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

Suppose that point P lies above line l. What is the first step in construction of a line through P parallel to line l?

For a construction problem, which instrument could you use?

-If m , m , and m , find x.

In a circle, chords and intersect at point X. If m = 98°, m = 54°, and m = 72°, which chord among , , , and would be longest?

What does the letter D represent in the formula ?

-For the rhombus shown, what expression represents both the sum of the squares of the lengths of the sides and also the sum of the squares of lengths of the diagonals?

Which three-letter symbol is used to indicate that two triangles are congruent because their three pairs of sides are congruent?

Find the locus of points in the plane that are equidistant from the sides of .

If m = 37° and m = 76° in , it follows that m = 77°.

In a right triangle, the sine ratio takes the form .

The measures of two supplementary angles are in the ratio 2:3. Find the measure of the larger angle.

For cyclic quadrilateral ABCD, m and m . Determine the value of x.

In , , , and . Which angle, if any, measures 90°?

Because it has rained the past 4 days, a person's intuition can be used to conclude that it will definitely rain again tomorrow.

Point P lies in the exterior of so that is tangent to the circle. Also, is a secant that intersects at B and C, where P-B-C. If PB = 9 and BC = 7, find PA.

In any right triangle for which is the measure of an acute angle, it follows that .

The reason "Identity," which is used to state that a line segment or angle is congruent to itself, is also known as the Reflexive Property of Congruence.

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

-For , what is the name of the circle that has its center O determined by the three perpendicular-bisectors of the sides of the triangle and radius of length OA?

Given that cos = 0.5, it follows that