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

Find the exact value of cos 30°.

-If m = 105° and m = 73°, find the measure of (not shown).

What is the specific name of the star-shaped figure that is formed when the sides of a convex pentagon are extended to meet at points in the exterior of the pentagon?

In regular hexagon ABCDEF, AB = 12. Find the length of diagonal .

-Given that , you can prove that:

-The figure shows right triangle ABC with . Also, . Where , , , , and , what reason allows you to conclude that ?

-In isosceles trapezoid HJKL, . If and , find an expression for the perimeter of trapezoid HJKL.

Describe the locus of points in a plane that are equidistant from two intersecting lines l and m.

-In the figure, and . If , , and , find the perimeter (the sum of lengths of all four sides) of quadrilateral XYZW.

In this order, points R, S, T, U, and V are equally spaced on a circle in such a way . What type of figure is formed by the chords , , , , and ?

-In the right triangle shown, m = 90°. What is the value of the expression ( )?

Where and , it follows that .

If two triangles have the same areas and the same length of altitude, these triangles must be congruent.

The volume of a cube is 8 . Find the volume of a cube whose edges are twice those of the first cube.

Which formula would be applied to prove the theorem, "The diagonals of a rectangle are congruent.?"

Any transformation of a geometric figure produces an image that is congruent to the given geometric figure.

-With and both tangent to the circle as shown, find an expression that represents the measure of both and .

-In the figure, suppose that auxiliary line segments and are drawn. What method allows you to conclude that ?

Two of the angles of a triangle have measures of 50° and 60°. Which number cannot be the measure of an exterior angle of this triangle?

- is tangent to at point B. If the length of radius of is r, AC = 1, and AB = 3, write an equation that involves r.