Geometry: Quiz 2: Similarity; Triangle Theorems

What are the angle measures in a 30-60-90 right triangles?

30, 60, 90

The smaller of two similar rectangles has dimensions 4 and 6. Find the dimensions of the larger rectangle if the ratio of the perimeters is 2 to 3.

6 by 9

Polygons must have which of the following characteristics to be considered similar?

A 1:1 correspondence in vertices Corresponding angles are equal. Both polygons are the same shape Corresponding sides are proportional.

18 is the geometric mean between 4 and 9.

False

For a pair of similar triangles, corresponding sides are always congruent.

False

To be considered similar, two polygons must have corresponding sides that are equal.

False

The Pythagorean Theorem deals with which relationship in a right triangle?

The lengths of the legs and the length of the hypotenuse

If the sides of one triangle are lengths 2, 4 and 6 and another triangle has sides of lengths 3, 6 and 9, then the triangles are similar.

True

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

True

The transitive property holds for similar figures.

True

Three is the geometric mean between itself.

True

To be considered similar, two polygons must have corresponding angles that are equal.

True

To be considered similar, two polygons must have corresponding sides that are in proportion.

True

Triangles similar to the same triangle are similar to each other.

True

In a pair of similar polygons, corresponding angles are congruent.

always

What type of triangle is a 45-45-90 right triangle?

isosceles

The focus so far has been on similar triangles, but there are also theorems that deal with similar...

polygons

Which type of triangle has special proportions?

right

If a line intersects two sides of a triangle, then it forms a triangle that is similar to the given triangle.

sometimes

The lengths of the sides of a triangle are 3, 4, 5. Can the triangle be a right triangle?

yes