Pre-algebra Similar Triangles

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 their corresponding sides are proportional.

Front

What does it mean for sides to be proportional in similar triangles?

Back

In similar triangles, the lengths of corresponding sides are in the same ratio. This means that if one triangle has sides of length a, b, and c, and the other has sides of length ka, kb, and kc (where k is a constant), then the triangles are similar.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 10 and side DE is 5, what is the ratio of their sides?

Back

The ratio of their sides is 10:5 or 2:1.

Front

True or False: The angles of similar triangles are always equal.

Back

True

Front

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

Back

Yes, they are similar because the sides are in proportion (6:3 = 2:1, 8:4 = 2:1, 10:5 = 2:1).

Front

Find side length X if triangle ABC is similar to triangle DEF and AB = 12, DE = 4, and BC = X, EF = 8.

Back

X = 6 (since the ratio of sides is 12:4 = 3:1, so BC must be 3 times DE).

Front

What is the scale factor between two similar triangles if one has a side length of 15 and the corresponding side length in the other triangle is 5?

Back

The scale factor is 3 (15:5 = 3:1).

Front

If triangle GHI is similar to triangle JKL and the length of side GH is 9 and side JK is 3, what is the length of side HI if side KL is 4?

Back

Side HI = 12 (since the ratio is 9:3 = 3:1, so HI must be 3 times KL).

Front

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

Back

The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding side lengths.

Front

If the sides of triangle MNO are 5, 12, and 13, and triangle PQR is similar to triangle MNO with a scale factor of 2, what are the lengths of the sides of triangle PQR?

Back

The sides of triangle PQR are 10, 24, and 26.