Question

Complete the proof please. A. SAS B. ASA C. AAS D.HL

Answer 1

Option B:

ASA congruence

Solution:

Step 1: Given

`\overline{Q S} \perp \overline{Q T}`

Step 2: Given

`\overline{R T} \perp \overline{R S}`

Step 3: Given

`\overline{Q U} \cong \overline{R U}` (Included side)

Step 4: All right angles are congruent.

`\angle Q \cong \angle R` (Angle)

Step 5: By vertical angle theorem

`\angle Q U T \cong \angle R U S` (Angle)

Step 6: By ASA congruence

QU and RU are included side of corresponding angles.

Therefore by ASA congruence rule,

`\Delta Q T U \cong \Delta R S U`

Option B is the correct answer.

Hence proved.