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 has 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. For help, see this worked example.
and
are right angles
and
are acute angles
Answer (1)
Answer:To prove a congruence of triangles using the HL (Hypotenuse-Leg) criterion, three pieces of information must be known: (1) the hypotenuse of one right triangle is equal to the hypotenuse of the other right triangle, (2) one leg of the first right triangle is equal to one leg of the second right triangle, and (3) both triangles are right triangles. In the context provided, side AC and side DF are equal in length, and both triangles have a right angle at vertices B and E respectively. Therefore, knowing these two sides are equal and that both triangles are right-angled allows us to apply the HL criterion for proving their congruence.Step-by-step explanation:
