Similar Figures Flashcard

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 the lengths of their corresponding sides are proportional.

Front

What is the principle of proportionality in similar triangles?

Back

In similar triangles, the ratios of the lengths of corresponding sides are equal. This means if triangle ABC is similar to triangle DEF, then AB/DE = BC/EF = AC/DF.

Front

How do you set up a proportion to find a missing side in similar triangles?

Back

To set up a proportion, write the ratio of the lengths of the corresponding sides of the triangles. For example, if triangle ABC is similar to triangle DEF, and you need to find side x, you can set up the proportion: AB/DE = x/EF.

Front

If a tree is 12 feet tall and casts a shadow of 9 feet, what is the height of a building that casts a shadow of 24 feet?

Back

The height of the building is 32 feet. (Set up the proportion: 12/9 = x/24, solving gives x = 32.)

Front

What is the height of a person if a similar triangle setup gives a height of 6.25 ft?

Back

The height of the person is 6.25 ft.

Front

Solve for x if the proportion is set up as 2/3 = x/6.

Back

x = 4.

Front

What is the height of a person if their shadow is 5 feet long and the shadow of a 6-foot tall person is 4 feet long?

Back

The height of the person is 7.5 feet. (Set up the proportion: 6/4 = x/5, solving gives x = 7.5.)

Front

If two triangles are similar and one has sides of 3, 4, and 5, what are the sides of the other triangle if the longest side is 10?

Back

The sides of the other triangle are 6, 8, and 10.

Front

What is the missing side x if the triangles are similar and the sides are in the ratio 1:4?

Back

x = 12 if the corresponding side is 3.

Front

If a triangle has sides of 5, 12, and 13, what is the ratio of its sides to a similar triangle with sides of 10, 24, and 26?

Back

The ratio is 1:2.