Question

Given: AD and EH , transversal BF ∠ACG and _______ are same side interior angles

Answer 1

Answer:

Step-by-step explanation:By definition, two angles are supplementary if the sum of them is 180 degrees. In this case (see figure attached with the answer) the line AD is transversal to lines AB and DC. This is a proof of the Same-side interior angle theorem.

This theorem states that if we have two lines that are parallel and we intercept those two lines with a line that is transversal to both, same-side interior angles are formed, and also sum 180º, in other words, they are supplementary angles.

Then:

By the definition of a parallelogram, AB∥DC. AD is a transversal between these sides, so ∠A and ∠D are same-side interior angles. Because AB and DC are parallel, the same-side interior angles must be supplementary by the same-side interior angles theorem. Therefore, ∠A and ∠D are supplementary.

Answer 2

∠ACG same side interior angles with ∠CGH and ∠CGE

Further explanation

When parallel lines get crossed by a transversal some angles will be formed (which has the same magnitude = equal)):

Corresponding Angles: The angles on the same corners

Alternate Interior Angles: Alternate sides of the Transversal, and on the Interior of the two crossed lines.

Alternate Exterior Angles: on the outer side of each of the two lines and on the opposite side of the transversal.

Consecutive Interior Angles: on one side of the transversal but inside the two lines. The Consecutive Interior Angles add up to 180 ° if the two lines are crossed are Parallel

From the attached image it can be seen:

Alternate Interior Angles: angles ∠ACG & ∠CGH and ∠DCG & ∠CGE

Consecutive Interior Angles: angles ∠ACG & ∠CGE and ∠DCG & ∠CGH

Then ∠ACG same side interior angles with ∠CGH (Alternate Interior Angles) and ∠CGE (Consecutive Interior Angles)

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