Geometry: 1,001 Practice Problems For Dummies (+ Free Online Practice)
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Say that you have two triangles and you need to prove that the sides of the triangles are in proportion to each other. How do you do it? Elementary! You just need to prove the triangles are similar by AA (angle-angle).

If two triangles are similar, this means the corresponding sides are in proportion.

The following practice problem asks you to finish a proof showing the sides of two triangles are in proportion.

Practice questions

Complete the following proof by giving the missing statements and reasons.




Fill in the blanks in the table by answering the following questions.

  1. What is the missing angle in Statement 2?

  2. What is the statement for Reason 3?

  3. What is the reason for Statement 4?

  4. What is the reason for Statement 6?

  5. What is the reason for Statement 7?

Answers and explanations

  1. image3.png

    When two lines intersect, they form vertical angles across from each other.

  2. image4.png

    You know that


    are vertical angles.

    You also know that if two angles are vertical angles, they're congruent, so

  3. Perpendicular lines form right angles.

    When two perpendicular lines intersect, they create right angles.

  4. AA

    If two angles of a triangle are congruent to two angles of a different triangle, the two triangles are similar.

  5. If two triangles are similar, their sides are in proportion.

About This Article

This article is from the book:

About the book authors:

Allen Ma and Amber Kuang are math teachers at John F. Kennedy High School in Bellmore, New York. Allen, who has taught geometry for 20 years, is the math team coach and a former honors math research coordinator. Amber has taught all levels of mathematics, from algebra to calculus, for the past 14 years.

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