Similar Triangles Flashcard (Applied)

Front

What are similar triangles?

Back

Triangles that have the same shape but may differ in size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Front

What is the AA criterion for similarity?

Back

If two angles of one triangle are equal to two angles of another triangle, then the triangles are similar.

Front

How do you find the length of a side in similar triangles?

Back

Use the proportion of corresponding sides. If triangle ABC is similar to triangle DEF, then AB/DE = AC/DF = BC/EF.

Front

What is the concept of proportionality in similar triangles?

Back

The ratios of the lengths of corresponding sides of similar triangles are equal.

Front

If triangle ABC is similar to triangle DEF, and AB = 4, DE = 8, what is the ratio of their areas?

Back

The ratio of their areas is the square of the ratio of their corresponding sides. (AB/DE)² = (4/8)² = 1/4.

Front

What is the height of a tree if Lance the alien is 5 feet tall and his shadow is 8 feet long, while the tree's shadow is 32 feet long?

Back

20 feet. Use the proportion: 5/8 = height/32.

Front

If two triangles have sides of lengths 6, 8, and 10, and 3, 4, and 5 respectively, are they similar?

Back

Yes, because the ratios of corresponding sides (6/3, 8/4, 10/5) are all equal to 2.

Front

What is the value of x if the sides of two similar triangles are in the ratio 2:3 and one side of the first triangle is 10?

Back

x = 15. Use the proportion: 10/x = 2/3.

Front

How do you determine if two triangles are similar using the SSS criterion?

Back

If the lengths of the corresponding sides of two triangles are in proportion, then the triangles are similar.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.