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A Tale of Three Intersecting Lines – Class 7 Mathematics notes, important questions and MCQs

NCERT Class 7 Mathematics, chapter 7. Notes, key terms, important questions with answers and MCQs.

Chapter overview

Three line segments joining three points form a triangle. Its angles add to 180°, and its sides follow the triangle inequality.

Angles of a triangle

Angle sum property: ∠A + ∠B + ∠C = 180°.
Exterior angle = sum of the two opposite interior angles.
Types by angles: acute, right, obtuse; by sides: equilateral, isosceles, scalene.

Sides of a triangle

Triangle inequality: the sum of any two sides is greater than the third side.
In an isosceles triangle, angles opposite the equal sides are equal.
The longest side is opposite the largest angle.

Key terms

Exterior angle: angle formed by one side and the extension of an adjacent side
Scalene triangle: triangle with all sides different
Isosceles triangle: triangle with two equal sides

Formulas

∠A + ∠B + ∠C = 180°
Exterior angle = sum of interior opposite angles

Important questions with answers

Can a triangle have sides 3 cm, 4 cm and 8 cm? Why?2 marks

No. The sum of any two sides must be greater than the third, but 3 + 4 = 7 < 8.

Classify triangles by sides and by angles with one example each.3 marks

By sides: equilateral (all equal), isosceles (two equal), scalene (none equal). By angles: acute (all angles < 90°, e.g. 60°, 60°, 60°), right (one 90°, e.g. 90°, 45°, 45°), obtuse (one > 90°, e.g. 120°, 30°, 30°).

Prove that the sum of the angles of a triangle is 180°, and use it to find the angles of a triangle whose angles are in the ratio 2 : 3 : 4.5 marks

Draw a line through one vertex A parallel to the opposite side BC. The two angles formed at A on either side are equal to ∠B and ∠C (alternate angles). These two angles and ∠A make a straight angle, so ∠A + ∠B + ∠C = 180°. For the ratio 2 : 3 : 4: 9x = 180°, x = 20°, angles 40°, 60°, 80°.

Quick revision

Angle sum 180°.
Two sides together are longer than the third.
Equal sides ⇒ equal opposite angles.

Exam tips

Check triangle inequality with the two smaller sides only.
An equilateral triangle has every angle 60°.

Practice MCQs

Sum of the angles of a triangle is
1. 90°
2. 180°
3. 270°
4. 360°
Show answer
Answer: (b) 180°. Angle sum property.
Each angle of an equilateral triangle is
1. 45°
2. 60°
3. 90°
4. 120°
Show answer
Answer: (b) 60°. 180 ÷ 3.
Two angles of a triangle are 50° and 70°. The third is
1. 120°
2. 50°
3. 70°
4. 60°
Show answer
Answer: (d) 60°. 180 − 120.
Can 3 cm, 4 cm and 8 cm form a triangle?
1. no
2. yes
3. only right-angled
4. only isosceles
Show answer
Answer: (a) no. 3 + 4 < 8.
Two angles of a triangle are 50° and 60°. The third is
1. 60°
2. 70°
3. 80°
4. 90°
Show answer
Answer: (b) 70°. 180 − 110.
An exterior angle of a triangle is 110° and one opposite interior angle is 45°. The other is
1. 65°
2. 70°
3. 55°
4. 135°
Show answer
Answer: (a) 65°. 110 − 45.
In an isosceles triangle the vertex angle is 40°. Each base angle is
1. 80°
2. 40°
3. 70°
4. 140°
Show answer
Answer: (c) 70°. (180 − 40)/2.
An exterior angle of a triangle is 120° and one opposite interior angle is 45°. The other opposite interior angle is
1. 135°
2. 60°
3. 75°
4. 15°
Show answer
Answer: (c) 75°. Exterior = sum of two opposite interior angles.

All chapters of Class 7 Mathematics

Written by Kundali IQ from standard, well-established facts to help with revision. This is not an official NCERT publication; always read your textbook too.