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Jamar draws three pairs of parallel lines that are each intersected by a third line. In each figure, he measures a pair of angles.


What is a reasonable conjecture for Jamar to make by recognizing a pattern and using inductive reasoning?


When a pair of parallel lines are intersected by a third line, the same-side interior angles are acute.


When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.


When a pair of parallel lines are intersected by a third line, all of the angles formed are supplementary.


When a pair of parallel lines are intersected by a third line, all of the angles formed are acute.

Verified Answer :

dxdph4pi

1 is not true generally, while 3 and 4 are never true. 2 is the only generally true conjecture.

fichoh

A reasonable conjecture which can be made using inductive reasoning about the scenario is that ; when a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary

  • The same side interior angles refers to the two angles on formed when a traversal cuts through two parallel lines.

  • The two angles sum to 180 (sum of angles on a straight line), hence forming a supplementary angle and not an acute angle.

  • Only the same-side interior angle forms a supplementary angle and not each angle formed.

Therefore, only the same side interior angle sums up to 180, hence, forming a complementary angle.

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