Question

problem 22: (first taught in lesson 29) select the converse of this statement, and determine whether it is true or false. if a triangle is a right triangle, then it has two acute angles. a b c d e if a triangle has one acute angle, then it is a right triangle; false

Explanation:

Step1: Recall converse definition

The converse of "if p then q" is "if q then p". Here, p is "a triangle is a right triangle" and q is "it has two acute angles".

Step2: Form the converse

The converse is "If a triangle has two acute angles, then it is a right - triangle".

Step3: Determine truth - value

A triangle with two acute angles could be an acute triangle (all angles less than 90°) or an obtuse triangle (one angle greater than 90°), not necessarily a right - triangle. So it is false.

Answer:

If a triangle has two acute angles, then it is a right - triangle; false