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

-For , points M, N, and P are the midpoints of the sides. If the perimeter of is 47 inches, find the perimeter of .

-When the midpoints of the sides of a square RSTV are joined in order, quadrilateral MNPQ is formed. Being as specific as possible, what type of quadrilateral is MNPQ?

Solve the proportion for x.

In order to determine one point that is equidistant from points A and B, which basic construction can be performed?

-In kite ABCD, AB = AD = y 5, BC = y, and . Find the perimeter of ABCD.

-Both the kite and the parallelogram have two pairs of congruent angles.

-For a quadrilateral to be "cyclic," what requirement must be satisfied?

In a circle (or congruent circles) containing two unequal chords, the shorter chord is nearer the center of the circle.

-In , bisects . If , , and , find XW.

-Points A, B, and C are said to be collinear if they lie on a line.

How is the apothem of a regular polygon related to the side of the polygon to which it is drawn?

A locus of points is the set of points and only those points that satisfy a given condition or set of conditions.

Consider in which m = 90°. Find the point at which the three altitudes are concurrent.

The notation SAS is used to prove that two triangles are congruent.

-With a base of n sides of length s, the lateral area L of a regular pyramid can be written . Using P for perimeter, write the more common form of this formula

-In , , , and . Find the length of side .

- is a tangent while is a secant for the circle shown. If TR = 6 and RS = 3, find RV.

-In , the lengths of the sides are a = 8, b = 10, and c = 12. To the nearest degree, find m .

In the proportion , the number b is known as the geometric mean for a and c.

-In , and . If AB = 16, BC = 12, and BH = 14, find the length of altitude to side .