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

-If X is the midpoint of and X-V-T on , , , , and , find the length of .

-Given that is congruent to , , , and , find .

In a production process 240 pounds of aluminum are used with 780 pounds of steel. How many pounds of aluminum would be used with 1,240 pounds of steel?

Given that , it follows that:

Which method for proving triangles congruent is used only for proving right triangles congruent?

Both pairs of opposite sides of quadrilateral WXYZ are congruent. Being as specific as possible, what type of quadrilateral is WXYZ?

Having proved that by the reason SSS, what reason allows you to conclude that ?

In , and . If and , find the perimeter of .

In isosceles trapezoid HJKL, . If m = 45°, JK = 6 cm, and the length of an altitude is 4 cm, find the exact perimeter of HJKL.

In regular octagon ABCDEFGH, AB = 6. Find the perimeter of trapezoid ABCH.

-Find the sum of the interior angles for an octagon.

For two similar triangle, the ratio of two corresponding sides is : = 1:3. Find the ratio of their areas : .

Which type of triangle has sides of lengths a = 8, b = 15, and c = 17?

In , AB = 12, AD = 18, and m = 56°. To the nearest square unit, find the area of .

Point D lies in the interior of . Line segments are drawn from vertices A, B, and C through point D to intersect at point E, at point F, and at point G. If , , , , and , find AG. [Hint: Use Ceva's Theorem.]

-Like the pyramid, the volume formula for a right circular cone can be expressed as . State another form of the formula for the volume of the cone.

Find the number of sides for a regular polygon in which each interior angle is 120° larger than each exterior angle.

-In rhombus MNPQ, diagonal is congruent to side . Find m .

-In an equilateral triangle whose radius has length 6, find the length of an apothem.

-For a pentagonal pyramid, the total number of edges is 10.