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

When lines and intersect at point , it follows that .

-The lateral area L of any prism whose altitude measures h and whose base has perimeter P is given by L = hP.

-In the figure, and are tangents to the circle from point D. If m = 84°, find m .

Let the vertices of be the points M(0,0), N(a,0), P( ), and Q(b,c). Which equation must hold true if the diagonals of are perpendicular?

-In , is a right angle. If a = 5 and c = 12, find the exact value of .

-If B is the midpoint of and BC = 2.78 inches, then AC measures:

-In the triangle shown, c = 12, m = 90°, and m = 63°. To the nearest tenth of a unit, find the length b.

-In , is a right angle. If a = 5 and c = 13, find sin B (also known as sin )

For rectangle ABCD, AB = 5 inches while the length of a diagonal is AC = 13 inches. Find the area of the rectangle.

-In the figure, bisects and D is the midpoint of . If and , find the value of x.

Find the exact value of the expression ° °.

-The triple (20,21,29) is a Pythagorean Triple.

-Given that and , which method justifies that ?

For any real numbers a and b for which , there is a positive number p for which .

The total area for a regular octahedron is . Find the length of each edge of the octahedron.

Find one point that is located at equal distances from the three vertices of in which is a right angle.

-In the figure, is a right angle. Find the value of sin A (also known as sin ).

-If m = 90° in right triangle , then is an altitude of that triangle.

-Given that quadrilateral quadrilateral MNPQ, .

-Each base edge of a regular pentagonal pyramid measures 10 cm. If the lateral area of this pyramid is 425 , find the length of the slant height of the pyramid.