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2-31.

Determine whether or not the triangles in each pair below are congruent. Justify your conclusion with a triangle congruence theorem.

  1. Two right triangles tessellated about the top vertex. The sides are, 6, 8, 10.

    Find the lengths of the missing sides using the Pythagorean Theorem.

    Congruent by .

  1. Two triangles both with one side marked with one tick mark, one angle marked with one tick mark, and the second angle marked with two tick marks. A, A, S

    What do the tick marks on the angles and sides mean?

  1. Two triangles connected together on one side. Another side on each has two tick marks. Both triangles have an angle with 1 tick mark.  In the first triangle, this angle is opposite the shared side. In the second triangle, this angle is opposite the side with a double tick mark.

    Do the tick marks prove the triangles are congruent, or is more information needed?

    They are not necessarily congruent. There is no such thing as .

  1. Two triangles with a shared side showing the alternate interior angles are the same. The other adjacent side to that angle has 1 tick mark on both triangles.

    Does the fact that they share a side help prove they are congruent?