Question

directions: classify each triangle by its angles and sides.

Explanation:

Step1: Recall triangle - classification rules

Classify by angles (acute: all angles < 90°, right: one angle = 90°, obtuse: one angle > 90°) and by sides (equilateral: all sides equal, isosceles: two sides equal, scalene: no sides equal).

Step2: Analyze triangle 1

Has two equal sides and all angles are acute. So it is an acute - isosceles triangle.

Step3: Analyze triangle 2

Has a right - angle and two unequal sides other than the hypotenuse. So it is a right - scalene triangle.

Step4: Analyze triangle 3

Has an obtuse angle and no equal sides. So it is an obtuse - scalene triangle.

Step5: Analyze triangle 4

Has three equal sides and all angles are acute. So it is an acute - equilateral triangle.

Step6: Analyze triangle 5

Has a right - angle and two equal sides. So it is a right - isosceles triangle.

Step7: Analyze triangle 6

All angles are acute and no equal sides. So it is an acute - scalene triangle.

Step8: Analyze triangle 7

Has an obtuse angle and two equal sides. So it is an obtuse - isosceles triangle.

Step9: Analyze triangle 8

Has an obtuse angle and two equal sides. So it is an obtuse - isosceles triangle.

Answer:

1. Acute - isosceles triangle
2. Right - scalene triangle
3. Obtuse - scalene triangle
4. Acute - equilateral triangle
5. Right - isosceles triangle
6. Acute - scalene triangle
7. Obtuse - isosceles triangle
8. Obtuse - isosceles triangle