NCERT Class 7 Maths Chapter 7
A Tale of Three Intersecting Lines
This chapter from Ganita Prakash Part 1 explores the properties of triangles for CBSE Class 7 students, focusing on angle sum property, exterior angles, and relationships between sides. Students investigate what happens when three lines intersect to form a triangle, discover the triangle angle sum property (sum of angles = 180°), and explore different types of triangles based on sides and angles.
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Key Terms
- Triangle
- A polygon with three sides, three vertices, and three interior angles. The sum of all interior angles of a triangle is always 180°.
- Angle Sum Property
- The property of triangles stating that the sum of the three interior angles of any triangle is always equal to 180°.
- Exterior Angle
- An angle formed outside a triangle when one side is extended. The exterior angle of a triangle equals the sum of the two non-adjacent interior angles (remote interior angles).
- Equilateral Triangle
- A triangle in which all three sides are equal in length and all three angles are equal to 60°.
- Isosceles Triangle
- A triangle with two equal sides. The angles opposite the equal sides (base angles) are also equal.
- Scalene Triangle
- A triangle in which all three sides are of different lengths and all three angles are different.
Frequently Asked Questions
What is the angle sum property of a triangle?▾
The angle sum property states that the sum of all three interior angles of a triangle is always 180°. For example, if two angles of a triangle are 60° and 80°, the third angle must be 180° – 60° – 80° = 40°.
What are the different types of triangles based on angles?▾
Triangles based on angles: Acute triangle (all angles less than 90°), Right triangle (one angle exactly 90°), and Obtuse triangle (one angle greater than 90°).
What are the different types of triangles based on sides?▾
Triangles based on sides: Equilateral triangle (all three sides equal, all angles 60°), Isosceles triangle (two sides equal, base angles equal), and Scalene triangle (all three sides different, all angles different).
What is the exterior angle property of a triangle?▾
An exterior angle of a triangle is equal to the sum of the two interior opposite angles (remote interior angles). For example, if the two remote interior angles are 50° and 70°, the exterior angle is 50° + 70° = 120°.
Can a triangle have two obtuse angles?▾
No, a triangle cannot have two obtuse angles. Since each obtuse angle is greater than 90°, two obtuse angles would already sum to more than 180°, which violates the angle sum property of triangles (all three angles must add up to exactly 180°).
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