In the last section, you used characteristics of corresponding parts of similar figures in order to define similarity. If the figures are oriented the same, it is relatively easy to identify corresponding parts of similar figures.

For example, in the figure below, quadrilateral ABCD is similar to quadrilateral JKLM.

Sometimes, identifying corresponding parts is a little trickier. In this section, you will practice using different ways to identify corresponding parts of similar figures.

In the figure below, kite ABCD is similar to kite WXYZ. Match each side or angle in kite WXYZ to its corresponding part of kite ABCD by dragging the label to the appropriate blank.

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Need a hint?

• Angles with the same marks are congruent.
• Use the congruent angles to locate endpoints of corresponding sides.
• The order of the points in the name of the kite matters. The first points correspond (point A with point W), the second points correspond (point B with point X), etc.

Conclusion Questions

• How can you use the angle markings to match corresponding angles?

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  Check Your Answer

  Look for angles with the same markings (one arc, two arcs, one arc with a hash mark, etc.). These two angles are congruent and since the figures are similar, are corresponding parts.

• How can you use known pairs of corresponding angles to determine corresponding sides?

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  Check Your Answer

  Use the vertices of the angles as endpoints of the line segments containing the sides of the triangle. For example, once you know that ∠A corresponds with ∠W and that ∠B corresponds with ∠X, then you can match AB and WX as corresponding sides.

  Pause and Reflect

  Why do you think it is important to be able to identify corresponding parts of similar figures?

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  Check Your Answer

  When you use similar figures to solve problems, you need to be able to match corresponding sides in order to know what proportion you can write.

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  Practice

  For each of the figures below, determine the angle that corresponds with ∠A and the side that corresponds with AB.

  1. Triangle ABC is similar to triangle MNP.
     
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     Need a hint?

     Use the angle markings to establish the angle that is congruent to ∠A and the angle that is congruent to ∠B. Use these vertices to establish the segment that corresponds with AB.
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     Check Your Answer

     ∠M corresponds with ∠A, and MN corresponds with AB.
  2. Triangle ABE is similar to triangle CDE.
     
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     Need a hint?

     Use the angle markings to establish the angle that is congruent to ∠A and the angle that is congruent to ∠B. Use these vertices to establish the segment that corresponds with AB.
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     Check Your Answer

     ∠C corresponds with ∠A, and CD corresponds with AB.
  3. Trapezoid ABCD is similar to trapezoid JKLM.
     
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     Need a hint?

     Use the angle markings to establish the angle that is congruent to ∠A and the angle that is congruent to ∠B. Use these vertices to establish the segment that corresponds with AB.
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     Check Your Answer

     ∠J corresponds with∠A, and JK corresponds with AB.