Chapter 5: Quadrilaterals

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

$\angle \mathrm{ADX}\cong \angle \mathrm{CBX}$

Give the reason for each step in the following proof of theorem 5-6

Given: $\mathrm{m}\angle \mathrm{A}=\mathrm{m}\angle \mathrm{C}=\mathrm{x};\mathrm{m}\angle \mathrm{B}=\mathrm{m}\angle \mathrm{D}=\mathrm{y}$

Prove: ABCD is a parallelogram.

Proof:

$\overleftrightarrow{\text{AE}},\overleftrightarrow{\text{BF}},\overleftrightarrow{\text{CG}}$and $\overleftrightarrow{\text{DH}}$are parallel, with $\text{EF}=\text{FG}=\text{GH}$. Complete.

If $\text{AB}=\mathbf{5}$, then $\text{AD}=$ ? .

In Exercises 5-10 quad. PQRS is a parallelogram. Find the values of a, b, x and y.

In the following figure, a trapezoid$ABCD$has median$\overline{MN}$. If $FC=9$then find.EN

For the following figure, complete the statement about the diagram. Then state the definition, postulate or theorem that justify the answer.

If $\angle 2\cong \angle 3$ then$\overline{EC}\cong \_\_$.

Draw and label a diagram. List what is given and what is to be proved. Then write a two-column proof of the theorem.

Theorem 5-4.

State the principal theorem that justifies the statement about the diagram.

If D is the midpoint of $\overline{\mathit{A}\mathit{B}}$, then $DE=6$.

Draw a quadrilateral such that exactly three sides are congruent and two pairs of angles are congruent.

Quadrilateral ABCD is a parallelogram. Name the principal theorem or definition that justifies the statement.

$\mathrm{m}\angle \mathrm{ABC}=\mathrm{m}\angle \mathrm{CDA}$