Question1. Given: parallelogram FLSH, diagonal FGAS, $\overline{L G} \perp \overline{F S}, \overline{H A} \perp \overline{F S}$ Prove: $$\triangle L G S \equiv \triangle H A F$$

Studdy Solution
Apply the criteria for triangle congruence:
- By the Hypotenuse-Leg (HL) theorem for right triangles: - Hypotenuses $\overline{LS}$ and $\overline{HF}$ are equal because they are opposite sides of parallelogram FLSH. - Legs $\overline{LG}$ and $\overline{HA}$ are perpendicular to the same line $\overline{FS}$.
Thus, $\triangle LGS \equiv \triangle HAF$ by the HL theorem.
The triangles $\triangle LGS$ and $\triangle HAF$ are congruent.