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

In regular hexagon ABCDEF, diagonals and are drawn. Find m .

If in the right triangle with acute angles and , it follows that .

-If in , then .

-For the right triangular prism shown, the base is a right triangle with sides of lengths 3 in, 4 in, and 5 in. If the prism has a height of 6 inches, find its volume.

Find the point of intersection for the lines that are the graphs of and .

-Use to find the exact total area of the right circular cone for which r = 3 cm and l = 5 cm.

-For the segment bounded by chord and arc , CD = 12 cm and m = 120°.Find the exact area of the segment.

In , and are supplementary.

-In , AB = 5.7 cm and BC = 8.2 cm. What is the perimeter of ?

-For , there is an exterior angle at vertex Z. If m = 68° and m = 47°, find m .

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

In trapezoid RSTV, and . If RS = 10 in, ST = 12 in, VT = 18 in, and RW = 8 in, find the area of RSTV.

-Points A, B, and C are collinear. If AB = 12 and BC = 7, find the two possible lengths of .

-For a given circle, the length of a 90° arc is one-third the circumference of the circle.

The lengths of sides for a regular pentagon are 6 inches each. To the nearest tenth of an inch, find the length of the radius of the pentagon.

-In the circle, m = 68° and m = 74°. Find m .

In , and . Name the longest side of .

-Using 3.14, find the approximate area of a circle with radius r = 10 cm.

In , the length of radius is 6 inches. If m = 90° and m = 60°, how much longer is chord than chord ?

-Find the measure of each exterior angle of a regular dodecagon (polygon with 12 sides).