Question

A triangle forms the front of the Pantheon in Rome, Italy. Classify the triangle based on its sides. Then classify it based on its angles.

Answer 1

(See explanation for further details)

Explanation:

Classification based on sides:

Equilateral - Three sides with same length.

Isosceles - Two sides with same length.

Scalene - No sides with same length.

Classification based on sides:

Acute-Angled - All angles are acute.
`(0^(\circ) < \theta < 90^(\circ), 0^(\circ) < \alpha < 90^(\circ), 0^(\circ) < \beta < 90^(\circ), \theta + \alpha + \beta = 180^(\circ))`

Right-Angled - One angle is right.
`(0^(\circ) < \theta < 90^(\circ);\alpha = 90^(\circ), 0^(\circ) < \beta < 90^(\circ), \theta + \alpha + \beta = 180^(\circ))`

Obtuse-Angled - One angle is obtuse.
`(0^(\circ) < \theta < 90^(\circ),90^(\circ)<\alpha < 180^(\circ), 0^(\circ) < \beta < 90^(\circ), \theta + \alpha + \beta = 180^(\circ))`