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