11. which best describes what is formed by the construction of $overline{ad}$?
a the angle bisector of $angle bac$
b a 60° angle including $overline{ab}$
c the mid - point of $overline{ab}$
d the perpendicular bisector of $overline{ab}$
for items 12 - 13, use the diagram shown.
12. if $mangle1=(4x + 2)$ and $mangle3=(5x - 25)$, what is the value of $x$?
a 27
b 28
c 30
d 32
13. select all statements that could be the first step of an indirect proof of the conditional below.
if $mangle2 = 95$, then $mangle3 = 95$.
□ a. if $mangle3
eq95$, then $mangle2
eq95$.
□ b. if $mangle2 = 95$, then $mangle3 = 95$.
□ c. assume if $mangle3
eq95$, then $mangle2
eq95$.
□ d. assume if $mangle2
eq95$, then $mangle3
eq95$.
□ e. assume if $mangle3 = 95$, then $mangle2 = 95$.
14. if $dm = 32$ and point $g$ bisects $overline{dm}$, what is the value of $r$?
a 11
b 16
c 22
d 72
15. given: $angle1$ and $angle2$ are complementary and $angle3$ and $angle2$ are complementary.
prove: $angle1congangle3$
use the reasons listed to complete the proof.
definition of congruence substitution
subtraction property of equality given
statements reasons
$mangle1 + mangle2 = 90$
$mangle3 + mangle2 = 90$
$mangle1 + mangle2=mangle3 + mangle2$
$mangle1 = mangle3$
$angle1congangle3$

Question

Accepted Answer

### 11.
# Explanation:
## Step1: Recall construction of angle bisector
The construction shown is of an angle - bisector. The arcs drawn from point $A$ and the intersection of the arcs to form $AD$ is the standard way to construct the angle bisector of $\angle BAC$.
# Answer:
A. the angle bisector of $\angle BAC$

### 12.
# Explanation:
## Step1: Set angles equal
Since $\angle1$ and $\angle3$ are vertical angles, $m\angle1=m\angle3$. So, we set up the equation $4x + 2=5x-25$.
## Step2: Solve for $x$
Subtract $4x$ from both sides: $2=x - 25$. Then add 25 to both sides: $x=27$.
# Answer:
A. 27

### 13.
# Explanation:
## Step1: Recall indirect proof
The first step of an indirect proof is to assume the opposite (negation) of the conclusion. The conditional is "If $m\angle2 = 95$, then $m\angle3 = 95$". The opposite of the conclusion $m\angle3 = 95$ is $m\angle3
eq95$. We assume the negation of the conclusion while keeping the hypothesis. So the first - step of the indirect proof is to assume "If $m\angle2 = 95$, then $m\angle3
eq95$" which is equivalent to assuming "If $m\angle3
eq95$, then $m\angle2
eq95$" (contra - positive).
# Answer:
A. If $m\angle3
eq95$, then $m\angle2
eq95$

### 14.
# Explanation:
## Step1: Use the property of a bisector
Since $G$ bisects $\overline{DM}$, $DG = GM$. So, $r + 5=3r-17$.
## Step2: Solve for $r$
Subtract $r$ from both sides: $5 = 2r-17$. Add 17 to both sides: $22=2r$. Divide both sides by 2: $r = 11$.
# Answer:
A. 11

### 15.
# Explanation:
## Step1: State the given
$m\angle1 + m\angle2=90$ (Given)
## Step2: State the given
$m\angle3 + m\angle2=90$ (Given)
## Step3: Use substitution
Since both $m\angle1 + m\angle2$ and $m\angle3 + m\angle2$ equal 90, we can say $m\angle1 + m\angle2=m\angle3 + m\angle2$ (Substitution)
## Step4: Use subtraction property of equality
Subtract $m\angle2$ from both sides: $m\angle1=m\angle3$ (Subtraction Property of Equality)
## Step5: Use definition of congruence
Since $m\angle1=m\angle3$, $\angle1\cong\angle3$ (Definition of Congruence)
# Answer:
| Statements | Reasons |
|--|--|
| $m\angle1 + m\angle2 = 90$ | Given |
| $m\angle3 + m\angle2 = 90$ | Given |
| $m\angle1 + m\angle2=m\angle3 + m\angle2$ | Substitution |
| $m\angle1=m\angle3$ | Subtraction Property of Equality |
| $\angle1\cong\angle3$ | Definition of Congruence |

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QUESTION IMAGE

Question

Explanation:

11.

Step1: Recall construction of angle bisector

Step1: Set angles equal

Step2: Solve for \(x\)

Step1: Recall indirect proof

Answer:

12.