Question

classify the triangle two ways (remember first name, last name)
6.
7.
8.
9.
10.
11.

Explanation:

Let's solve each triangle classification one by one. We'll classify them by angles (acute, right, obtuse) and by sides (equilateral, isosceles, scalene).

Problem 6

• Angles: One angle is \(90^\circ\) (right angle), so it's a right triangle.
• Sides: Two angles are \(45^\circ\), so the sides opposite them are equal (isosceles triangle property). Thus, it's an isosceles triangle.
• Classification: Right, Isosceles

Problem 7

• Angles: All angles are \(60^\circ\) (acute, since \(60^\circ < 90^\circ\)), so it's an acute triangle.
• Sides: All angles are equal, so all sides are equal (equilateral triangle property). Thus, it's an equilateral triangle (which is also isosceles, but equilateral is more specific).
• Classification: Acute, Equilateral

Problem 8

• Angles: One angle is \(100^\circ\) (obtuse, since \(100^\circ > 90^\circ\)), so it's an obtuse triangle.
• Sides: Two angles are \(40^\circ\), so the sides opposite them are equal. Thus, it's an isosceles triangle.
• Classification: Obtuse, Isosceles

Problem 9

• Angles: One angle is \(90^\circ\) (right angle), so it's a right triangle.
• Sides: Angles are \(30^\circ\), \(60^\circ\), \(90^\circ\) (all different), so all sides are different (scalene triangle property). Thus, it's a scalene triangle.
• Classification: Right, Scalene

Problem 10

• Angles: All angles (\(39^\circ\), \(64^\circ\), \(77^\circ\)) are acute (\(< 90^\circ\)), so it's an acute triangle.
• Sides: All angles are different, so all sides are different (scalene triangle property). Thus, it's a scalene triangle.
• Classification: Acute, Scalene

Problem 11

• Angles: Let's check the third angle: \(180^\circ - 35^\circ - 25^\circ = 120^\circ\) (obtuse, since \(120^\circ > 90^\circ\)), so it's an obtuse triangle.
• Sides: All angles are different, so all sides are different (scalene triangle property). Thus, it's a scalene triangle.
• Classification: Obtuse, Scalene

Final Answers

1. Right, Isosceles
2. Acute, Equilateral
3. Obtuse, Isosceles
4. Right, Scalene
5. Acute, Scalene
6. Obtuse, Scalene

Answer:

Let's solve each triangle classification one by one. We'll classify them by angles (acute, right, obtuse) and by sides (equilateral, isosceles, scalene).

Problem 6

• Angles: One angle is \(90^\circ\) (right angle), so it's a right triangle.
• Sides: Two angles are \(45^\circ\), so the sides opposite them are equal (isosceles triangle property). Thus, it's an isosceles triangle.
• Classification: Right, Isosceles

Problem 7

• Angles: All angles are \(60^\circ\) (acute, since \(60^\circ < 90^\circ\)), so it's an acute triangle.
• Sides: All angles are equal, so all sides are equal (equilateral triangle property). Thus, it's an equilateral triangle (which is also isosceles, but equilateral is more specific).
• Classification: Acute, Equilateral

Problem 8

• Angles: One angle is \(100^\circ\) (obtuse, since \(100^\circ > 90^\circ\)), so it's an obtuse triangle.
• Sides: Two angles are \(40^\circ\), so the sides opposite them are equal. Thus, it's an isosceles triangle.
• Classification: Obtuse, Isosceles

Problem 9

• Angles: One angle is \(90^\circ\) (right angle), so it's a right triangle.
• Sides: Angles are \(30^\circ\), \(60^\circ\), \(90^\circ\) (all different), so all sides are different (scalene triangle property). Thus, it's a scalene triangle.
• Classification: Right, Scalene

Problem 10

• Angles: All angles (\(39^\circ\), \(64^\circ\), \(77^\circ\)) are acute (\(< 90^\circ\)), so it's an acute triangle.
• Sides: All angles are different, so all sides are different (scalene triangle property). Thus, it's a scalene triangle.
• Classification: Acute, Scalene

Problem 11

• Angles: Let's check the third angle: \(180^\circ - 35^\circ - 25^\circ = 120^\circ\) (obtuse, since \(120^\circ > 90^\circ\)), so it's an obtuse triangle.
• Sides: All angles are different, so all sides are different (scalene triangle property). Thus, it's a scalene triangle.
• Classification: Obtuse, Scalene

Final Answers

1. Right, Isosceles
2. Acute, Equilateral
3. Obtuse, Isosceles
4. Right, Scalene
5. Acute, Scalene
6. Obtuse, Scalene