Question

are the triangles below acute, obtuse, or right?
triangle a
triangle b
triangle c
triangle d
acute
acute
acute
acute
obtuse
obtuse
obtuse
obtuse
right
right
right
right

Explanation:

Step1: Recall triangle - type definitions

An acute triangle has all angles less than \(90^{\circ}\). A right triangle has one angle equal to \(90^{\circ}\). An obtuse triangle has one angle greater than \(90^{\circ}\).

Step2: Analyze Triangle A

All angles of Triangle A are \(60^{\circ}\). Since \(60^{\circ}<90^{\circ}\), by the definition of an acute triangle (all angles \(< 90^{\circ}\)), Triangle A is acute.

Step3: Analyze Triangle B

Triangle B has a \(90^{\circ}\) angle (right - angle symbol). By the definition of a right triangle (one angle \( = 90^{\circ}\)), Triangle B is right.

Step4: Analyze Triangle C

Triangle C has a \(90^{\circ}\) angle (right - angle symbol). By the definition of a right triangle (one angle \(=90^{\circ}\)), Triangle C is right.

Step5: Analyze Triangle D

Triangle D has an angle of \(120^{\circ}\). Since \(120^{\circ}>90^{\circ}\), by the definition of an obtuse triangle (one angle \(>90^{\circ}\)), Triangle D is obtuse.

Answer:

Triangle A: Acute; Triangle B: Right; Triangle C: Right; Triangle D: Obtuse