Question

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

Write formal proofs the LA Theorm.

Answer 1

Question 4

1) $\angle B$ and $\angle E$ are right angles, $\overline{AB} \cong \overline{DE}$, $\angle A \cong \angle D$ (given)

2) $\triangle CBA$ and $\triangle FED$ are right triangles (a triangle with a right angle is a right triangle)

3) $\triangle CBA \cong \triangle FED$ (LA)

• Note: I wrote the names of the triangles in an alternate order because of the word filter.

Question 5

1) $\overline{XY} \perp\overline{WZ}$, $\overline{UV} \perp \overline{WZ}$, $\overline{VW} \cong \overline{YZ}$, and $\angle Z \cong \angle W$ (given)

2) $\angle XYZ$ and $\angle UVW$ are right angles (perpendicular lines form right angles)

3) $\triangle XYZ$ and $\triangle UVW$ are right triangles (a triangle with a right angle is a right triangle)

4) $\triangle XYZ \cong \triangle UVW$ (LA)

5) $\overline{UW} \cong \overline{XZ}$ (CPCTC)

Question 6

1) $\overline{PQ} \perp \overline{QT}$, $\overline{ST} \perp \overline{QT}$, $\overline{PQ} \perp \overline{ST}$ (given)

2) $\angle PQR$ and $\angle RTS$ are right angles (perpendicular lines form right angles)

3) $\triangle PQR$ and $\triangle STR$ are right triangles (a triangle with a right angle is a right triangle)

4) $\angle PRQ \cong \angle SRT$ (vertical angles are congruent)

5) $\triangle PQR \cong \triangle STR$ (LA)

6) $\overline{QR} \cong \overline{TR}$ (CPCTC)