Prove the following indirectly using paragraph form:

Question

If two angles of a triangle are not congruent, then the triangle is not isosceles.

Answer 1

Use the law of sines

a/sinA = b/sinB = c/sinC

the ratio of a side divided by the sine of the angle opposite that side is a constant

If the triangle is isosceles then either a=b, b=c, or a=c

two of the sides are equal.

then either sinA=sinB or sinB=sinC or sinC=sinA

then either angle A=B or B=C or C=A,

which makes 2 angles equal and congruent

if that's not true, then the triangle can not isosceles