Question

"Which step should be used to prove that point A is equidistant from points C and B?

In triangles ABD and ACD, all three angles are equal.

In triangles ABC and ABD, one side and one common angle are equal.

In triangles ABC and ADC, two sides are unequal.

In triangles ABD and ACD, two sides and an included angle are equal. "

Answer 1

So based on the given figure above, the step that should be used to prove that point A is equidistant from points C and B is that, in triangles ABD and ACD, two sides and an included angle are equal. If sides AC and AB are equal, therefore, the angles ADC and ADB is also equal, which makes point A, equidistant to point C and B. Hope that this answer helps.

Answer 2

Combine points A with C and A with B. Consider ΔABD and ΔACD:

1. AD is common side, then
`AD\cong AD;`

2.
`CD\cong BD` - given in the diagram;

3.
`\angle ADB\cong \angle ADC`.

By SAS Postulate,
`\triangle ABD\cong \triangle ACD`. Congruent triangles have congruent corresponding sides and congruent corresponding angles, so
`AC\cong AB`.

From this proof you can see that correct choice is option D (In triangles ABD and ACD, two sides and an included angle are equal.)