Question

State the postulate or theorem that justifies each statement.

$\angle 3\cong \angle 6$

Short answer

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

Step-by-step solution

Step 1. First observation from figure

Arrowheads are shown on lines $I$and $P$, so these lines are parallel.

Step 2. Second observation from figure

Line $t$is transversal to the parallel lines $I$and$P$.

Step 3. Third observation from figure

$\angle 3$and $\angle 6$are alternate interior angles.

Theorem 3-2: If two parallel lines are cut by a transversal then the alternate interior angles are congruent.

$\angle 3\cong \angle 6$

Thus, theorem 3-2 justifies given statement.