Question

1. 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, all of the angles formed are supplementary.

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 acute.

2. Timothy draws three isosceles triangles. In each figure, he measures a pair of angles.

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

In an isosceles triangle, two of the angles are obtuse.

In an isosceles triangle, one angle is always obtuse.

In an isosceles triangle, all of the angles are congruent.

In an isosceles triangle, two of the angles are congruent.

Answer 1

The correct answers are:

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

#2) In an isosceles triangle, two of the angles are congruent.

Step-by-step explanation:

#1) When a pair of parallel lines is intersected by a third line (called a transversal), certain angles are congruent and certain angles are supplementary.

Some of the angles will be acute and some will be obtuse.

However, one thing that is always true is that same-side interior angles are supplementary.

#2) An isosceles triangle is defined as a triangle in which two sides are congruent. The angles formed by each of those two sides and the third side will be congruent as well, due to them being the same length.

Answer 2

It would be easier if you provided illustration to your problems. Anyway, I think, I can solve theese tasks without pictures, as I've seen it before. Here are my answers, check it out:
1. When a pair of parallel lines are intersected by a third line, the same-side interior angles are supplementary.
2. In an isosceles triangle, two of the angles are congruent.

Hope it's helpful for you