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

-If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.

The number of diagonals D for a polygon of n sides is given by . Find the number of sides for a polygon that has 14 diagonals.

-In , angle-bisectors , , and are concurrent at point X. If m = 27° and m = 32°, find m .

Find the slope of any line that is parallel to the line that is the graph of the equation .

-Find the area of the triangle with vertices at (2a,0), (2c,0), and (0,2b).

-Given that and , which method establishes that ?

The instrument used to construct circles and arcs is the:

What two qualities are needed in order that a polygon be classified as a REGULAR polygon?

(not shown) has vertices A(0,0), B(2a,2b), and C(0,2c). Where M is the midpoint of and N is the midpoint of , how are the lengths of and related?

-In kite ABCD, . It follows that:

-The statement, "If 2 parallel lines are cut by a transversal, then corresponding angles are congruent" can be used to prove that 2 lines are parallel.

-If the midpoints of the sides of are joined to form , then the perimeter of will be twice that of .

Find the distance between the points (-7,-5) and (5,4).

-In , = 47°, = 3y - 7, and = 2(y + 10). Find the value of y.

The line that contains ( ) and (6,b) has slope . Find the value of b.

If the diagonals of a quadrilateral are perpendicular, the quadrilateral must be a square.

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

The 8 faces of a regular octahedron are congruent equilateral triangles.

To inscribe a circle in a square, the center can be found by the intersection of the two diagonals.

-If the diagonals of a rhombus have lengths 6 and 8, then the perimeter of the rhombus is 28.