Kathryn draws three pairs of intersecting lines. In each figure, she measures a pair of angles. What is a reasonable conjecture
for Kathryn to make by recognizing a pattern and using inductive reasoning?
When a pair of lines intersect, the vertical angles are acute.
When a pair of lines intersect, the vertical angles are congruent.
When a pair of lines intersect, all of the angles formed are congruent.
When a pair of lines intersect, all of the angles formed are right angles.
When a pair of lines intersect, the vertical angles are acute.
When a pair of lines intersect, the vertical angles are congruent.
When a pair of lines intersect, all of the angles formed are congruent.
When a pair of lines intersect, all of the angles formed are right angles.
1 answer:
When two lines intersect, they will have a point of intersection where angles around this point will add up to 360°
Since the lines can intersect in many different ways, we cannot assume that the angles form will all be right angles (although this is possible, it doesn't always happen). The four angles can't also be all of the same sizes.
Refer to the diagram below, the intersection will definitely two pairs of vertical angles, x and y.
Answer: <span>When a pair of lines intersect, the vertical angles are congruent.
</span>
Since the lines can intersect in many different ways, we cannot assume that the angles form will all be right angles (although this is possible, it doesn't always happen). The four angles can't also be all of the same sizes.
Refer to the diagram below, the intersection will definitely two pairs of vertical angles, x and y.
Answer: <span>When a pair of lines intersect, the vertical angles are congruent.
</span>
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