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

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

A. When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.

B. When a pair of parallel lines are intersected by a third line, the alternate interior angles are acute.

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

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

Consider the picture, and check the choices:

A. The alternate interior angles, are also called Z angles, because of the Z shape they create.

examples of Z angles, are the green angles and purple angles shown in the picture.

They really look identical (congruent)

B.

No: check the green angles in figure 1, and purple angles if figure 2. they are not acute.

C.

No. In each case, we have the same number of acute angles and obtuse angles,

except case3, where the intersecting line, is perpendicular to the parallel lines.

D.
No, by the same reasoning used in part C. Only when the intersecting line cuts the 2 parallel lines perpendicularly, all the angles are congruent.

Answer: A

divyamadaan8054 divyamadaan8054 · Answer 2 · 2021-10-19T21:00:47+02:00

Answer:

When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.

Step-by-step explanation:

Given: Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of angles.

Let us draw a pair of parallel lines [tex]l \parallel m[/tex] which is intersected by line [tex]p[/tex].

From the figure,

[tex]\angle 4=\angle 5[/tex] and [tex]\angle 3=\angle 6[/tex] (Alternate interior angles are equal as [tex]l \parallel m[/tex] )

Therefore, When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.

Hence, the correct option is [tex]A[/tex].

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