Section 1
Properties of Parallelograms
Refer to $\square C R E W.$If $O E=4$ and $W E=8 .$ name two segments congruent to $\overline{W E}$.
Refer to $\square C R E W.$If $\overline{W R} \perp \overline{C E}$, name all angles congruent to $\angle R C E.$
Refer to $\square C R E W.$If $\overline{W R} \perp \overline{C E}$. name all segments congruent to $\overline{W E}$.
Refer to $\square C R E W.$If $R E=E W$, name all angles congruent to $\angle E R W.$
$P Q R S$ is a parallelogram. Find the values of $a, b$ $x,$ and $y.$FIGURE CAN'T COPY.
Find the perimeter of $\square R I S K$ if $R I=17$ and $I S=13.$
The perimeter of $\square S T O P$ is $54 \mathrm{cm} .$ and $\overline{S T}$ is $1 \mathrm{cm}$ longer than $\overline{S P} .$ Find $S T$ and $S P.$
Prove Theorem $5-1.$
Prove Theorem $5-2 .$ (Draw and label a diagram. List what is given and what is to be proved.)
Prove Theorem $5-3.$
Given: $A B C X$ is a $\square:$$D X F E \text { is a } \square$Prove: $\angle B \cong \angle E$
The coordinates of three vertices of $\square A B C D$ are given. Plot the points and find the coordinates of the fourth vertex.A(1,0), B(5,0), C(7,2), D(?, \quad ?)
The coordinates of three vertices of $\square A B C D$ are given. Plot the points and find the coordinates of the fourth vertex.$A(3,2), B(8,2), C(?, \quad ?), D(0,5)$
Is a parallelogram with its diagonals drawn. Find the values of $x$ and $y.$FIGURE CAN'T COPY.
Quad. DECK is a parallelogram. Complete.If $K T=2 x+y, D T=x+2 y, T E=12,$ and $T C=9$ then $x=\underline{?}$ $=$and $y=\underline{?}$
Quad. DECK is a parallelogram. Complete.If $\quad D E=x+y$ E C=12 C K=2 x-y and $K D=3 x-2 y,$ then $x=\frac{?}{}, y=\frac{?}{},$ and the perimeter and the perimeter of $\square D E C K$$=\frac{?}{}$
Quad. DECK is a parallelogram. Complete.If $m \angle 1=3 x, m \angle 2=4 x,$ and $m \angle 3=x^{2}-70,$ then $x=\frac{?}{}$ and $m \angle C E D=\frac{?}{}$ (numerical answers.)
Quad. DECK is a parallelogram. Complete.If $m \angle 1=42, \quad m \angle 2=x^{2},$ and $m \angle C E D=13 x,$ then $m \angle 2=\stackrel{?}{-}$ or $m \angle 2=\underline{?}$ (numerical answers).
Given: $\square P Q R S ; \overline{P J} \cong \overline{R K}$Prove: $\overline{S J} \cong \overline{Q K}$
Given: $\square J Q K S ; \overline{P J} \cong \overline{R K}$Prove: $\angle P \cong \angle R$
Given: $A B C D$ is a $\square ; \overline{C D} \cong \overline{C E}$Prove: $\angle A \cong \angle E$
Given: $A B C D$ is a $\square ; \angle A \cong \angle E$Prove: $\overline{A B} \cong \overline{C E}$
Find something interesting to prove. Then prove it. Answers may vary.Given: $\square A B C D: \angle 1 \cong \angle 2$FIGURE CAN'T COPY.
Find something interesting to prove. Then prove it. Answers may vary.Given: $\square E F I H ; \quad \square E G J H ; \angle 1 \cong \angle 2$FIGURE CAN'T COPY.
The coordinates of three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.$$(3,4),(9,4),(6,8)$$
The coordinates of three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.$$(-1,0),(2,-2),(2,2)$$
a. Given: Plane $P \|$ plane $Q: j \| k$ Prove: $A X=B Y$b. State a theorem about parallel planes and lines that you proved in part (a).
Prove: If a segment whose endpoints lie on opposite sides of a parallelogram passes through the midpoint of a diagonal, that segment is bisected by the diagonal.
Write a paragraph proof: The sum of the lengths of the segments drawn from any point in the base of an isosceles triangle perpendicular to the legs is equal to the length of the altitude drawn to one leg.