Question

sheri sketched out a pair of parallel line segments and formed a triangle in between those lines.
decide if each statement about the figure is true or false.
statement true false
$\angle1 + \angle2 + \angle3 = 180^\circ$ $\bigcirc$ $\bigcirc$
$\angle1 \cong \angle4$ $\bigcirc$ $\bigcirc$
$\angle3 \cong \angle6$ $\bigcirc$ $\bigcirc$

Explanation:

Step1: Analyze first statement

Angles $\angle1$, $\angle2$, $\angle3$ form a straight angle. The sum of angles on a straight line is $180^\circ$.
$\angle1 + \angle2 + \angle3 = 180^\circ$

Step2: Analyze second statement

$\angle1$ and $\angle4$ are alternate interior angles (from parallel lines). Alternate interior angles are congruent, so $\angle1 \cong \angle4$, not $\angle2 \cong \angle4$.

Step3: Analyze third statement

$\angle3$ and $\angle6$ are alternate interior angles (from parallel lines). Alternate interior angles are congruent, so $\angle3 \cong \angle6$.

Answer:

1. $\angle1 + \angle2 + \angle3 = 180^\circ$: True
2. $\angle2 \cong \angle4$: False
3. $\angle3 \cong \angle6$: True