Is the statement given below true or false? give
ajustification if true or a counterexample if false
all isosceles triangles with congruent vertex angles
aresimilar.

Yes, "All isosceles triangles with congruent vertex angles are similar".

Step-by-step explanation:

Consider the provided statement.

All isosceles triangles with congruent vertex angles are similar.

As we know that the two sides of an isosceles triangle are same.

It is given that the isosceles triangles with congruent vertex angles.

If vertex angles are congruent it means the opposite side of those angles are congruent. Also the sums of the base angles are the same,

As we know the base angles of an isosceles triangle are congruent, so by the AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".

Or

let say ΔABC and ΔDEF are isosceles triangles where AB=DE and AC=DF

It means ∠B=∠E and ∠C=∠F also it is given that ∠A=∠D

Thus. from AAA similarity we can say "All isosceles triangles with congruent vertex angles are similar".

x = ± 6i

step-by-step explanation:

x^2 = -36

take the square root of each side

sqrt(x^2) = sqrt(-36)

we know sqrt(ab) = sqrt(a) sqrt(b)

x = ±sqrt(36) sqrt(-1)

we know that sqrt (-1) = i

x = ± 6i

the answer is b.

step-by-step explanation:

by the trigonometric ratio tangent, tangent equals opposite divided by adjacent.

therefore, tan(50) equals ac/3

multiply each side by 3 to get: ac=3tan(50)

the answer is b.