Question

name tyra li
2-1 lesson quiz
envision geometry
use the figure shown for items 1 and 2.

1. which of the following statements are true? select all that apply.

a ∠3≅∠2 because they are alternate 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°.

Explanation:

Step1: Analyze Option A

$\angle3$ and $\angle2$ are not alternate angles. Alternate angles have a specific position - alternate - exterior or alternate - interior. $\angle3$ and $\angle2$ are not in such positions, so 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, $m\angle1 + m\angle3=180^{\circ}$, and B 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, $\angle3\cong\angle6$, and C is true.

Step4: Analyze Option D

Since $\angle3\cong\angle6$ (alternate interior angles) and $m\angle1 + m\angle3 = 180^{\circ}$ (linear pair), by substitution, $m\angle1 + m\angle6=180^{\circ}$, which means $\angle1$ and $\angle6$ are supplementary. So, D is true.

Answer:

B. $m\angle1 + m\angle3 = 180^{\circ}$ 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 $m\angle1 + m\angle3 = 180^{\circ}$.