Question

What three pieces of information must be known to prove by the hl criterion? Triangle ABC and triangle DEF are represented side-by-side. Side AC and side DF have equal length. Side AB and BC meet at vertex B at a right angle. Side EF and side DE meet at vertex E at a right angle. Select all the correct answers.

1) Side AB and side DE have equal length
2) Side BC and side EF have equal length
3) Angle ABC is congruent to angle DEF
4) Angle BAC is congruent to angle EDF
5) Angle ACB is congruent to angle DFE

Answer 1

To prove by the HL criterion, three pieces of information must be known: side AB and side DE have equal length, angle ABC is congruent to angle DEF, and there is no given information about the equality of side BC and side EF.

Step-by-step explanation:

To prove by the HL criterion, the following three pieces of information must be known:

1. Side AB and side DE have equal length: In the given information, side AB and side DE meet at vertex B and vertex E respectively at a right angle. Therefore, they are perpendicular to each other and will have equal length.
2. Side BC and side EF have equal length: Although side AC and side DF have equal length, there is no given information about the equality of side BC and side EF.
3. Angle ABC is congruent to angle DEF: Since side AB and BC meet at vertex B at a right angle, angle ABC is a right angle. Similarly, side DF and DE meet at vertex E at a right angle, so angle DEF is a right angle. As both angles are right angles, they are congruent.