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In a triangle, the angles are 90°, 45°, and 45°. Which type of triangle is it by sides?

Class 7The Triangle and its PropertiesTriangles
  • AIsosceles right triangle
  • BEquilateral triangle
  • CScalene right triangle
  • DObtuse triangle

Step-by-Step Solution

It has a 90° angle (right) and two equal 45° angles, so two sides are equal — an isosceles right triangle.
Answer: A) Isosceles right triangle

Key idea: Triangle inequality

**The sum of any two sides of a triangle is greater than the third side.**

So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.

Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.

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