What is the missing step in the proof? a, statement: ∠gac and ∠gab are supplementary. reason: linear pair theoremb, statement: ∠afe ≅ ∠afd reason: transitive property of equalityc, statement: ∠gac ≅ ∠baf reason: vertical angles theoremd, statement: ∠gac and ∠afd are supplementary. reason: linear pair theorem

The answer is B. Statement:∠AFE ≅ ∠AFD  Reason: Transitive Property of Equality

Step-by-step explanation:

∠AFE ≅ ∠AFD equal each other, and Transitive Property of Equality  is the correct reason.

This answer is correct as a Edmentum student!

Option B is correct.

Statement: ∠AFE ≅ ∠AFD

Reason: Transitive Property of Equality

Explanation:

Given that:

and

Prove that :

Proof:  

Given:

         ....[1]

By theorem of corresponding angles:

For parallel lines cut by transversal , the corresponding angles are congruent.

then;

          ....[2]

Transitive property of equality states that if x = y and y = z then; x = z

Using transitive property of equality in [1] and [2] we have;

By Linear pair theorem states that if the two pairs are adjacent to each other then they are supplementary.

⇒ and are supplementary.

We know that:

If two congruent angles are supplementary, then each angle is of right angle i.,e 90 degree

⇒

By definition of perpendicular line:

If two line meet at a right angle i.,e 90 degree, then those lines are perpendicular.

⇒ Hence proved!

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

b

step-by-step explanation: