Question

practice b: (first taught in lesson 48) read the true statement below and then tell whether its converse, inverse, and contrapositive are also true. if a triangle is equiangular, then one angle has a measure of 60. converse inverse contrapositive if a triangle has one angle with a measure of 60, then it is equiangular. true false

Explanation:

Step1: Analyze the converse

A triangle having one 60 - degree angle doesn't mean it's equiangular. For example, a triangle with angles 60°, 30°, 90° has one 60° angle but isn't equiangular.

Step2: Analyze the inverse

The inverse of “If a triangle is equiangular, then one angle has a measure of 60” is “If a triangle is not equiangular, then no angle has a measure of 60”. But a non - equiangular triangle can have a 60° angle (e.g., 60°, 70°, 50°).

Step3: Analyze the contrapositive

The contrapositive of “If \(p\) (triangle is equiangular) then \(q\) (one angle is 60°)” is “If not \(q\) (no angle is 60°) then not \(p\) (triangle is not equiangular)”. In an equiangular triangle, all angles are 60°, so if no angle is 60°, it can't be equiangular.

Answer:

Converse: False; Inverse: False; Contrapositive: True