Similarity Application

Front

What is similarity in geometry?

Back

Similarity in geometry refers to figures that have the same shape but may differ in size. Corresponding angles are equal, and corresponding sides are in proportion.

Front

What is a proportion?

Back

A proportion is an equation that states that two ratios are equal. It can be used to solve for unknown values in similar figures.

Front

How can you find the height of an object using shadows?

Back

You can find the height of an object using similar triangles formed by the object and its shadow compared to a person and their shadow.

Front

What does it mean for lines to be congruent?

Back

Congruent lines are lines that have the same length.

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 a tree casts a shadow of 10 feet and a person casts a shadow of 5 feet, how tall is the tree if the person is 6 feet tall?

Back

The height of the tree can be found using proportions: (height of tree)/(10 ft) = (6 ft)/(5 ft). The tree is 12 feet tall.

Front

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

Back

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

Front

What is the significance of corresponding sides in similar figures?

Back

In similar figures, corresponding sides are proportional, meaning the ratios of their lengths are equal.

Front

How do you set up a proportion to solve for an unknown height?

Back

Set up a proportion using the known heights and shadow lengths, then cross-multiply to solve for the unknown.

Front

What is the relationship between the heights of two similar triangles?

Back

The heights of two similar triangles are proportional to the lengths of their corresponding bases.