Similar Polygons and Triangles

Front

What are similar polygons?

Back

Polygons that have the same shape but not necessarily the same size. Their corresponding angles are equal, and the lengths of corresponding sides are proportional.

Front

What is the criteria for triangles to be similar?

Back

Triangles are similar if they satisfy one of the following conditions: AA (Angle-Angle), SSS (Side-Side-Side), or SAS (Side-Angle-Side).

Front

If two triangles are similar, how do you find the length of a side in one triangle if you know the corresponding side in the other triangle?

Back

Use the proportion of the lengths of corresponding sides. If triangle ABC is similar to triangle DEF, then AB/DE = AC/DF = BC/EF.

Front

What is the significance of the AA criterion for triangle similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, the triangles are similar, regardless of the lengths of their sides.

Front

How do you solve for a missing side in similar triangles?

Back

Set up a proportion using the lengths of the corresponding sides and solve for the unknown.

Front

What is the relationship between the areas of similar polygons?

Back

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

Front

If triangle ABC is similar to triangle DEF and AB = 4, DE = 8, what is the ratio of their areas?

Back

The ratio of their areas is (AB/DE)² = (4/8)² = 1/4.

Front

What is the formula for finding the height of an object using similar triangles?

Back

Height = (Height of object / Distance from object) * Distance from observer.

Front

If ΔABC ∼ ΔADE and AB = 6, DE = 9, what is the length of AC if AD = 12?

Back

AC = (AB/DE) * AD = (6/9) * 12 = 8.

Front

What does it mean for two polygons to be congruent?

Back

Two polygons are congruent if they have the same shape and size, meaning all corresponding sides and angles are equal.