Chapter 12.1, Problem 46E

To determine

To find: the classification of each triangle by its appearance.

Answer to Problem 46E

The option a is equilateral acute, b is isosceles acute, c is obtuse scalene and d is a right isosceles.

Explanation of Solution

Given:

  

Concept used:

Equilateral triangle has same side and angle.

Isosceles triangle has two same side.

Right triangle has one angle ${90}^0$ .

Acute triangle has all angle less than ${90}^0$ .

Obtuse angle is one angle of the triangle is more than ${90}^0$ and other two is acute angle.

Scalene triangle is triangle having different sides.

Calculation:

According to the given option:

1. Equilateral acute: equal sides and angles are under ${90}^0$ .
2. Isosceles acute: there is $2$ equal sides and all side are under ${90}^0$ .
3. Obtuse scalene: all side are different and one angle is greater than ${90}^0$ .
4. Right isosceles: there is $2$ equal sides and there is a right angle.

Hence, a is equilateral acute, b is isosceles acute, c is obtuse scalene and d is a right isosceles.