Question

(03.02 LC)

Look at the figure below:

Triangle ABC with a segment joining vertex A to point D on side BC.

Which information is required to prove that angle ABD is congruent to angle ACD? (6 points)


Segment AC is congruent to segment AB.

Segment AD is congruent to segment AC.

Segment BD is congruent to segment AD.

Segment AB is congruent to segment BD.

Answer 1

SEgment AC is congruent to segment AB

Explanation:

given is a triangle ABC with a segment joining A to D on side BC.

To prove that ABD is congruent to ACD

Let us compare these two triangles.

AD = AD (reflexive) Thus one side is equal.

IF AB = AC, then by isosceles triangles property we have angle B = angle C

Thus we get two sides equal. But this is a necessary condition not sufficient.

Because to prove congruence we need one more condition either CD = BD or Angle CAD = angle DAB

Thus if either AD is angle bisector, or D is mid point besides AC = AB we get

the two triangles are congruent.