CFA: Similar Figures & Indirect Measure

Front

What are similar figures?

Back

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

Front

What does it mean for sides to be proportional in similar polygons?

Back

In similar polygons, the lengths of corresponding sides are in the same ratio, meaning they can be expressed as a fraction that is equal for all pairs of corresponding sides.

Front

What is the AA criterion for triangle similarity?

Back

The AA (Angle-Angle) criterion states that if two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

What is the SAS criterion for triangle similarity?

Back

The SAS (Side-Angle-Side) criterion states that if two sides of one triangle are proportional to two sides of another triangle and the included angles are equal, then the triangles are similar.

Front

What is the ASA criterion for triangle similarity?

Back

The ASA (Angle-Side-Angle) criterion states that if two angles and the included side of one triangle are equal to two angles and the included side of another triangle, then the triangles are similar.

Front

How can you use indirect measurement to find the height of an object?

Back

Indirect measurement involves using similar triangles to find the height of an object by comparing it to a known height and shadow length.

Front

If a 5.5 ft tall girl casts a 4 ft shadow, and a tower casts a 90 ft shadow, how do you find the height of the tower?

Back

Set up a proportion: (height of girl)/(shadow of girl) = (height of tower)/(shadow of tower). Solve for the height of the tower.

Front

What is the relationship between corresponding angles in similar figures?

Back

In similar figures, corresponding angles are congruent, meaning they have the same measure.

Front

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

Back

The formula is: height of object = (height of reference object * shadow of object) / (shadow of reference object).

Front

What does it mean for angles to be congruent in similar polygons?

Back

Congruent angles are angles that have the same measure. In similar polygons, corresponding angles are always congruent.