Question

answer check

Answer 1

You're good

Answer 2

am i right

Answer 3

Do you know the definition of an isosceles triangle?

Answer 4

yes

Answer 5

An isosceles triangle is a triangle that has at least two congruent sides.
This means an isosceles triangle can have 2 congruent sides or 3 congruent sides.

Answer 6

In an isosceles triangle, the angles opposite the congruent sides are congruent.

Answer 7

If an isosceles triangle is also equilateral, then all angles are also congruent.

Answer 8

Let's look at an equilateral triangle first.
Since you want one angle to measure 65 deg, then all angles would have to measure 65 degrees.
This is a problem, because
65 + 65 + 65 > 180
and the sum of the measure of the angles of a triangle is 180, not more than 180.
We now know we are not dealing with an equilateral triangle.

Answer 9

okay

Answer 10

This means we are dealing with an isosceles triangle with only two congruent sides and only two congruent angles.

Answer 11

Here is a case of an isosceles triangle having 2 65-deg angles.
This is perfectly fine since 65 + 65 + 50 = 180.
The top angle measures 50 degrees.

Answer 12

okay

Answer 13

Now we know that at least one isosceles triangle with a 65-deg angle exists.
The question we still have is whether there is another isosceles triangle with a 65-deg angle.

Answer 14

so it is A

Answer 15

What about the isosceles triangle above?
It also has a 65-degree angle, but it's the vertex angle, not the base angles.

Answer 16

Correct.

Answer 17

thanks

Answer 18

You're welcome.