Proofs with Proportional Triangles — Practice Geometry Questions

By Allen Ma, Amber Kuang

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.