Question

Ricardo draws three right triangles. in each figure, he measures a pair of angles. what is a reasonable conjecture for ricardo to make by recognizing a pattern and using inductive reasoning? in a right triangle, all of the angles are acute. in a right triangle, all of the angles are right angles. in a right triangle, the acute angles are complementary. in a right triangle, the acute angles are congruent.

Answer 1

In a right triangle, the acute angles are complementary.

Explanation:

Inductive reasoning is a method of reasoning in which the conclusion can be drawn from the premises.

A right-angled triangle is a triangle in which one angle is a right angle and other angles are acute.

In a right-angled triangle, the sum of all the angles is 180 degrees.

So, if one angle is 90 degrees, it means the sum of other angles is 90 degrees i.e., other angles are complementary.

( Angles whose sum is 90 degrees are said to be complementary )

Also, other angles are acute as each of the angles must be less than 90 degrees.

So, in a right triangle, the acute angles are complementary.

Answer 2

The reasonable conjecture for Ricardo to make by recognizing a pattern and using inductive reasoning is I think "In a right triangle, the acute angles are complementary."

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