Question

1. classify the triangles based on their side lengths and angle measures.

Explanation:

Step1: Classify the first triangle

• By side lengths: Since all sides are of different lengths (marked with different number of ticks), it is a scalene triangle.
• By angle measures: All angles are less than \(90^{\circ}\) (\(30^{\circ}\), \(89^{\circ}\), and the third angle \(180-(30 + 89)=61^{\circ}\)), so it is an acute triangle.

Step2: Classify the second triangle

• By side lengths: All sides are of different lengths (marked with different number of ticks), it is a scalene triangle.
• By angle measures: One angle is \(90^{\circ}\) (right - angle), so it is a right - triangle.

Step3: Classify the third triangle

• By side lengths: All sides are of different lengths (marked with different number of ticks), it is a scalene triangle.
• By angle measures: One angle is \(130^{\circ}>90^{\circ}\), so it is an obtuse triangle.

Step4: Classify the fourth triangle

• By side lengths: All sides are equal (marked with the same number of ticks), it is an equilateral triangle.
• By angle measures: In an equilateral triangle, all angles are \(60^{\circ}\) (since \(180\div3 = 60\)), so it is an acute triangle.

Answer:

Scalene acute triangle, Scalene right - triangle, Scalene obtuse triangle, Equilateral acute triangle.