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Home > GC > Chapter 7 > Lesson 7.2.3 > Problem 7-66

7-66.

Identify if each pair of triangles below is congruent or not. Remember that the diagrams may not be drawn to scale. Justify your conclusion. Redraw and label the diagrams as needed.  

Read the Math Notes box on triangle congruence conditions.

  1. Quadrilateral, with horizontal diagonal from left vertex to right vertex, top left & bottom left sides, each has 1 tick mark, top right & bottom right sides, each has 2 tick marks.

    What do the tick marks on the sides mean? Do they help prove the triangles are congruent?

    How many sides are congruent in the two triangles is that enough to prove the triangles congruent?

  1. 2 line segments intersect, & segments enclose left & right sides to create 2 triangles connected with a shared vertex, sides labeled as follows: triangle on left, left side, 4, top right, 5, triangle on right, top left, 4, bottom left, 5.

    How could you prove the triangles are congruent? Is there enough information? Are the parts in the correct order?

  1. 2 triangles, share a part of their horizontal sides, bottom triangle horizontal top side extends to the left, top triangle horizontal bottom side extending to the right, each extended section labeled 3, angles marked as follows: bottom, top left, 2 tick marks, top right, 1 tick mark, top, bottom left, 1 tick mark, bottom right, 2 tick marks.

    How do the tick marks on the angles provide enough information to prove they are congruent?

    Are there any congruent sides in this figure?

  1. A triangle with a line drawn from the top vertex to the base. The left angle the line creates with the base is 90 degrees. The triangle's long sides are both marked with one tick mark.

    What type of triangle is this? What information do you know about the triangle by knowing its name?

    What relationship could be used to prove they are congruent?