Similar Triangles - Word Problems

Front

What are similar triangles?

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 principle of proportionality in similar triangles?

Back

The principle of proportionality states that in similar triangles, the ratios of the lengths of corresponding sides are equal.

Front

How can you find the height of an object using similar triangles?

Back

You can use the concept of similar triangles by creating a proportion between the height of the object and the length of its shadow compared to a smaller object with a known height and shadow length.

Front

If a tree casts a shadow of 10 feet and a 5-foot person casts a shadow of 2 feet, how tall is the tree?

Back

Using the proportion: (Height of tree / 10 ft) = (5 ft / 2 ft). The height of the tree is 25 feet.

Front

What is the formula for finding the length of a side in similar triangles?

Back

If triangle A is similar to triangle B, then (side length of A) / (side length of B) = (corresponding side length of A) / (corresponding side length of B).

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 of two objects, then cross-multiply to solve for the unknown height.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If a building casts a shadow of 14 m and a 10 m pole casts a shadow of 8 m, how tall is the building?

Back

Using the proportion: (Height of building / 14 m) = (10 m / 8 m). The height of the building is 17.5 m.

Front

What is the scale factor in similar triangles?

Back

The scale factor is the ratio of the lengths of corresponding sides of two similar triangles.

Front

How do you find the length of a side when given the scale factor?

Back

Multiply the length of the corresponding side in the smaller triangle by the scale factor to find the length in the larger triangle.