Question

Use The Alternate Interior Angles Theorem diagram to answer the question. Give the missing reason in this proof for the letter given



FILL IN THE BLANK:
a. (1 point)
b. (1 point)
c. (1 point)

Answer 1

The missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:

a. Corresponding angles

b. Vertical Angles, and

c. Alternate interior angles

• Two angles lying opposite each other along a transversal, and are within the two lines crossed by the transversal are referred to as alternate interior angles.

• According to the Alternate Interior Angles Theorem, the two alternate interior angles are congruent to each other.

• Let's state out our proof using the image given:

Statement 1: line l is parallel to line m

Reason: Given

Statement 2: $\angle 2 \cong \angle 6$

Reason: Corresponding Angles (both angles occupy the same corner, hence they correspond to each other. Corresponding angles have the same measure).

Statement 3: $\angle 4 \cong \angle 2$

Reason: Vertical angles (both angles are directly opposite each other as they share the same point, which makes them vertical angles. Vertical angles have equal measure).

Statement 4: $\angle 6\cong \angle 4$

Reason: Alternate Interior Angles (applying the transitive property which says if a = b, and b = c, then a = c, therefore, since $\angle 2 \cong \angle 6, and \angle 4 \cong \angle 2, then \angle 6 \cong \angle 4$)

In conclusion, the missing reasons in the proof using the Alternate Interior Angles Theorem diagram that is given are:

a. Corresponding angles

b. Vertical Angles, and

c. Alternate interior angles

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