What is missing to solve the problem

Question

In the image provided, ⊙A has AD←→ drawn through the center and intersecting CB¯¯¯¯¯¯¯¯ at E.

Which of the following is not provided in the image above but is necessary in order to prove that ∠ABC≅∠ACB?

(1 point)

1. AB=AC
2. △ABC is isosceles.
3. AD=AB=AC
4. EC=EB

Highlight

1. Item 1. Unattempted. Table of Contents. Navigate between items using your Left and Right arrow keys.
2. Item 2. Unattempted. Table of Contents. Navigate between items using your Left and Right arrow keys.
3. Item 3. Unattempted. Table of Contents. Navigate between items using your Left and Right arrow keys.
4. Item 4. Unattempted. Table of Contents. Navigate between items using your Left and Right arrow keys.
5. Item 5. Unattempted. Table of Contents. Navigate between items using your Left and Right arrow keys.

Answer 1

Intersection does not necessarily mean "bisect". It should have said bisecting but otherwise the base segments need to be specified as equal. So the last statement is the missing piece. Merely stating the triangle is isosceles is not enough because any chord can be drawn through the apex point to the bottom base. the third statement is true but again, it is true of any chord drawn through the triangle to the base.

Answer 2

AB=AC is not provided in the image above, but is necessary in order to prove that ∠ABC≅∠ACB, since if 2 sides of a triangle are equal to each other, then the opposite angles of each of those sides are also equal to each other, by the law of sines.