Quiz 1

Name _____________________________________________________

Problem 1

Triangle ABC is a right triangle with right angle at C. Point D is on segment AB so that line CD is perpendicular to AB.

If AD = x and BD = y, find AB, showing your reasoning carefully.

Problem 2 (Construction)

Given the segment AB and point D on AB, construct a point C so that triangle ABC is a right triangle with right angle at C and line CD is perpendicular to AB.

Problem 3

Let ABCD be four points on a circle c. If ABCD is a parallelogram, prove (if true) that ABCD must be a rectangle.

Problem 4

Let m and n be lines that are parallel at distance d apart. Also, let p and q be lines parallel at the same distance d apart. But m is not parallel to p. Prove that the four points of intersection of the lines form a rhombus.