Question

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 congruent.

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

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

In an isosceles triangle, one angle is always obtuse.

Answer 1

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

Explanation:

An isosceles triangle is a triangle with two equal sides.

We know that there is a theorem that tells that angles opposite to the congruent side of triangles are congruent.

Thus, we know that isosceles triangle has two angles congruent.

We know that the inductive reasoning is a specific reasoning which conclude a general conclusion.

Thus, a reasonable conjecture for Timothy to make by recognizing a pattern and using inductive reasoning is "In an isosceles triangle, two of the angles are congruent."

Answer 2

If Timothy is using inductive reasoning then he has to make a conclusion by observing some patterns in the activity that he is performing.

The conclusion that Timothy makes as a result of recognizing a pattern is called a
`<b>conjecture.</b>`



All isosceles triangles have two of their angles equal. This is an established fact about isosceles triangles. Therefore a reasonable conjecture that Timothy will make if he measures the angles correctly is

'In an isosceles triangle, two of the angles are equal.'


Hence the correct answer is the first option.