Question

select all the true statements a. ∠3 ≅ ∠2 because they are alternate interior angles b. m∠1 + m∠3 = 180 because they form a straight angle c. ∠3 ≅ ∠6 because they are alternate interior angles d. ∠1 and ∠6 are supplementary because ∠3 ≅ ∠6 and m∠1 + m∠3 = 180 e. ∠1 ≅ ∠3 because they are vertical angles

Explanation:

Step1: Analyze option A

$\angle3$ and $\angle2$ are not alternate - interior angles. Alternate - interior angles are between two parallel lines and on opposite sides of the transversal. So option A is false.

Step2: Analyze option B

$\angle1$ and $\angle3$ form a straight - line. The sum of angles on a straight - line is $180^{\circ}$. So $m\angle1 + m\angle3=180$ is true.

Step3: Analyze option C

$\angle3$ and $\angle6$ are alternate - interior angles. When two parallel lines are cut by a transversal, alternate - interior angles are congruent. So $\angle3\cong\angle6$ is true.

Step4: Analyze option D

Since $\angle3\cong\angle6$ and $m\angle1 + m\angle3 = 180$, by substitution, $m\angle1 + m\angle6=180$, so $\angle1$ and $\angle6$ are supplementary. Option D is true.

Step5: Analyze option E

$\angle1$ and $\angle3$ are not vertical angles. Vertical angles are opposite each other when two lines intersect. So option E is false.

Answer:

B. $m\angle1 + m\angle3 = 180$ because they form a straight angle.
C. $\angle3\cong\angle6$ because they are alternate interior angles.
D. $\angle1$ and $\angle6$ are supplementary because $\angle3\cong\angle6$ and $m\angle1 + m\angle3 = 180$