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

has a perimeter of 84 cm. If cm and ST = 25 cm, find the angle of greatest measure in .

To the nearest degree, find the measure of angle if .

-Given that point P is the midpoint of both and , it follows that .

-Given that m = 90° and that the triangular region is revolved about side , the related solid of revolution is a right circular cone with radius BC and altitude AC.

Two circles that are internally tangent have three common tangent lines.

Find the area of , which has vertices at (0,0), (8,0), and (5,6).

-Name the expression that completes this form of the Law of Sines:

-For , radii and and arc bound a sector. If m = 100° and PX = 5.6 inches, find the area of the sector correct to the nearest tenth of a square inch.

Complete the conclusion from the following true statements: (1) If two triangles are similar, then they have the same shape. (2) Triangle ABC and triangle DEF are similar. (C) Triangle ABC and triangle DEF have ? ? ?

and intersect at point E. If is a right angle, what relationship exists between and ?

The owner and a partner in a small business share profits in the ratio 2:1. For a month in which the business realizes a profit of $15,600. what is the owner's share of the profit?

-The vertices of quadrilateral ABCD lie on . It is correct to say that:

-In , m = 60° and BC = 12. Find AB.

The distance between the points and is 13. Determine all possible value(s) of a.

What is the locus of points in space that are at a given distance r from line l?

What is the name of the point at which the three altitudes of a triangle are concurrent?

A circle can be inscribed within or circumscribed about any regular polygon.

-For a triangle with sides of lengths 13 cm, 14 cm, and 15 cm, the altitude to the 14 cm side separates that side into segments of lengths 5 cm and 9 cm. For the solid of revolution determined by revolving the triangular region about the 14 cm side, find its volume.

In rectangle ABCD, , , and . Find the value of x.

-The sides of the square base of a regular pyramid measure 8 inches each while the altitude measures 10 inches. To the nearest degree, find the measure of the angle formed by the slant height and the apothem of square base of the pyramid shown.