Homework 6: Parts of Similar Triangles

Front

What is a similar triangle?

Back

Similar triangles are triangles that have the same shape but may differ in size. Their corresponding angles are equal, and the lengths of their corresponding sides are proportional.

Front

What is the Angle Bisector Theorem?

Back

The Angle Bisector Theorem states that the angle bisector of an angle in a triangle divides the opposite side into two segments that are proportional to the lengths of the other two sides.

Front

If two triangles are similar, what can be said about their corresponding angles?

Back

If two triangles are similar, their corresponding angles are equal.

Front

If two triangles are similar, what can be said about their corresponding sides?

Back

If two triangles are similar, the lengths of their corresponding sides are in proportion.

Front

How do you find the length of a side in similar triangles?

Back

To find the length of a side in similar triangles, set up a proportion using the lengths of corresponding sides from the two triangles.

Front

What is the formula for the ratio of the areas of two similar triangles?

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 and side DE is 9, what is the ratio of their corresponding sides?

Back

The ratio of their corresponding sides is 6:9, which simplifies to 2:3.

Front

What is the relationship between the angles of similar triangles?

Back

The angles of similar triangles are congruent, meaning they have the same measure.

Front

If the sides of triangle XYZ are in the ratio 3:4:5, what type of triangle is it?

Back

Triangle XYZ is a right triangle, as it follows the Pythagorean theorem (3^2 + 4^2 = 5^2).

Front

How can you determine if two triangles are similar?

Back

Two triangles can be determined to be similar if they satisfy one of the following criteria: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side) similarity.