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# How can an isosceles triangle have a right angle?

Last updated date: 11th Aug 2024
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Hint: Here in this given question, we have to explain how an isosceles triangle can have a right angle. As we know the sum of angles of a triangle equals the straight angle i.e., 180 degrees. By considering the right angle triangle if the other two angles of a right angled triangle are equal (means 45 degrees each), then this triangle is isosceles, in addition to being right angled. In other words, it is an isosceles right angled triangle.

Complete step by step solution:
An isosceles triangle is a triangle that has two sides of equal length.
Interior Angles of a Triangle Rule this may be one the most well known mathematical rules-The sum of all 3 interior angles in a triangle is ${180^ \circ }$ , if you add up all of the angles in a triangle the sum must equal ${180^ \circ }$.
Now consider a right angled triangle

Can an isosceles triangle be right angled? Answer : Yes
The right angle ABC then angle of
$\left| \!{\underline {\, B \,}} \right. = {90^ \circ }$ .i f the other two angles of a right angled triangle $\left| \!{\underline {\, A \,}} \right.$ and $\left| \!{\underline {\, C \,}} \right.$ are equal (means 45 degrees each), then this triangle is isosceles, in addition to being right angled. In other words, it is an isosceles right angled triangle.
But all the right angle triangles are not isosceles triangles. Because A right angled triangle is one with an angle 90 degrees. The other two angles of this triangle can be equal or not.

Note: The property of an isosceles triangle has a property that the two sides of a triangle should be the same and likewise there is a property that the two angles must be the same. We must know about the property of the triangle and different kinds of triangles and their definition. Hence we can solve these kinds of problems with this information.