91Ó°ÊÓ

One angle of an isosceles trapezoid has measure \(57 .\) Find the measures of the other angles.

T A=A B=B C and T D=D E=E F Write an equation that relates \(A D, B E,\) and \(C F\) (Hint: Think of trapezoid \(C F D A\).)

The coordinates of three vertices of a rectangle are given. Plot the points and find the coordinates of the fourth vertex. Is the rectangle a square? $$A(2,1), B(4,1), C(4,5), D(\text{___, ___})$$

\(E F G H\) is a parallelogram whose diagonals intersect at \(P . M\) is the midpoint of \(\overline{F G}\). Prove that \(M P=\frac{1}{2} E F\)

The coordinates of three vertices of a rectangle are given. Plot the points and find the coordinates of the fourth vertex. Is the rectangle a square? $$O(0,0), E(4,0), F(4,3), G(\text{___,___})$$

Draw \(\triangle A B C\) and label the midpoints of \(\overline{A B}, \overline{A C},\) and \(\overline{B C}\) as \(X . Y .\) and \(Z .\) respectively. Let \(P\) be the midpoint of \(\overline{B Z}\) and \(Q\) be the midpoint of \(\overline{C Z}\). Prove that \(P X=Q Y\)

Draw a quadrilateral of the type named. Join, in order, the midpoints of the sides. What special kind of quadrilateral do you appear to get? non-isosceles trapezoid

Draw a quadrilateral of the type named. Join, in order, the midpoints of the sides. What special kind of quadrilateral do you appear to get? Carefully draw an isosceles trapezoid and measure its diagonals. What do you discover? Write a proof of your discovery.

A kite is a quadrilateral that has two pairs of congruent sides, but opposite sides are not congruent. Draw a convex kite. Discover, state, and prove whatever you can about the diagonals and angles of a kite.

A kite is a quadrilateral that has two pairs of congruent sides, but opposite sides are not congruent. a. Draw a convex kite. Join, in order, the midpoints of the sides. What special kind of quadrilateral do you appear to get? b. Repeat part (a), but draw a nonconvex kite.