Question

1. which best describes what is formed by the construction of ab? a the angle bisector of ∠bac b a 90° angle including ab c the midpoint of ab d the perpendicular bisector of ab

for items 12 - 13, use the diagram shown.

1. if m∠1=(4x + 2) and m∠3=(5x - 25), what is the value of x? a 27 b 28 c 30 d 32
2. select all statements that could be the first step of an indirect proof of the conditional below. if m∠2 = 95, then m∠3 = 95. □ a. if m∠3≠95, then m∠2≠95. □ b. if m∠2 = 95, then m∠3 = 95. □ c. assume if m∠3≠95, then m∠2≠95. □ d. assume if m∠2≠95, then m∠3≠95. □ e. assume if m∠3 = 95, then m∠2 = 95.
3. if de = 32 and point g bisects de, what is the value of dg? a 11 b 16 c 22 d 22
4. given: ∠1 and ∠2 are complementary and ∠3 and ∠2 are complementary. prove: ∠1≅∠3

use the reasons listed to complete the proof. definition of congruence, substitution, subtraction property of equality, given
statements reasons
m∠1 + m∠2 = 90
m∠3 + m∠2 = 90
m∠1 + m∠2 = m∠3 + m∠2
m∠1 = m∠3
∠1≅∠3

Explanation:

12.

Step1: Set angles equal

Since vertical - angles are congruent and $\angle1$ and $\angle3$ are vertical - angles, we set $m\angle1=m\angle3$. So, $4x + 2=5x-25$.

Step2: Solve for $x$

Subtract $4x$ from both sides: $4x + 2-4x=5x-25-4x$, which gives $2=x - 25$. Then add 25 to both sides: $2 + 25=x-25 + 25$, so $x = 27$.

In an indirect proof, we start by assuming the opposite of what we want to prove. The conditional is "If $m\angle2 = 95$, then $m\angle3 = 95$". The opposite of the conclusion is $m\angle3
eq95$. We assume the negation of the conditional statement's conclusion while keeping the hypothesis. So we assume "If $m\angle2 = 95$, then $m\angle3
eq95$" or equivalently "Assume if $m\angle3
eq95$, then $m\angle2
eq95$".

Step1: First statement reason

$m\angle1 + m\angle2=90$ is given, so the reason is "Given".

Step2: Second statement reason

$m\angle3 + m\angle2=90$ is given, so the reason is "Given".

Step3: Third statement reason

Since $m\angle1 + m\angle2=90$ and $m\angle3 + m\angle2=90$, we can set $m\angle1 + m\angle2=m\angle3 + m\angle2$ by substitution.

Step4: Fourth statement reason

Subtract $m\angle2$ from both sides of $m\angle1 + m\angle2=m\angle3 + m\angle2$ using the Subtraction Property of Equality to get $m\angle1=m\angle3$.

Step5: Fifth statement reason

Since $m\angle1=m\angle3$, by the Definition of Congruence, $\angle1\cong\angle3$.

Answer:

A. 27

13.