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

In the form , find the equation of the line that contains (5,2) and has the slope of .

The statement, "The midpoint of a line segment is unique" is proven by the indirect method.

-In the figure, . If and , find x.

-Find the exact value of tan 60°.

When a quadrilateral is circumscribed about a circle, how are the sides of the quadrilateral related to the circle?

. If , , , and , find DF.

Just as SSS, SAS, ASA, AAS, and HL are methods for proving that triangles are congruent, use three letters to state two methods that are not valid.

Given hypotenuse , describe the locus of points in a plane that are the vertices of a right triangle.

-In , chord is 12 inches long and m = 90°. Find the exact area of the segment bounded by and .

In , radii and are congruent to chord . Find m .

Given lines and m with , it follows that:

In , one side has the length 5 inches and another side has length 12 inches. Find all possible lengths of the third side so that the triangle is a right triangle.

In the form , find the equation of the line through (-2,-5) and (1,4).

-Points A, B, C, and D are collinear in the order A-B-C-D. If AC = 10.8 inches, BD = 7.7 inches, and BC = 3.2 inches, find AD.

-The angle shown measures 60°. How would you construct an angle that measures 30°?

-For the isosceles triangle shown, the coordinates of the vertex have not been provided. In order, use a, b, c, etc as needed to name the coordinates of the vertex.

-Using rectangle HJKL as shown, what type of quadrilateral is determined by joining the midpoints of the sides of HJKL in order?

-For a quadrilateral to be a rectangle, how must the diagonals be related?

Quadrilateral ABCD is inscribed in . If m = 49°, find m .

-In the circle shown, m = m . Are these arcs congruent?