What is financial infrastructure?

The network of banks, payment systems and stock markets that helps manage money

What are the main things a bank does?

Holds deposits and lends money as loans

How do banks make money?

They pay lower interest on deposits and charge higher interest on loans

Earning interest on previous interest as well as on the original amount

State the triangle inequality.

Each side of a triangle must be less than the sum of the other two sides.

Can 10, 15 and 30 be the sides of a triangle?

No, because \(30 > 10 + 15\), so the inequality fails.

Can 4, 5 and 8 form a triangle?

Yes, because \(8 < 4 + 5\) and the other comparisons also hold.

What is the angle sum property of a triangle?

The three interior angles add up to \(180^\circ\).

If two angles of a triangle are 36° and 72°, find the third.

The third angle is \(180^\circ - 36^\circ - 72^\circ = 72^\circ\).

What is an isosceles triangle?

A triangle with exactly two sides of equal length.

What is an altitude of a triangle?

A perpendicular segment from a vertex to its opposite side.

When can two given angles form a triangle?

When their sum is less than \(180^\circ\).

What is an exterior angle of a triangle?

The angle between an extended side and the adjacent side; \(\angle ACD\) when \(BC\) is extended.

A Tale of Three Intersecting Lines

Q: Can 4, 5 and 8 form a triangle?

Yes, because \(8 < 4 + 5\) and the other comparisons also hold.

Q: What is the angle sum property of a triangle?

The three interior angles add up to \(180^\circ\).

Q: If two angles of a triangle are 36° and 72°, find the third.

The third angle is \(180^\circ - 36^\circ - 72^\circ = 72^\circ\).

Q: What is an equilateral triangle?

A triangle with all three sides equal and all angles \(60^\circ\).

Q: What is an isosceles triangle?

A triangle with exactly two sides of equal length.

Q: What is an altitude of a triangle?

A perpendicular segment from a vertex to its opposite side.

Q: When can two given angles form a triangle?

When their sum is less than \(180^\circ\).

Q: What is an exterior angle of a triangle?

The angle between an extended side and the adjacent side; \(\angle ACD\) when \(BC\) is extended.

Class 7 Mathematics · Ganita Prakash Part 1 · Chapter 7

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CBSE Class 7 · Mathematics

8 chapters: lakhs and crores to fractions

Marks booster + cheatsheet: key concepts in 2 lines each, common traps
Triangle inequality, Ch 7
Angle pairs of parallel lines, Ch 5
Common traps, corrected
Magic squares and Virahāṅka numbers, Ch 6
Brahmagupta's fraction formulas, Ch 8

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Five congruence conditions to equations

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Integer sign rules, Ch 2
HCF and LCM by prime factors, Ch 3
Multiplying and dividing decimals, Ch 4
Mean, median and outliers, Ch 5
Ruler-and-compass constructions, Ch 6

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Summary

This chapter is about triangles — their construction, existence and angle properties. Using a compass and ruler you construct equilateral triangles (all sides equal), isosceles triangles (two sides equal) and scalene triangles (all sides different) by drawing arcs from the endpoints of a base. A central idea is the triangle inequality: a triangle exists only when each side is shorter than the sum of the other two. So lengths like 10, 15, 30 cannot form a triangle because \(30 > 10 + 15\), whereas 4, 5, 8 can because \(8 < 4 + 5\). You also construct triangles from two sides and the included angle, or two angles and the included side, and discover that a triangle needs the two given angles to sum to less than \(180^\circ\). By drawing a line parallel to the base through the top vertex, you prove the angle sum property: the three angles of any triangle add to \(180^\circ\). You meet exterior angles, altitudes (perpendiculars from a vertex to the opposite side), and classify triangles by sides and by angles (acute, right, obtuse).

Constructing equilateral, isosceles and scalene trianglesTriangle inequality and existence of trianglesConstructing triangles from sides and anglesAngle sum property and exterior anglesAltitudes and classifying triangles

Key terms

Equilateral triangle

A triangle with all three sides equal (and all angles \(60^\circ\)).

Isosceles triangle

A triangle with exactly two sides equal.

Scalene triangle

A triangle with all three sides of different lengths.

Triangle inequality

Each side of a triangle is shorter than the sum of the other two sides.

Angle sum property

The three angles of any triangle add up to \(180^\circ\).

Exterior angle

The angle between a side of a triangle extended and the adjacent side.

Altitude

A perpendicular line segment from a vertex to the opposite side (or its extension).

Extra questions & answers

Try one from this chapter

The triangle inequality states that each side of a triangle is:

Flashcards & interactive practice