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

-In , m and m . Find the value of x.

-Find the lateral area for a regular hexagonal prism in which the base edges are 4 inches long and the altitude is h = 6 inches.

The diagonals of quadrilateral MNPQ are perpendicular-bisectors of each other. Being as specific as possible, what type of quadrilateral is MNPQ?

What does the question mark represent in this extended proportion?

A right circular cone has a radius of base of 4.6 inches. The angle formed by a radius and a slant height of the cone measures 62°. Correct to the nearest whole number, find the volume of the cone. [Recall: .]

If the word MOM is relected across a horizontal line that lies beneath this word, what word is formed?

-If and in quadrilateral ABCD, then ABCD is an isosceles trapezoid.

If the area of a regular octagon is 25 , find the area of the regular octagon whose sides are twice those of the first octagon.

-Each lateral face of a regular hexagonal pyramid has lateral edges of length 10 inches and a base edge of 12 inches. What is the lateral area of the pyramid?

-In quadrilateral WXYZ, . If and , determine a value of x so that WXYZ must be a parallelogram.

-A pyramid has a square base with sides of length e. If the altitude of the pyramid also measures e, what is the volume of the pyramid?

For , intersects sides and so that . If and , what is the constant of proportionality k for the extended proportion ?

-In , M is the midpoint of and N is the midpoint of . If the length of is represented by , what expression (containing x) represents the length of ?

In the construction a regular hexagon, we constructed an exterior angle of the hexagon. What is the measure of each exterior angle of the regular hexagon?

-How many common tangents do these circles have?

For all points on the plane x - 4y + 3z = where x = , what relationship exists between y and z?

The bisector of one angle of a triangle always separates the triangle into two smaller and congruent triangles.

Given line l, how many lines in space can be drawn parallel to l?

-In , m m .

-With chords and intersecting in the interior of the circle, what expression can be used to find m ?