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

In , and the length of the hypotenuse is 10. If one leg is twice as long as the other leg, find the length of the shorter leg. Express answer as a simplified square root.

In geometry, what is a postulate?

For a triangle whose perimeter measures 36 units, the radius of the inscribed circle is 3.Find the area of the triangle.

The method CPCTC can be used to prove that two triangles are congruent.

Congruent circles have the same length of radius while concentric circles have the same center.

-If AB = 3 and BC = 4 in rectangle ABCD, then the length of diagonal is 5.

-In , and . If the length of is represented by 2a, find an expression for the length of .

For any quadrilateral with perpendicular diagonals of lengths and , the area is given by A = .

-In the figure, the measure of exterior angle BCD is twice the measure of .What type of triangle is ?

What expression represents the exact circumference of a circle with radius 6 inches?

-For to be an isosceles triangle with , state an equation that relates s, t, and v.

-A right pyramid has a rectangular base that is 6 ft by 8 ft. If the altitude of the pyramid is 10 feet, find its volume.

In order to justify the construction of the angle-bisector of , we verify that two triangles are congruent by which method?

A diagonal of a parallelogram separates the parallelogram into two congruent triangles.

-A right circular cone has a diameter for its base of length 16 inches and an altitude of 15 inches. Use to find the exact lateral area of the cone.

In kite HJKL, HJ = HL and JK = LK. If m = 90°, HJ = 12, and JK = 5, find the length of diagonal .

Given that , it follows that .

-If m 90° in the triangle shown, then sin .

Find the general form for the line through the points (-2,3) and (4,-1).

-In the figure, and bisects . Name the reason that justifies why .