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The diagrams below are not necessarily drawn to scale. For each pair of triangles:

  • Determine if the two triangles are congruent.

  • If the triangles are congruent, write a congruence statement (such as ) and give the congruence theorem (such as ).

  • If the triangles are not congruent, or if there is not enough information to determine congruence, write “cannot be determined” and explain why not.

A shared side is a congruent side.
AAA does not prove congruency.
Order matters: SAS proves congruence but SSA does not.

  1. is a straight segment:
    Triangle A, B, C. Two internal triangles A, B, D and D, B, C are created by a line segment drawn from the vertex, B, perpendicular to the base, A, C, at D. Angle D is 90 degrees. Angle A, B, D and angle D, B, C are both marked with one tick mark.

  1. Quadrilateral A,B,D,C,, with diagonal from, B, to, C, creating 2 triangles: A,B,C, & B,C,D, labeled as follows: Side, BD, 2 tick marks, angle D,B,C, 1 tick mark, side, AC, 2 tick marks, angle, B,C,A, 1 tick mark.

  1. Line segments, AD, &, BE, intersect at, C, with segments from, A, to, B, & from D, to, E, creating 2 triangles with a common vertex, labeled as follows: Sides, AB, &, DE, each with 1 arrow, side BC, 6, side CD, 6.

  1. 2 triangles, A,D,B, &, A,B,C, overlap, with, AC, &, BD, intersecting at point, E, creating a third internal triangle, A,E,B, labeled as follows: angle C,A,B, 1 tick mark, angle A,B,D, 1 tick mark, angle, D, 2 arcs, angle, C, 2 arcs.

  1. 2 triangles, H,O,N, & Z,W,N, such that, W, is on side, NH, labeled as follows: Angle, O,N,H, 1 tick mark, angle, O, 2 tick marks, angle H, 2 arcs, angle, W,N,Z, 1 tick mark, angle, N,W,Z, 2 tick marks, angle, Z, 2 arcs.

  1. 2 triangles Q,R,S, &, G,H,K, labeled as follows: Side, QR, 31, side, QS, 40, side, RS, 42, Side, HK, 42, side, HG, 40, & side, GK, 31.