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

- is an altitude for . If RV = 5, RS = 7, and WT = 4, find the length of altitude .

Where ,find the slope m of the line that contains the points (a,3) and (b,3).

For , the radius has length 4 inches. Describe the locus of points in the plane at a distance of 1 inch from .

For coplanar lines r, s, and t, if r ⊥ t and s ⊥ t, then r || s.

Given that and are complementary, what conclusion may you draw?

-In isosceles trapezoid HJKL, . Suppose that points M, N, P, and Q are the midpoints of the sides , , , and respectively. If the length of diagonal is 10 cm, find the perimeter of MNPQ.

For isosceles triangle XYZ with and point W on base , is an altitude. If XZ = 12 and YW = 8, find XY.

-A church steeple that needs to be reshingled has the shape of a regular square pyramid. If base edges of the steeple measure 16 feet while lateral edges measure 17 feet, what is the lateral area (area to reshingle) of the steeple?

-For parallel lines a and b, and are corresponding angles. If and , find x.

For the triangle with sides of lengths a, b, and c, find an expression for the semiperimeter s of the triangle.

-For a regular pentagonal pyramid, each lateral face has an area of 12 . If the area of the pentagonal base is 15 , find the total (surface) area of the pyramid.

For a square with apothem of length a, the perimeter equals 4a.

-In a triangle, the angle measures are , , and and opposite sides have lengths a, b, and c respectively. Based upon the Law of Cosines, what expression is equivalent to ?

-In , s = 6, t = 9, and m = 38°. Find m to the nearest degree.

- is not a right triangle. If m = 72°, m = 38°, AB = 12.4, and BC = 19.2, find the length of correct to the nearest whole unit.[Hint: Consider altitude .]

-Suppose that lines r and s are both perpendicular to line t. Then r is parallel to s if:

Find the sum of the interior angles of a hexagon.

-Suppose that you have proved that and , in turn, that . What reason would you use to further conclude that ?

For the right triangle with sides of lengths 8, 15, and 17, find the length of the radius of the inscribed circle.

-In the figure, and are known as vertical angles.