Chapter 5: Quadrilaterals

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer.$m\angle 1+m\angle 2+m\angle 3=\_\_$

$\text{M}$, $\text{N}$ and $\text{T}$ are the midpoints of the sides of $\Delta \text{XYZ}$.

Suppose $\text{XY}=10$, $\text{YZ}=14$ and $\text{XZ}=8$.

State the lengths of the three sides of:

a. $\Delta \text{TNZ}$

b. $\Delta \text{MYN}$

c. $\Delta \text{XMT}$

d. $\Delta \text{NTM}$

Must quad. EFGH be a parallelogram? Can it be a parallelogram? Explain.

In each exercise, you could prove that quadrilateral $\mathbf{SANG}$is a parallelogram if one more fact, in addition to those stated were given. State the fact.

$\overline{\mathrm{SZ}}\cong \overline{\mathrm{NZ}}$

Draw the trapezoid described. If such a trapezoid cannot be drawn, explain why not.

With two right angles.

M, N and T are the midpoints of the sides of $\Delta \text{XYZ}$.

State the theorem suggested by Exercise 6.

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

Study the markings on each figure and decide whether ABCD must be a parallelogram. If the answer is yes, state the definition or theorem that applies.

Name all the points shown that must be midpoints of the sides of the large triangle.

Given that $▱ABCD$ and M is the midpoint of $\overline{AB}$. Then prove that $MO=\frac{1}{2}AD$.