Question

Given: AC and BD are perpendicular, G is the midpoint of FE and BD, BA is congruent to DC

Prove: AGF congruent to CGE

(Please help me proof and find out the properties it’s using as well this is due in 2 hours)

Answer 1

The proof utilizes the Midpoint Theorem and the Side-Angle-Side (SAS) congruence property to establish the congruence of the triangles.

To prove that triangles (AGF) and (CGE) are congruent, we can use the following approach:

Given: (AC) and (BD) are perpendicular, (G) is the midpoint of (FE) and (BD), (BA) is congruent to (DC)

To prove: (AGF) is congruent to (CGE)

Proof:

Since (G) is the midpoint of (BD), it follows that (BG) is congruent to (GD).

Given that (AC) and (BD) are perpendicular, and (G) is the midpoint of (BD), we can conclude that (AG) is congruent to (GC) (Midpoint Theorem).

Additionally, (BA) is congruent to (DC) (Given).

Therefore, by the Side-Angle-Side (SAS) congruence property, triangles (AGF) and (CGE) are congruent.