Similarity & Missing Sides of Triangles

Front

What does it mean for two triangles to be similar?

Back

Two triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.

Front

If triangle ABC is similar to triangle DEF, and the length of side AB is 6 cm while side DE is 9 cm, what is the ratio of their sides?

Back

The ratio of the sides is 6:9 or 2:3.

Front

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

Back

Use the proportion of the lengths of corresponding sides. Set up a ratio and solve for the missing side.

Front

If a triangle has sides of lengths 3 cm, 4 cm, and 5 cm, what type of triangle is it?

Back

It is a right triangle, as it follows the Pythagorean theorem (3^2 + 4^2 = 5^2).

Front

What is the formula for finding the height of an object using similar triangles?

Back

Height = (Length of shadow of object / Length of shadow of person) * Height of person.

Front

If a person is 1.5 meters tall and casts a shadow of 2 meters, and a tree casts a shadow of 10 meters, how tall is the tree?

Back

Height of tree = (10 m / 2 m) * 1.5 m = 7.5 m.

Front

What is the significance of corresponding angles in similar triangles?

Back

Corresponding angles in similar triangles are equal, which helps establish the similarity of the triangles.

Front

If triangle XYZ is similar to triangle PQR, and the length of side XY is 8 cm while side PQ is 4 cm, what is the scale factor?

Back

The scale factor is 8:4 or 2:1.

Front

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

Back

The ratio of their areas is the square of the ratio of their corresponding sides.

Front

If two triangles are similar and one has an area of 50 cm², what is the area of the other triangle if the ratio of their sides is 2:1?

Back

Area of the other triangle = 50 cm² / (2^2) = 50 cm² / 4 = 12.5 cm².