Exam 12: Geometry Problems: Complementary Angles, Collinear Points, and Similar Triangles

-An octagonal prism has 9 faces.

For a given polyhedron, there are 24 vertices and 32 faces. How many edges does the polyhedron have? [Hint: .]

The upper case H has point symmetry.

A property of geometry that is accepted as correct without proof is a(n):

-The measures of the three interior angles of a triangle are x, 2x, and 3x. What type of triangle is the triangle described?

-For a right circular cone, the altitude has the same measure as its radius. If the volume of the cone is approximately 56 , find the length of radius to the nearest tenth of a foot.

For the angle-measure indicated, which angle cannot be constructed?

The area of the trapezoid with base lengths and and altitude h is given by A = h( + ).

When lines a and b are cut by transversal d, and are a pair of alternate exterior angles that are formed. If and , find x.

In kite ABCD, and . Diagonals and intersect at point E. If AC = 18.6 and BD = 9.2, find the length of .

In isosceles triangle RST, . If , find the length of .

Find the measure of the angle formed by the hands of a clock at exactly 4:10 PM.

Any two squares are similar to each other.

For any point in Cartesian space, explain why the point is the point of symmetry with respect to the origin.

Which is NOT a method for proving two triangles congruent?

-In , m = 58°. Find m .

Determine the value of x so that the points (-2,4), (1,1), and (x,6) are collinear.

-For the right rectangular prism (or box) shown, the dimensions are l = 12 in, w = 4 in,and h = 3 in. How long is a diagonal of the box?

Determine the number of sides in a regular polygon whose central angles each measure 24°.

For any angle measure (where ° and °), find the value of the expression .