Geometric Proofs with Overlapping Triangles — Practice Questions - dummies

Geometric Proofs with Overlapping Triangles — Practice Questions

By Allen Ma, Amber Kuang

In geometry, you may be asked to formulate a proof with overlapping triangles. In order to prove parts of a triangle are congruent, you first need to prove that the triangles are congruent to each other.

The following example asks you to do just that.

Practice questions

Use the following figure to answer the questions regarding overlapping triangles.

image0.png

Given:

image1.png

Prove:

image2.png

The following questions ask you to fill in the blanks in the table.

image3.png

  1. What is the reason for Statement 2?

  2. What is the reason for Statement 3?

  3. What is the reason for Statement 4?

  4. What is the reason for Statement 5?

  5. What is the reason for Statement 6?

Answers and explanations

  1. Reflexive property

    image4.png

    because a segment is congruent to itself.

  2. Addition postulate

    The addition postulate states that if two segments are congruent to two other segments, then the sums of the segments are also congruent to each other. Therefore,

    image5.png

  3. If two sides of a triangle are congruent, the angles opposite those sides are also congruent.

    image6.png

    because they’re the angles opposite the congruent sides

    image7.png

  4. 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). Therefore,

    image8.png

  5. CPCTC

    image9.png

    because corresponding parts of congruent triangles are congruent to each other.