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

-Draw a conclusion based upon true statements (i.) and (ii.). (i.) If two triangles are congruent, then they are similar. (ii.) is not similar to .

Given the endpoints and , find the midpoint of the line segment .

-If M and N are the midpoints of sides and of , then .

Determine the exact volume of the sphere .

-In this figure, and are complementary. Also, and are complementary. Regarding and , what conclusion may you draw?

-For the isosceles triangle shown, the measure of the vertex angle is m = 38°.If AB = BC = 6.8, find AC to the nearest tenth of a unit.

-With O as the center of the regular pentagonal base and P as the vertex of the pyramid shown, what relationship must hold in order for the pyramid to be known as a regular pentagonal pyramid?

-For trapezoid HJKL, . It follows that:

In a 45°-45°-90° triangle, the length of a leg is the number a. What expression represents the length of the hypotenuse of this triangle?

-In the form , verify Euler's Formula for the pyramid shown.

Show that for any value of , the point having the form lies on the plane whose equation is .

-If (not shown) bisects and m = 37°, then m equals:

-In the figure, m = 90° and m = 29°. If c = 17.4, find b to the nearest tenth of unit..

-Given the coplanar lines and the fact that , which lines must be parallel?

-Given that is congruent to , , and , find .

Where , and . Find .

The volume V of a sphere with a diameter of length d can be written .

For a quadrilateral to be "cyclic," what requirement must be satisfied?

Find the exact value of sin 30°.

In the form , find the equation of the line that contains (g,h) and is perpendicular to .