Similar Triangles

What is the definition of proportional sides in similar triangles?

• Proportional sides mean that the ratios of the lengths of corresponding sides are equal.

• Proportional sides are sides that are equal in length.

• Proportional sides refer to sides that are perpendicular to each other.

• Proportional sides are sides that can be added together to form a triangle.

If the sides of two similar triangles are in the ratio 2:3, what can be said about their areas?

• The areas of the triangles are in the ratio of 2:3.

• The areas of the triangles are in the ratio of 3:4.

• The areas of the triangles are in the ratio of 4:9.

• The areas of the triangles are equal.

If two triangles are similar, what can be said about their corresponding angles?

• The corresponding angles of similar triangles are equal.

• The corresponding angles of similar triangles are different.

• The corresponding angles of similar triangles are complementary.

• The corresponding angles of similar triangles are supplementary.

If the sides of two similar triangles are 5 cm and 15 cm, what is the ratio of their corresponding heights?

• 1:2

• 1:3

• 2:3

• 1:4

True or False: Sides in similar figures must be proportional.

• True

• False

• Not always

• Depends on the figure

If triangle XYZ is similar to triangle PQR and the length of side XY is 4 and side PQ is 8, what is the ratio of their areas?

• @@rac{1}{2}@@

• @@rac{1}{4}@@

• @@rac{1}{8}@@

• @@rac{1}{16}@@

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

• The perimeters are equal.

• The perimeters are in the same ratio as the lengths of their corresponding sides.

• The perimeters are always greater than the lengths of their corresponding sides.

• The perimeters are unrelated to the lengths of their corresponding sides.

Two objects that are the same shape but not the same size are _______.

• Congruent

• Similar

• Identical

• Equivalent

What are similar triangles?

• Triangles that have the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are proportional.

• Triangles that have different shapes and sizes, with no equal angles.

• Triangles that are identical in size and shape, with all sides equal.

• Triangles that have one angle equal and the other two angles different.

Solve for n: @@\frac{n}{4}=\frac{8}{7}@@

• @@\frac{32}{7}@@

• @@\frac{16}{7}@@

• @@\frac{24}{7}@@

• @@\frac{40}{7}@@