11. given ∠1 and ∠2 are complementary and ∠3 and ∠2 are complementary.
prove: ∠1 ≅ ∠3
use the reasons listed to complete the proof.

Question

Accepted Answer

# Explanation:
## Step1: Identify the reason for $m\angle1 + m\angle2=90$
Given that $\angle1$ and $\angle2$ are complementary. By the definition of complementary angles (two angles whose sum of measures is $90^{\circ}$), so the reason for $m\angle1 + m\angle2 = 90$ is "Definition of complementary angles".
## Step2: Identify the reason for $m\angle3 + m\angle2=90$
Given that $\angle3$ and $\angle2$ are complementary. By the definition of complementary angles (two angles whose sum of measures is $90^{\circ}$), so the reason for $m\angle3 + m\angle2 = 90$ is "Definition of complementary angles".
## Step3: Use the substitution property
Since $m\angle1 + m\angle2=90$ and $m\angle3 + m\angle2 = 90$, we can substitute $90$ in the first equation with $m\angle3 + m\angle2$. So $m\angle1 + m\angle2=m\angle3 + m\angle2$ (Substitution property).
## Step4: Use the subtraction property of equality
Subtract $m\angle2$ from both sides of the equation $m\angle1 + m\angle2=m\angle3 + m\angle2$.
$$
\begin{align*}
m\angle1 + m\angle2-m\angle2&=m\angle3 + m\angle2 - m\angle2\
m\angle1&=m\angle3
\end{align*}
$$
If the measures of two angles are equal, then the angles are congruent. So $\angle1\cong\angle3$ (by the definition of congruent angles: two angles are congruent if their measures are equal)

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Step1: Identify the reason for \(m\angle1 + m\angle2=90\)

Step2: Identify the reason for \(m\angle3 + m\angle2=90\)

Step3: Use the substitution property

Step4: Use the subtraction property of equality

Answer:

Statement	Reason
\(m\angle3 + m\angle2=90\)	Definition of complementary angles
\(m\angle1 + m\angle2=m\angle3 + m\angle2\)	Substitution property
\(m\angle1=m\angle3\)	Subtraction property of equality
\(\angle1\cong\angle3\)	Definition of congruent angles