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# California Geometry

## Educators

### Problem 1

A _______ is the locus of all points in a plane that are equidistant from the endpoints of a segment. (perpendicular bisector or angle bisector).

Kaci L.

### Problem 2

Use the diagram
(FIGURE CAN'T COPY)
Given that $P S=53.4, Q T=47.7,$ and $Q S=53.4$ find $P Q$

Kaci L.

### Problem 3

Use the diagram
(FIGURE CAN'T COPY)
Given that $m$ is the perpendicular bisector of $\overline{P Q}$ and $S Q=25.9,$ find $S P$

Kaci L.

### Problem 4

Use the diagram
(FIGURE CAN'T COPY)
Given that $m$ is the perpendicular bisector of $\overline{P Q}, P S=4 a,$ and $Q S=2 a+26,$ find $Q S$

Kaci L.

### Problem 5

Use the diagram
(FIGURE CAN'T COPY)
Given that $\overrightarrow{B D}$ bisects $\angle A B C$ and $C D=21.9,$ find $A D$

Kaci L.

### Problem 6

Use the diagram
(FIGURE CAN'T COPY)
Given that $A D=61, C D=61,$ and $\mathrm{m} \angle A B C=48^{\circ}$
find $\mathrm{m} \angle C B D$

Kaci L.

### Problem 7

Use the diagram
(FIGURE CAN'T COPY)
Given that $D A=D C, \mathrm{m} \angle D B C=(10 y+3)^{\circ}$
and $\mathrm{m} \angle D B A=(8 y+10)^{\circ},$ find $\mathrm{m} \angle D B C$

Kaci L.

### Problem 8

Carpentry For a king post truss to be constructed correctly, $P$ must lie on the bisector of $\angle J L N .$ How can braces $\overline{P K}$ and $\overline{P M}$ be used to ensure that $P$ is in the proper location?

Kaci L.

### Problem 9

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$M(-5,4), N(1,-2)$

Kaci L.

### Problem 10

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$U(2,-6), V(4,0)$

Kaci L.

### Problem 11

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$J(-7,5), K(1,-1)$

Kaci L.

### Problem 12

Use the diagram
(FIGURE CANT COPY)
Given that line $t$ is the perpendicular bisector of $\overline{J K}$ and $G K=8.25,$ find $G J$

Kaci L.

### Problem 13

Use the diagram
(FIGURE CANT COPY)
Given that line $t$ is the perpendicular bisector If $\overline{I K}, I G=x+12,$ and $K G=3 x-17,$ find $K G$

Kaci L.

### Problem 14

Use the diagram
(FIGURE CANT COPY)
Given that $G=70.2, J H=26.5,$ and $G K=70.2,$ find $J K$

Kaci L.

### Problem 15

Use the diagram
(FIGURE CANT COPY)
Given that $\mathrm{m} \angle R S Q=\mathrm{m} \angle T S Q$ and $T Q=1.3,$ find $R Q$

Kaci L.

### Problem 16

Use the diagram
(FIGURE CANT COPY)
Given that $\mathrm{m} \angle R S Q=58^{\circ}, R Q=49,$ and $T Q=49$
find $\mathrm{m} \angle R S T$

Kaci L.

### Problem 17

Use the diagram
(FIGURE CANT COPY)
Given that $R Q=T Q, \mathrm{m} \angle Q S R=(9 a+48)^{\circ}$
and $\mathrm{m} \angle Q S T=(6 a+50)^{\circ},$ find $\mathrm{m} \angle Q S T$

Kaci L.

### Problem 18

The planners for a new section of the city want every location on Main Street to be equidistant from Elm Street and Grove Street. How can the planners ensure that this is the case?

Kaci L.

### Problem 19

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$E(-4,-7), F(0,1)$

Kaci L.

### Problem 20

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$X(-7,5), Y(-1,-1)$

Kaci L.

### Problem 21

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$$M(-3,-1), N(7,-5)$$

Kaci L.

### Problem 22

Write an equation in point-slope form for the perpendicular bisector of the segment with the given endpoints.
$\overline{P Q}$ is the perpendicular bisector of $\overline{S T}$ Find the values of $m$ and $n .$
(FIGURE CAN'T COPY)

Ashley H.

### Problem 23

Use the diagram of a shuffleboard and the following information to find each length.
$\overline{K Z}$ is the perpendicular bisector of $\overline{G N}, \overline{H M},$ and $\overline{J L}$
$$J K$$

Ashley H.

### Problem 24

Use the diagram of a shuffleboard and the following information to find each length.
$\overline{K Z}$ is the perpendicular bisector of $\overline{G N}, \overline{H M},$ and $\overline{J L}$.
$$G N$$

Ashley H.

### Problem 25

Use the diagram of a shuffleboard and the following information to find each length.
$\overline{K Z}$ is the perpendicular bisector of $\overline{G N}, \overline{H M},$ and $\overline{J L}$.$$M L$$

Ashley H.

### Problem 26

Use the diagram of a shuffleboard and the following information to find each length.
$\overline{K Z}$ is the perpendicular bisector of $\overline{G N}, \overline{H M},$ and $\overline{J L}$
$$H Y$$

Ashley H.

### Problem 27

Use the diagram of a shuffleboard and the following information to find each length.
$\overline{K Z}$ is the perpendicular bisector of $\overline{G N}, \overline{H M},$ and $\overline{J L}$
$$J L$$

Ashley H.

### Problem 28

Use the diagram of a shuffleboard and the following information to find each length.

Ashley H.

### Problem 43

For the points $R(-4,2), S(1,4), T(3,-1),$ and $V(-7,-5),$ determine whether the Infin ars narallsh nernendiswlar, ar neither.
$\overleftarrow{R S}$ and $\overleftarrow{V T}$

Ashley H.

### Problem 44

For the points $R(-4,2), S(1,4), T(3,-1),$ and $V(-7,-5),$ determine whether the Infin ars narallsh $\overleftarrow{R V}$ and $\overleftarrow{S T}$

Ashley H.

### Problem 45

For the points $R(-4,2), S(1,4), T(3,-1),$ and $V(-7,-5),$ determine whether the Infin ars narallsh nernendiswlar, ar neither.
$\overrightarrow{R T}$ and $\overrightarrow{V R}$

Ashley H.

### Problem 46

Write the equation of each line in slope-intercept form
the line through the points $(1,-1)$ and $(2,-9)$

Ashley H.
The line with $x$ -intercept $-4$ and $y$ -intercept 5