Question

Complete this proof.

Given: EC AC, DB AC, ∠A = ∠F
Prove: ΔMDF ∼ ΔNCA

Answer 1

Statement:

1. line EC is perpendicular to line AC, line is perpendicular to DB line AC, ∠A = ∠F

2. ∠F = ∠A

3. ∠1 =∠2

4. ΔMDF ∼ ΔNCA

Reason:

1. Given

2. Given

3. Alternate interior angles are equal

4. AA

Answer 2

Proved

Explanation:

Given: EC || AC, DB || AC, ∠A = ∠F

Prove: ΔMDF ∼ ΔNCA

Solution

See diagram attached to the solution to better understand the following workings.

Redrawing ΔMDF or rotating to be facing the same direction.

EC is parallel to AC

DB parallel to AC

Using similar triangle theorem:

If ΔMDF ∼ ΔNCA

Ratio of Corresponding sides would be equal

(adjacent of ΔMDF)/(adjacent of ΔNCA) = (Opposite of ΔMDF)/(opposite of ΔNCA) = (hypotenuse of ΔMDF)/(hypotenuse of ΔNCA)

DF/ CA = MD/NC = FM/AN

∠A = ∠F

∠M = ∠N

∠D = ∠C

Since the ratio of Corresponding sides and angle are equal, ΔMDF is similar to ΔNCA.

ΔMDF ∼ ΔNCA