Question

determine whether the diagram provides enough evidence to prove the statement is correct.
yes no
$\angle 6=\angle 11$
$\angle 6=\angle 8$
$\angle 7=\angle 11$
$\angle 6=\angle 10$
$\angle 7=\angle 9$
$\angle 7=\angle 10$

Explanation:

Step1: Check $\angle6=\angle11$

$\angle6$ is a right angle ($90^{\circ}$) and $\angle11$ is not a right angle. So $\angle6
eq\angle11$.

Step2: Check $\angle6=\angle8$

$\angle6$ is a right angle ($90^{\circ}$) and $\angle8$ is not a right angle. So $\angle6
eq\angle8$.

Step3: Check $\angle7=\angle11$

$\angle7$ and $\angle11$ are vertical angles. Vertical angles are equal. So $\angle7 = \angle11$.

Step4: Check $\angle6=\angle10$

$\angle6$ and $\angle10$ are both right angles. So $\angle6=\angle10$.

Step5: Check $\angle7=\angle9$

$\angle7$ and $\angle9$ are corresponding angles. Since lines $e$ and $f$ are parallel (because of the right - angle markings which imply perpendicularity to line $g$ and thus $e\parallel f$ by the converse of the perpendicular to the same line theorem), and $h$ is a transversal. Corresponding angles of parallel lines are equal. So $\angle7=\angle9$.

Step6: Check $\angle7=\angle10$

$\angle7$ is not a right angle and $\angle10$ is a right angle. So $\angle7
eq\angle10$.

Answer:

$\angle6 = \angle11$: No
$\angle6 = \angle8$: No
$\angle7 = \angle11$: Yes
$\angle6 = \angle10$: Yes
$\angle7 = \angle9$: Yes
$\angle7 = \angle10$: No