Question

Look at the figure shown below.

CB is a segment on which a perpendicular bisector AD is drawn. D is the midpoint of CB.

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

ok

Answer 2

Now from the information given you get 1.ADC and ADB are right triangles because the bisector is perpendicular to segment CB

Answer 3

The other information given by the picture is that triangles ADC and ADB share a side

Answer 4

which is AD

Answer 5

However that only gives two parts needed to prove the triangles are equal, which if you have learned, you need three parts like SAS, or ASA etc. The third information given is the fact AD is a bisector, and the definition of a bisector is that it splits segments into two equal parts

Answer 6

So the need and given information you can find out is:
1.AD perpendicular to CB, thus ADC and ADB are right angles and share the same angle
2.ADC and ADB share the same side AD, thus the same/equal side
3.AD is a bisector of segment CB, thus segments CD and DB are equal

Answer 7

so now the picture looks like this