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For each diagram below, determine the value of , if possible. If the triangles are congruent, state which triangle congruence condition you used. If the triangles are not congruent or if there is not enough information, state, “Cannot be determined”.

  1. below is a triangle.

    Triangle A, B, C.  Side A, B is labeled, 10. Two right triangles are formed by a line segment, 8, drawn perpendicular from vertex, B, to side A, C.  Side A, C is divided into two equal segments with the segment on the right labeled x.

    is made of two right triangles with the same base and height. Calculate using the Pythagorean Theorem.

  1. Quadrilateral A, B, C, D. Side A, B is, 9. Side B, C is, x.  Side A, D is, 10. Side A, B is parallel to side D, C. A line is drawn from point B to point D forming two triangles. Angle A, D, B = Angle D, B, C.

    The diagram indicates and are parallel. Which angles does that make congruent?

    Since the segments are parallel,. Therefore, the triangles are congruent by ASA , so .

  1. Rectangle A, B, C, D. Side A, D is, 11.  Side D, C is, x.  Side B, C is,11. A line is drawn from point A to point C forming two internal triangles.  Angle C, A, B is 35 degrees.

    Since is a right triangle, use the tangent ratio to find . Review the Math Notes boxes in Lessons 3.2.5 and 2.3.2.

  1. and are straight line

    Line segments A, C and B, D intersect forming 2 triangles, A, B, and point of intersection and D, C, and point of intersection.  Side A, B is 4.  Side D, C is, x. Angle B and Angle D are both 47 degrees. Angles, A, and C, both have 1 tick mark.

    Review the triangle congruence theorems in the Math Notes box in Lesson 2.1.1.