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If the base angles of a triangle are congruent, use the Law of Sines to show the triangle is isosceles.

60 Points I Need This Answer ASAP Plz If The Base Angles Of A Triangle Are Congruent Use The Law Of Sines To Show The Triangle Is Isosceles class=

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The Isosceles Triangle Theorem States that if a triangle contains 2 congruent sides, then the angles opposite those sides are congruent. This theorem can be proved using the Law of Sines: The Law of Sines states that: asinA=bsinB=csinC If a=c, making △ABC an isosceles triangle, then asinA=asinC!

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The law of sins says: a/SinA = b/SinB = c/sinC

For this to be an isosceles triangle then side a must equal side c

so then a/sinA = c/sinC

Then you can divide both sides by a and raise to the power of -1 and you would get angle A = angle C which makes this isosceles.

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