# Geometry

## Educators  Problem 1

Exercises $1-4$ refer to $\square C R E W$
If $O E=4$ and $W E=8 .$ name two segments congruent to $\overline{W E} .$ Amrita B.

Problem 2

Exercises $1-4$ refer to $\square C R E W$
If $\overline{W R} \perp \overline{C E},$ name all angles congruent to $\angle R C E$ . Gregory C.

Problem 3

Exercises $1-4$ refer to $\square C R E W$
If $\overline{W R} \perp \overline{C E}$ . name all segments congruent to $\overline{W E} .$ Amrita B.

Problem 4

Exercises $1-4$ refer to $\square C R E W$
If $R E=E W,$ name all angles congruent to $\angle E R W$ Gregory C.

Problem 5

In Exercises $5-10$ quad. $P Q R S$ is a parallelogram. Find the values of $a, b,$ $x,$ and $y .$ Amrita B.

Problem 6

In Exercises $5-10$ quad. $P Q R S$ is a parallelogram. Find the values of $a, b,$ $x,$ and $y .$ Gregory C.

Problem 7

In Exercises $5-10$ quad. $P Q R S$ is a parallelogram. Find the values of $a, b,$ $x,$ and $y .$ Amrita B.

Problem 8

In Exercises $5-10$ quad. $P Q R S$ is a parallelogram. Find the values of $a, b,$ $x,$ and $y .$ Gregory C.

Problem 9

In Exercises $5-10$ quad. $P Q R S$ is a parallelogram. Find the values of $a, b,$ $x,$ and $y .$ Amrita B.

Problem 10

In Exercises $5-10$ quad. $P Q R S$ is a parallelogram. Find the values of $a, b,$ $x,$ and $y .$ Gregory C.

Problem 11

Find the perimeter of $\square R I S K$ if $R I=17$ and $I S=13$ Amrita B.

Problem 12

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 $S P .$ Gregory C.

Problem 13

Prove Theorem $5-1$ Amrita B.

Problem 14

Prove Theorem $5-2$ . (Draw and label a diagram. List what is given and what is to be proved.) Gregory C.

Problem 15

Prove Theorem 5.3 Amrita B.

Problem 16

Given: $A B C X$ is a $\square$ :
$D X F E$ is a $\square$ :
Prove: $\angle B \cong \angle E$ Gregory C.

Problem 17

The coordinates of three vertices of $\square A B C D$ are given. Plot the points and
find the coordinates of the fourth vertex.
$$A(1,0), B(5,0), C(7,2), D(\underline{2}, \underline{?})$$ Amrita B.

Problem 18

The coordinates of three vertices of $\square A B C D$ are given. Plot the points and
find the coordinates of the fourth vertex.
$$A(3,2), B(8,2), C(\longrightarrow, \stackrel{2}{\longrightarrow}), D(0,5)$$ Gregory C.

Problem 19

Each figure in Exercises $19-24$ is a parallelogram with its diagonals drawn. Find the values of $x$ and $y .$ Amrita B.

Problem 20

Each figure in Exercises $19-24$ is a parallelogram with its diagonals drawn. Find the values of $x$ and $y .$ Gregory C.

Problem 21

Each figure in Exercises $19-24$ is a parallelogram with its diagonals drawn. Find the values of $x$ and $y .$ Amrita B.

Problem 22

Each figure in Exercises $19-24$ is a parallelogram with its diagonals drawn. Find the values of $x$ and $y .$ Gregory C.

Problem 23

Each figure in Exercises $19-24$ is a parallelogram with its diagonals drawn. Find the values of $x$ and $y .$ Amrita B.

Problem 24

Each figure in Exercises $19-24$ is a parallelogram with its diagonals drawn. Find the values of $x$ and $y .$ Gregory C.

Problem 25

Quad. $D E C K$ 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 $y=?$ Amrita B.

Problem 26

Quad. $D E C K$ is a parallelogram. Complete.
If $\quad D E=x+y, \quad E C=12, \quad C K=2 x-y, \quad$ and $K D=3 x-2 y,$ then $x=\underline{?}, y=\underline{?},$ and the perimeter of $\square D E C K=?$ Gregory C.

Problem 27

Quad. $D E C K$ is a parallelogram. Complete.
If $m \angle 1=3 x, m \angle 2=4 x,$ and $m \angle 3=x^{2}-70,$ then $x=\underline{?}$ and $m \angle C E D=\stackrel{?}{(\text { numerical answers })}$ Amrita B.

Problem 28

Quad. $D E C K$ is a parallelogram. Complete.
If $m \angle 1=42, \quad m \angle 2=x^{2},$ and $m \angle C E D=13 x,$ then $m \angle 2=\underline{?}$ or $m \angle 2=\underline{?}$ (numerical answers). Gregory C.

Problem 29

Quad. $D E C K$ is a parallelogram. Complete.
Given: $\square P Q R S : \overline{P J} \cong \overline{R K}$
Prove: $\overline{S J} \cong \overline{Q K}$ Amrita B.

Problem 30

Quad. $D E C K$ is a parallelogram. Complete.
Given: $\square J Q K S ; \overline{P J} \cong \overline{R K}$
Prove: $\angle P \cong \angle R$ Gregory C.

Problem 31

Quad. $D E C K$ is a parallelogram. Complete.
Given: $A B C D$ is a $\square ; \overline{C D} \cong \overline{C E}$
Prove: $\angle A \cong \angle E$ Amrita B.

Problem 32

Quad. $D E C K$ is a parallelogram. Complete.
Given: $A B C D \cong \frac{\text { is a }}{C E}$
Prove: $\frac{A B C D}{\cong} \cong \frac{\text { is a }}{C E}$ Gregory C.

Problem 33

Find something interesting to prove. Then prove it. Answers may vary.
Given: $\square A B C D : \angle 1 \cong \angle 2$ Amrita B.

Problem 34

Find something interesting to prove. Then prove it. Answers may vary.
Given: $\square E F I H ; \quad \square E G J H ; \angle 1 \cong \angle 2$ Gregory C.

Problem 35

The coordinates of three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.
$$(3,4),(9,4),(6,8)$$ Amrita B.

Problem 36

The coordinates of three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.
$$(-1,0),(2,-2),(2,2)$$ Gregory C.

Problem 37

The coordinates of three vertices of a parallelogram are given. Find all the possibilities you can for the coordinates of the fourth vertex.
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). Amrita B.

Problem 38

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. Gregory C. 