Question

Can someone help me out on these geometry questions? ASAP!!!

Write formal proofs the HL Theorm.

Answer 1

Question 2

1) $\overline{PR} \perp\overline{QS}, \overline{PQ} \cong \overline{PS}$ (given)

2) $\overline{PR} \cong \overline{PR}$ (reflexive property)

3) $\angle PRQ, \angle PRS$ are right angles (perpendicular lines form right angles)

4) $\triangle PRQ, \triangle PRS$ are right triangles (a triangle with a right angle is a right triangle)

5) $\triangle PRQ \cong \triangle PRS$ (HL)

Question 3

1) $\angle C$ is a right angle, $\overline{AC} \cong \overline{AE}, \overline{DE} \perp \overline{AB}$ (given)

2) $\angle DEA$ is a right angle (perpendicular lines form right angles)

3) $\triangle ACD, \triangle DAE$ are right triangles (a triangle with a right triangle is a right angle)

4) $\overline{AD} \cong \overline{AD}$ (reflexive property)

5) $\triangle ACD \cong \triangle AED$ (HL)

6) $\angle CAD \cong \angle DAE$ (CPCTC)

7) $\overline{AD}$ bisects $\angle BAC$ (if a segment splits an angle into two congruent parts, it is an angle bisector)