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Examine the triangle pairs below, which are not necessarily drawn to scale. For each pair, determine:

  • If they must be congruent. If they are congruent, write a correct congruence statement (such as ) and state the congruence property (such as ).

  • If there is not enough information or if they cannot be congruent, explain why you cannot ensure congruence.

  1. Triangle A,B,C, with line segment from vertex B, to point D, between A, & C, labeled as follows: Angles A,B,D, & C,B,D, each with 1 tick mark, Sides A,B, & B,C, each with 1 tick mark.

    Review the Math Notes box in section 7.1.7.
    The shared side BD is congruent to itself by the Reflexive property.

  1. 2 triangles, D,E,F, & A,B,C, labeled as follows: side E,F, 13, angle E, 45 degrees, angle F, 62 degrees, angle A, 73 degrees, angle C, 62 degrees, side B,C, 13.

    Calculate the missing angle for each triangle.
    Review the Math Notes box in section 7.1.7.