Proving Triangle Similarity Algebraically

This lesson teaches how to prove triangle similarity algebraically using ratios of corresponding sides. It begins with a review of proportional quantities and area ratios, followed by an explanation of the side-side-side similarity theorem. The lesson includes a flowchart proof demonstrating the similarity of two triangles, ABC and DEF, by showing that their corresponding sides are proportional. The lesson concludes with a recap of the key concepts covered.

What is the ratio of the sum of areas of two triangles to the total area if the sum is 3 square centimeters?

• 2 to 3

• 1 to 2

• 4 to 5

• 3 to 4

According to the side-side-side similarity theorem, what must be true for two triangles to be similar?

• Their angles must be equal.

• Their corresponding sides must be in proportion.

• Their areas must be equal.

• Their perimeters must be equal.

What is the simplified ratio of the sides of the larger triangle to the smaller triangle in the example given?

• 3 to 1

• 2 to 1

• 1 to 2

• 1 to 3

In the flowchart proof, what is the ratio of side AB to side DE?

• 1 to 1

• 2 to 1

• 3 to 2

• 4 to 3

What conclusion is reached in the flowchart proof regarding triangles ABC and DEF?

• They are identical.

• They are similar.

• They are not related.

• They are congruent.