1 Answer

Tim Harper · Answer 1 · 2023-01-28T12:36:17+0000

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)

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