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 both right angles, then
they are congruent.
converse inverse contrapositive
if two angles are congruent, then they
are both right angles.
true false

Explanation:

Step1: Define converse, inverse, contrapositive

Let the original statement be “If \(p\) (two angles are both right angles), then \(q\) (they are congruent)”.

• Converse: “If \(q\), then \(p\)”
• Inverse: “If not \(p\), then not \(q\)”
• Contrapositive: “If not \(q\), then not \(p\)”

Step2: Analyze converse

Converse: “If two angles are congruent, then they are both right angles”. Congruent angles can be of any measure (e.g., \(30^{\circ}\) and \(30^{\circ}\)), not just \(90^{\circ}\). So converse is false.

Step3: Analyze inverse

Inverse: “If two angles are not both right angles, then they are not congruent”. Non - right angles can be congruent (e.g., two \(60^{\circ}\) angles). So inverse is false.

Step4: Analyze contrapositive

Contrapositive: “If two angles are not congruent, then they are not both right angles”. Since right angles are congruent (\(90^{\circ}=90^{\circ}\)), if angles are not congruent, they can't both be right angles. So contrapositive is true.

Answer:

Converse: False; Inverse: False; Contrapositive: True