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

When two parallel lines are cut by a transversal, and are a pair of corresponding angles that are formed. If and , find x.

For a circle of radius r, the area is given by A = 2 r.

-Given that , , and in , it follows that .

-For any regular polygon, the center can be determined by the intersection of any two angle-bisectors of the polygon.

-Suppose that you have utilized congruent vertical angles to prove that by the method SAS. By what reason can you, in turn, state that ?

For (not shown), it follows that:

The area of an equilateral triangle with sides of length s is given by A = .

-To construct an isosceles triangle with vertex angle A and sides of length a, what arc would you draw first?

-In isosceles triangle , XY = YZ = 10, and XZ = 16. Where C is the centroid of , find the distance from C to side of the triangle.

According to the Midpoint Formula, the midpoint of the line segment that joins ( ) and ( ) is .

It is possible to draw a triangle whose sides measure 5 inches, 9 inches, and 14 inches.

-In a circle of radius length 5, use an inequality of the form a < x < b to express possible lengths x for a chord.

-According to the Angle-Addition Postulate, m m = m .

-In the figure, bisects the acute angle of to form isosceles triangle ABD with base . Which side of is longest?

-If points A and B are the endpoints of a diameter and C is any other point on , find the measure .

-If AB = 7.4 and BC = 13.7, then AC = 20.1.

-The point at which the three angle-bisectors of the angles of a triangle are concurrent is known as the circumcenter of the triangle.

-In , m = 37° and m = 69°. Find m .

In a right triangle, the length of the hypotenuse is 13 inches and the length of one of the legs is 12 inches. Find the length of the other leg.

Correct to the nearest tenth of a square foot, find the surface area of a sphere that has a diameter of length 12.8 feet. Use the calculator value of .