91Ó°ÊÓ

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

Given: $\mathrm{Plane}\mathrm{X}âˆ\yen \mathrm{Plane}\mathrm{Y};\stackrel{¯}{\mathrm{LM}}â‰\dots \stackrel{¯}{\mathrm{ON}}$

Prove: LMNO is a parallelogram.

Prove that the base angles of an isosceles trapezoid are congruent.

$\stackrel{¯}{\text{RA}}$is an altitude of $\mathrm{Δ}\text{SAT}$. P and Q are midpoints of $\stackrel{¯}{\text{SA}}$and $\stackrel{¯}{\text{TA}}$. $\text{SR}=9,\text{RT}=16,\text{QT}=10,$and $\text{PR}=7.5$

Find the perimeter of $\mathrm{Δ}\text{SAT}$.

Given: $â–\pm \text{ABZY}$; $\stackrel{¯}{\text{ZY}}â‰\dots \stackrel{¯}{\text{BX}}$; $∠1â‰\dots ∠2$

Prove: ABZY is a rhombus.

Each diagram shows a trapezoid and its median. Find the value of x.

Given: $â–\pm \mathrm{JQKS};\stackrel{¯}{PJ}â‰\dots \stackrel{¯}{RK}$, Prove: $∠\mathrm{P}â‰\dots ∠\mathrm{R}$.

Given: ABCD is a $â–\pm ,\stackrel{¯}{CD}â‰\dots \stackrel{¯}{CE}$

Prove: $∠\mathrm{A}â‰\dots ∠\mathrm{E}$

Given: $\stackrel{¯}{\mathbf{AD}}â‰\dots \stackrel{¯}{\mathbf{BC}}$; $\stackrel{¯}{\mathbf{AD}}âˆ\yen \stackrel{¯}{\mathbf{BC}}$.

Prove: $\stackrel{¯}{\mathbf{EF}}â‰\dots \stackrel{¯}{\mathbf{FG}}$.

Prove Theorem 5-12.