Indirect Geometric Proofs — Practice Questions - dummies

By Allen Ma, Amber Kuang

In an indirect geometric proof, you assume the opposite of what needs to be proven is true. Therefore, when the proof contradicts itself, it proves that the opposite must be true.

Practice questions

Use the following figure to answer the questions regarding this indirect proof.

image0.png

Given:

image1.png

are straight lines.

Prove:

image2.png

do not bisect each other.

image3.png

  1. What is the statement for Reason 2?

  2. What is the reason for Statement 3?

  3. What is the statement for Reason 4?

  4. What is the reason for Statement 5?

  5. What is the reason for Statement 6?

  6. What is the reason for Statement 7?

  7. What is the reason for Statement 8?

Answers and explanations

  1. image4.png

    bisect each other.

    In an indirect proof, assume the opposite of what needs to be proven is true.

  2. A bisector divides a segment into two congruent segments.

  3. image5.png

    are vertical angles.

    Intersecting lines form vertical angles.

  4. If two angles are vertical angles, then they’re congruent.

  5. SAS

    If two sides and the included angle of one triangle are congruent to two sides and the included angle of another triangle, then the triangles are congruent by SAS (side-angle-side).

  6. CPCTC

    Corresponding parts of congruent triangles are congruent to each other.

  7. Contradiction

    Step 7 contradicts Step 1; therefore, the opposite must be true.