Question

The line is drawn through a point upper D, triangle vertex upper B, and a point upper E, and is parallel to triangle segment upper A upper C. The angle at upper B upper A upper C and the angle at upper D upper B upper A are both marked with a single arc. The angle at upper E upper B upper C and the angle at upper A upper C upper B both are marked with double arcs.
mage Long DescriptionThe line is drawn through a point upper D, triangle vertex upper B, and a point upper E, and is parallel to triangle segment upper A upper C. The angle at upper B upper A upper C and the angle at upper D upper B upper A are both marked with a single arc. The angle at upper E upper B upper C and the angle at upper A upper C upper B both are marked with double arcs.

What could be proved using the diagram?

(1 point)
Responses

Two lines are parallel if they have the same slope.
Two lines are parallel if they have the same slope.

The measure of an exterior angle equals the sum of the two remote interior angles.
The measure of an exterior angle equals the sum of the two remote interior angles.

the Pythagorean Theorem
the Pythagorean Theorem

the Triangle Angle Sum Theorem
the Triangle Angle Sum Theorem
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Answer 1

the Triangle Angle Sum Theorem

Reason: The line through B parallel to AC makes the two base angles equal to the alternate interior angles at B; those two plus angle ABC form a straight line (180°), so the three interior angles of triangle ABC sum to 180°.