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Geometry

Ray C. Jurgensen,Richard G. Brown,John W. Jurgensen

Chapter 5

Quadrilaterals

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

Problem 11

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

Amrita B.
Numerade Educator

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.
Numerade Educator

Problem 13

Prove Theorem $5-1$

Amrita B.
Numerade Educator

Problem 14

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

Gregory C.
Numerade Educator

Problem 15

Prove Theorem 5.3

Amrita B.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

Problem 19

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

Amrita B.
Numerade Educator

Problem 20

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

Gregory C.
Numerade Educator

Problem 21

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

Amrita B.
Numerade Educator

Problem 22

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

Gregory C.
Numerade Educator

Problem 23

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

Amrita B.
Numerade Educator

Problem 24

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

Gregory C.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

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.
Numerade Educator

Problem 39

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.

Amrita B.
Numerade Educator