Learn on PengiBig Ideas Math, Course 2Chapter 7: Constructions and Scale Drawings

Lesson 3: Triangles

In this Grade 7 lesson from Big Ideas Math, Course 2 (Chapter 7), students learn to classify triangles by angle type (acute, obtuse, right, and equiangular) and by side length (scalene, isosceles, and equilateral), then apply those classifications while constructing triangles using a protractor and ruler with given angle measures or side lengths. Students practice identifying congruent sides and angles and explore whether specific combinations of side lengths can form a valid triangle.

Section 1

Classifying Triangles by Angle Measures

Property

Triangles can be classified by the specific sizes of their interior angles into three categories:

  • Right Triangle: Contains exactly one right angle (90°).
  • Obtuse Triangle: Contains exactly one obtuse angle (greater than 90°).

Section 2

Classifying Triangles by Side Lengths

Property

Triangles can be classified by the lengths of their sides:

  • All three sides of an equilateral triangle are equal in length.
  • In an isosceles triangle, two sides are equal in length.
  • In a scalene triangle, all three sides have different lengths.

Examples

  • A triangle with side lengths of 7 cm, 7 cm, and 7 cm is an equilateral triangle.
  • A triangle with side lengths of 5 inches, 5 inches, and 8 inches is an isosceles triangle.
  • A triangle with side lengths of 4 m, 6 m, and 9 m is a scalene triangle.

Explanation

A triangle's name can also come from its side lengths. 'Equilateral' means all sides are equal. 'Isosceles' means two sides are equal. 'Scalene' means no sides are equal—they all have different lengths.

Lesson overview

Expand to review the lesson summary and core properties.

Expand

Section 1

Classifying Triangles by Angle Measures

Property

Triangles can be classified by the specific sizes of their interior angles into three categories:

  • Right Triangle: Contains exactly one right angle (90°).
  • Obtuse Triangle: Contains exactly one obtuse angle (greater than 90°).

Section 2

Classifying Triangles by Side Lengths

Property

Triangles can be classified by the lengths of their sides:

  • All three sides of an equilateral triangle are equal in length.
  • In an isosceles triangle, two sides are equal in length.
  • In a scalene triangle, all three sides have different lengths.

Examples

  • A triangle with side lengths of 7 cm, 7 cm, and 7 cm is an equilateral triangle.
  • A triangle with side lengths of 5 inches, 5 inches, and 8 inches is an isosceles triangle.
  • A triangle with side lengths of 4 m, 6 m, and 9 m is a scalene triangle.

Explanation

A triangle's name can also come from its side lengths. 'Equilateral' means all sides are equal. 'Isosceles' means two sides are equal. 'Scalene' means no sides are equal—they all have different lengths.