Similar Triangles

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 Angle-Angle (AA) similarity criterion?

Back

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

Front

What is the Side-Side-Side (SSS) similarity criterion?

Back

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

Front

What is the Side-Angle-Side (SAS) similarity criterion?

Back

If one angle of a triangle is equal to one angle of another triangle and the sides including these angles are in proportion, then the triangles are similar.

Front

How do you find the height of an object using similar triangles?

Back

By setting up a proportion between the height of the object and the lengths of the corresponding sides of a triangle formed by a line of sight.

Front

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

Back

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

Front

If two triangles have sides in the ratio 3:5, what is the ratio of their perimeters?

Back

The ratio of their perimeters is also 3:5.

Front

If the height of a tree is represented as 'h' and the distance from the tree to a point is 'd', how can you express 'h' using similar triangles?

Back

h = k * d, where k is a constant derived from the proportions of the similar triangles.

Front

What is the relationship between the angles of similar triangles?

Back

The corresponding angles of similar triangles are equal.

Front

If triangle XYZ is similar to triangle PQR, and XY = 6 cm, PQ = 9 cm, what is the length of side QR if side YZ = 4 cm?

Back

QR = (9/6) * 4 cm = 6 cm.