The image shows a segment of a geometric proof with a "Statements" and "Reasons" table. The missing reasons need to be filled based on the statements.

Here’s a breakdown of the information and reasoning to complete the proof:

Statements:

1. $h \parallel k, j \perp h$
2. $m\angle 2 = 90^\circ$
3. $\angle 2 \cong \angle 6$
4. $m\angle 2 = m\angle 6$
5. $m\angle 6 = 90^\circ$

Reasons:

1. Given
2. Definition of perpendicular lines: $j \perp h$ implies that the angle formed (like $\angle 2$) is 90 degrees.
3. Congruent angles have equal measures: $\angle 2 \cong \angle 6$ means they have the same measure.
4. Definition of congruent angles: Congruence implies equal measures, hence $m\angle 2 = m\angle 6$.
5. Transitive Property of Equality: Since both $m\angle 2$ and $m\angle 6$ are 90°, we can conclude this from the previous statements.

Does that make sense, or would you like a more detailed explanation?

Follow-up questions:

1. What is the definition of the transitive property of equality?
2. How do we prove lines are parallel or perpendicular using angles?
3. What other properties can be used to prove angle congruence?
4. How can you use the definition of perpendicular lines in different geometric proofs?
5. How do you handle cases where angles are supplementary or complementary in a proof?

Tip:

Always check whether angles in a geometric diagram form perpendicular or parallel relationships to derive key angle measures easily.