Question

matching triangles in exercises 10 - 15, match the triangle description with the most specific name.

1. side lengths: 2 cm, 3 cm, 4 cm a. equilateral
2. side lengths: 3 cm, 2 cm, 3 cm b. scalene
3. side lengths: 4 cm, 4 cm, 4 cm c. obtuse
4. angle measures: 60°, 60°, 60° d. equiangular
5. angle measures: 30°, 60°, 90° e. isosceles
6. angle measures: 20°, 145°, 15° f. right

Explanation:

Step1: Analyze triangle by side lengths

• A scalene triangle has all sides of different lengths. For side lengths \(2\) cm, \(3\) cm, \(4\) cm (Exercise 10), all sides are different. So it matches B.
• An isosceles triangle has at least two sides equal. For side lengths \(3\) cm, \(2\) cm, \(3\) cm (Exercise 11), two sides (\(3\) cm) are equal. So it matches E.
• An equilateral triangle has all three sides equal. For side lengths \(4\) cm, \(4\) cm, \(4\) cm (Exercise 12), all sides are equal. So it matches A.

Step2: Analyze triangle by angle measures

• An equiangular triangle has all angles equal. For angle measures \(60^{\circ},60^{\circ},60^{\circ}\) (Exercise 13), all angles are equal. So it matches D.
• A right - triangle has one angle equal to \(90^{\circ}\). For angle measures \(30^{\circ},60^{\circ},90^{\circ}\) (Exercise 14), one angle is \(90^{\circ}\). So it matches F.
• An obtuse triangle has one angle greater than \(90^{\circ}\). For angle measures \(20^{\circ},145^{\circ},15^{\circ}\) (Exercise 15), \(145^{\circ}>90^{\circ}\). So it matches C.

Answer:

1. B. Scalene
2. E. Isosceles
3. A. Equilateral
4. D. Equiangular
5. F. Right
6. C. Obtuse