if $ \angle a \cong \angle c $, and $ \angle b \cong \angle c $, then
your answer

if $ \angle 6 $ is supplementary to $ \angle 9 $, and $ \angle 3 $ is supplementary to $ \angle 9 $, then
your answer

if $ \angle 5 $ and $ \angle 12 $ form a linear pair, and $ \angle 4 $ and $ \angle 12 $ form a linear pair,
then

Question

if $ \angle a \cong \angle c $, and $ \angle b \cong \angle c $, then
your answer

if $ \angle 6 $ is supplementary to $ \angle 9 $, and $ \angle 3 $ is supplementary to $ \angle 9 $, then
your answer

if $ \angle 5 $ and $ \angle 12 $ form a linear pair, and $ \angle 4 $ and $ \angle 12 $ form a linear pair,
then

Accepted Answer

# Explanation:
## First problem:
### Step1: Use the transitive property of congruence
If $ \angle A\cong\angle C$ and $ \angle B\cong\angle C$, by the transitive property of congruence (if $a = c$ and $b = c$, then $a = b$), we can say $ \angle A\cong\angle B$

## Second problem:
### Step1: Use the congruent supplements theorem
If two angles are supplementary to the same angle, then they are congruent. Since $ \angle6$ is supplementary to $ \angle9$ ($\angle6+\angle9 = 180^{\circ}$) and $ \angle3$ is supplementary to $ \angle9$ ($\angle3+\angle9=180^{\circ}$), then $ \angle6\cong\angle3$

## Third problem:
### Step1: Use the congruent - linear - pairs theorem
If two angles form a linear pair with the same angle, then they are congruent. Since $ \angle5$ and $ \angle12$ form a linear pair ($\angle5+\angle12 = 180^{\circ}$) and $ \angle4$ and $ \angle12$ form a linear pair ($\angle4+\angle12=180^{\circ}$), then $ \angle5\cong\angle4$

# Answer:
1. $ \angle A\cong\angle B$
2. $ \angle6\cong\angle3$
3. $ \angle5\cong\angle4$

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

First problem:

Step1: Use the transitive property of congruence

Second problem:

Step1: Use the congruent supplements theorem

Third problem:

Step1: Use the congruent - linear - pairs theorem

Answer: