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isosceles triangle with two known sides

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happyapple123
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isosceles triangle with two known sides [#permalink] New post   21 May 2020, 06:35
If we know two sides have the same length but do not know the angles. Can we conclude the triangle is an isosceles triangle? I've done quite a few practice questions. They all say different things :(

Have also been spending 20 minutes on Google searching for the answer but still don't know the answer. Can someone please help :cry:
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Re: isosceles triangle with two known sides [#permalink] New post   21 May 2020, 06:39
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happyapple123 wrote:
If we know two sides have the same length but do not know the angles. Can we conclude the triangle is an isosceles triangle? I've done quite a few practice questions. They all say different things :(

Have also been spending 20 minutes on Google searching for the answer but still don't know the answer. Can someone please help :cry:


Yes, Two sides of a triangle are equal is enough fact to confirm that the triangle is an isosceles triangle

It also confirms that the angles opposite to equal sides will be equal (irrespective of their values)

:) :thumbsup:
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Re: isosceles triangle with two known sides [#permalink] New post   21 May 2020, 08:56
happyapple123 wrote:
If we know two sides have the same length but do not know the angles. Can we conclude the triangle is an isosceles triangle? I've done quite a few practice questions. They all say different things :(

Have also been spending 20 minutes on Google searching for the answer but still don't know the answer. Can someone please help :cry:


Yes, we can conclude triangle is isosceles. However, we'll not be able to figure out which of the two sides are equal unless we have something further telling us about the angles or the third side. depending on question you may be able to come to an answer.
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Re: isosceles triangle with two known sides [#permalink] New post   21 May 2020, 09:01
Yes, if two sides of a triangle are equal in length, then it is an isosceles triangle and the angles they make on the base side will also be equal.
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Re: isosceles triangle with two known sides [#permalink] New post   22 May 2020, 07:24
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• If two sides of a triangle are equal in length, then the two angles opposite those sides must be equal
• If two angles in a triangle are equal, then the two sides opposite those angles must be equal in length

In either case, the triangle is isosceles by definition.

None of the above needs to be true, however, for 4-sided shapes (or for shapes with more than 4 sides). For example, a rectangle has four equal (90 degree) angles, but unless the rectangle is a square, it will have some sides of different lengths.
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Re: isosceles triangle with two known sides [#permalink]
22 May 2020, 07:24
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