Question

Can someone help me on this pls? It’s urgent, so ASAP (it’s geometry)

Write formal proofs using HL Theorem.

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` and
`\angle PRS` are right angles (perpendicular lines form right angles)

4)
`\triangle PRQ` and
`\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` and
`\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)