Topic Details (Notes format)

How to Classify Triangles by Sides and Angles

Subject: Mathematics

Book: Maths Mastery

Triangles can be classified by sides—equilateral (all sides equal), isosceles (two equal sides), scalene (all sides different)—or by angles—acute (all angles < 90°), right (one angle = 90°), obtuse (one angle > 90°). For example, a triangle with side lengths 3, 3, 5 is isosceles, while one with angles 30°, 60°, 90° is right-angled. Such classifications underlie geometry proofs and real-world designs like roof trusses, bridging shape fundamentals with practical engineering. Identifying the triangle type sets the stage for using the right formulas or theorems to solve deeper geometric questions.

Practice Questions

If a:b = 3:4 and b:c = 5:6, what is a:c?

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If 8x = 512, what is the value of x?

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If the angles of a triangle are in the ratio 2:3:4, what is the measure of the largest angle?

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What is the slope of a line passing through the points (2, 3) and (4, 7)?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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What is the sum of all odd numbers from 1 to 99?

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If a square has a perimeter of 64 cm, what is its area?

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The area of an equilateral triangle with side length 6 cm is:

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What is the sum of the first 50 positive integers?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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