 2 tick marks, angle W,Y,X, & angle Z,Y,T, each have 1 tick mark, angle x, & angle z, each have 2 tick marks.

    ; or .