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

-In isosceles triangle RST, . If and , find the value of x.

If both a parallelogram and triangle have the same base and altitude, then the area of the parallelogram is twice the area of the triangle.

-One pyramid has a volume of 356 . A larger pyramid has base edges twice as long as that of the first pyramid and a height that is 3 times the height of the first pyramid. What is the volume of the larger pyramid?

Find the locus of points in space that are equidistant from points A and B.

-Write the acronym (the abbreviated form) for the statement, "Corresponding sides of similar triangles are proportional."

When two lines are cut by a transversal, and are one pair of alternate interior angles that are formed. If and , what relationship (in simplified form) exists between x and y?

When using induction, one draws a conclusion based upon numerous examples or test results.

-For the triangular prism, the areas of the lateral faces are 18 , 26 , and 34 . If the area of the base is 16 , find the total area of the prism.

What is the name of the point at which the three angle-bisectors of the angles of a triangle are concurrent?

If the diagonals of a parallelogram are congruent, then the parallelogram is a rhombus.

The sphere has the center (0,0,0) and a radius of length 50.

-For a trapezoid, the lengths of the two bases are a and b. What expression represents the length of the median of the trapezoid?

The measures of the three interior angles of are in the ratio 2:3:7. What type of triangle is ?

What is the locus of points in a plane that are equidistant from parallel lines a and b?

-Given trapezoid RSTV with median , find the length of if RS = 12.7 inches and VT = 17.5 inches.

- has been constructed tangent to at point T and to at point W. How are radii and related?

For right triangle ABC, m = 90°. If b = 8 and c = 12, find cos B (or cos ).

For , points A, B, C, D, and E are equally spaced on the circle in that order. If tangents are constructed at these points, what type of polygon circumscribes this circle?

For square ABCD, two of the vertices are A = (0,0) and B = (a,0). Provide coordinates for the remaining vertices.

-For what type of triangle are the angle-bisectors, perpendicular-bisectors of sides, altitudes, and medians the same?