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 the sum of the squares of two consecutive positive integers is 365, what are the integers?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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If x^2 - 6x + 9 = 0, what is the value of x?

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If a cylinder has a radius of 7 cm and height of 10 cm, what is its volume?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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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 the radius of a circle is 7 cm, what is its circumference?

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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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If the sides of a triangle are 6 cm, 8 cm, and 10 cm, what is the area of the triangle?

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The base of a triangle is 10 cm and its height is 6 cm. What is its area?

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