Question

problem 14: (first taught in lesson 48) read the true statement below and then tell whether the converse, inverse, and contrapositive are also true. if two angles are the acute angles of a right triangle, then they are complementary. converse inverse contrapositive if two angles are complementary, then they are the acute angles of a right triangle. true false go

Explanation:

Step1: Analyze the converse

The converse is “If two angles are complementary, then they are the acute angles of a right triangle.” But two complementary angles could just be two separate angles not in a triangle at all. So the converse is false.

Step2: Analyze the inverse

The inverse is “If two angles are not the acute angles of a right triangle, then they are not complementary.” There are non - triangle - related pairs of complementary angles. So the inverse is false.

Step3: Analyze the contrapositive

The contrapositive is “If two angles are not complementary, then they are not the acute angles of a right triangle.” In a right triangle, the sum of the two acute angles is \(90^{\circ}\) (complementary). So if two angles are not complementary, they can't be the acute angles of a right triangle. The contrapositive is true.

Answer:

Converse: False, Inverse: False, Contrapositive: True