Question

classify each triangle by its angles and sides. classify the triangle by its angle first, then by its sides.
a. triangle abe:
b. triangle bec:
c. triangle def:
d. triangle cdf:

Explanation:

Step1: Classify triangle ABE

• Angle: Since \(\angle A = 90^{\circ}\), it is a right triangle.
• Sides: No information about side - equality (except the right - angle side), so it is a scalene triangle.

Step2: Classify triangle BEC

• Angle: All angles are less than \(90^{\circ}\), so it is an acute triangle.
• Sides: No information about side - equality, so it is a scalene triangle.

Step3: Classify triangle DEF

• Angle: All angles are less than \(90^{\circ}\), so it is an acute triangle.
• Sides: Two sides are marked as equal, so it is an isosceles triangle.

Step4: Classify triangle CDF

• Angle: All angles are less than \(90^{\circ}\), so it is an acute triangle.
• Sides: No information about side - equality, so it is a scalene triangle.

Answer:

a. Right - scalene
b. Acute - scalene
c. Acute - isosceles
d. Acute - scalene