Question

a triangle is a polygon. the sum of the angles in a triangle is 180°. to see this, draw a diagonal through a square. the square is divided into two equal triangles. notice that the diagonal divides two of the right angles in half. the sum of the three angles in either of the triangles is 45° + 45° + 90° = 180°. equal sides are opposite equal angles. in the triangle abc, ∠a and ∠c are equal. both measure 45°. the sides across from them, ab and bc, are also equal. the longest side is opposite the largest angle. in triangle abc, ∠b is the largest angle. the side across from it, side ac, is the longest side. the names of the triangles come from the relationships among the angles and the sides. name: equilateral, properties: three equal sides, three equal angles, examples: 2 cm, 2 cm, 2 cm, 60°, 60°, 60°. name: isosceles, properties: two equal sides, two equal angles, examples: 2 cm, 2 cm, 70°, 70°. name: right, properties: one right angle, examples: right - angled triangle. name: scalene, properties: no equal sides, no equal angles, examples: 2.1 cm, 2 cm, 1 cm, 25°, 65°, 100°. identify each triangle. 1. 65° (isosceles triangle) 2. 3 cm, 3 cm, 3 cm (equilateral triangle) 3. 78°, 78° (isosceles triangle) 4. 1.5 cm, 2 cm, 2.4 cm (scalene triangle) 110 unit 4

Explanation:

Step1: Recall triangle - type rules

Use the properties of side - lengths and angles to classify triangles.

Step2: Analyze triangle 1

It has one right - angle and two non - equal acute angles. Since it has one right - angle, it is a right triangle. Also, since the non - right angles are different, the sides opposite them are different, so it is not isosceles.

Step3: Analyze triangle 2

All side - lengths are 3 cm. A triangle with three equal sides is an equilateral triangle.

Step4: Analyze triangle 3

Two angles are 78°. Equal angles are opposite equal sides, so it has two equal sides. Thus, it is an isosceles triangle.

Step5: Analyze triangle 4

All side - lengths are different (1.5 cm, 2 cm, 2.4 cm) and all angles are different. A triangle with no equal sides and no equal angles is a scalene triangle.

Answer:

1. Right triangle
2. Equilateral triangle
3. Isosceles triangle
4. Scalene triangle