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

Find the slope m of the line that contains the points (-3,-4) and (1,4).

For , . If , , and , find AS.

-In the right triangle shown, it follows that tan 45° = 1.

The radius of an equilateral triangle measures 4 inches. Find the area of this equilateral triangle.

Find the midpoint of the line segment that joins (-1,4) and (7,-8).

In a right triangle, the tangent ratio of an angle has the form .

Explain why the lines decribed below are parallel. and

-The region bounded by chord and arc is known as a segment of the circle.

-In the figure, S-T-U-V and . Draw a conclusion regarding and .

-For , m = 103° and it follows that is the longer diagonal.

-In a right triangle, the legs have lengths of 5 ft and 12 ft. Using these measures, which ratio (sine, cosine, or tangent) would be used to find the measure of the acute angle that is formed by the hypotenuse and the leg of length 12 feet?

-Consider the triangle with sides of lengths a, b, and c. How would you construct a larger triangle similar to the first triangle but with a constant of proportionality of 2?

-The diagonals of a quadrilateral ABCD are shown. If and bisect each other, what type of quadrilateral is ABCD? Be as specific as possible.

-If and , then .

- is circumscribed about the circle. If DF = 14, FG = 16, and DG = 12, find DM.

Which statement is a corollary of the theorem, "The sum of the three interior angles of a triangle is 180°."

The most simplified form of the extended ratio 30° : 60° : 90° is 15 : 30 : 45.

-If , then .

Name the point of symmetry for the sphere .

When two planes intersect, their intersection is a(n):