Question

Please help, it is due in like 5 minutes, i dont get it, its proving btw

Answer 1

Proof that AD || CB:

Given: AB 1 BD, BD 1 DC, LA = ∠C

Prove: AD || CB

Proof:

Since AB 1 BD, ∠ABD = 180° - ∠AB = ∠DAB (alternate interior angles) (Image 1)

Similarly, since BD 1 DC, ∠BDC = 180° - ∠BD = ∠CDB (alternate interior angles) (Image 1)

Since LA = ∠C, ∠DAB + ∠BDC = 180° (same side interior angles) (Image 1)

Substituting equations 1 and 2 into equation 3, we get:

(∠ABD + ∠BDC) = 180°

(180° - ∠AB) + (180° - ∠BD) = 180°

360° - ∠AB - ∠BD = 180°

∠AB + ∠BD = 360° - 180°

∠AB + ∠BD = 180°

Since ∠AB + ∠BD = 180°, AD || CB (supplementary angles) (Image 1)

Therefore, AD || CB.