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 find the height of an object by creating a similar triangle with a known height and distance, using a mirror or a shadow to establish the proportions.

Front

If two triangles are similar, what can you say about their angles?

Back

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

Front

If a gymnasium is 96 feet long and 75 feet wide, what is the ratio of length to width?

Back

The ratio of length to width is 96:75, which simplifies to 32:25.

Front

How do you set up a proportion to solve for an unknown side in similar triangles?

Back

To set up a proportion, you can use the formula: (length of side in triangle 1) / (length of corresponding side in triangle 2) = (length of unknown side in triangle 1) / (length of corresponding side in triangle 2).

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 calculate the width of a gymnasium on a blueprint if the length is 5.5 inches?

Back

Use the ratio of the actual dimensions to the blueprint dimensions to find the width: (actual width / actual length) = (blueprint width / blueprint length).

Front

What is the height of a tree if you see its reflection in a mirror placed on the ground?

Back

The height of the tree can be found using the principle of similar triangles, where the distance from the observer to the mirror and the distance from the mirror to the tree are used to establish proportions.

Front

If AB is 15 meters in a triangle, what can you infer about the other sides if the triangles are similar?

Back

If triangles are similar, the lengths of the other sides can be found using the same ratio as AB to the corresponding side in the other triangle.