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

  1. 2 right triangles, arranged so first triangle has right angle at bottom left, second triangle is slanted, so short leg is part of hypotenuse of first triangle, with right angle vertex shared with first triangle top vertex, & second's long leg is slanted up & right, long leg of each triangle, is labeled 8, short leg of second triangle is labeled 6, difference of first's hypotenuse & second's short leg, is labeled 4.

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

    Congruent by .

  1. Two triangles, each with one side marked with one tick mark, one angle marked with one tick mark, and the angle opposite the side with 1 tick mark, marked with two tick marks.

    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. Quadrilateral, left & right sides each has 1 tick mark, with diagonal from top left to bottom right vertices, creating 2 triangles, top left angle of triangle on left, & bottom right angle of triangle on right, each has 1 tick mark.

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