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Home > GC > Chapter 6 > Lesson 6.2.3 > Problem 6-61


2 line segments intersect, segments at left & right ends, create 2 triangles, left & right ends each have 1 arrow, triangle on left, has top right side of 20, bottom right side of 24, triangle on right, top left side of, x + 2, bottom left side of, x.Examine the triangles in the diagram at right.  

  1. Are the triangles similar? Justify your conclusion.

    There are some parallel lines in the diagram.
    Review Math Notes in Lesson 2.1.4 for help identifying the relationships between the angles lettered , , , and below.

    Labels added, on left triangle, top vertex, e, on bottom vertex, h, intersection point, z, on right triangle, top vertex, f, bottom vertex, G, angle labels added as follows: Angle, e, small letter a, angle g, small letter d, angle, E Z H, small letter b, angle, F Z G, small letter c.

  2. Solve for . Show all work.

    When two triangles are similar, the ratios of corresponding sides are equal.
    You could use a proportion.