MATH SOLVE

5 months ago

Q:
# Triangle ABC has been dilated to form triangle A'B'C'. If sides AB and A'B' are proportional, what is the least amount of additional information needed to determine if the two triangles are similar? Angles B and B' are congruent, and angles C and C' are congruent. Segments AC and A'C' are congruent, and segments BC and B'C' are congruent. Angle C=C', angle B=B', and segments BC and B'C' are congruent. Segment BC=B'C', segment AC=A'C', and angles B and B' are congruent.

Accepted Solution

A:

When considering similar triangles, we need congruent angles and proportional sides.

Hence

"Angles B and B' are congruent, and angles C and C' are congruent." is sufficient to prove similarity of two triangles.

"Segments AC and A'C' are congruent, and segments BC and B'C' are congruent." does not prove anything because we know nothing about the angles.

"Angle C=C', angle B=B', and segments BC and B'C' are congruent." would prove ABC is congruent to A'B'C' if and only if AB is congruent to A'B' (not just proportional).

"Segment BC=B'C', segment AC=A'C', and angles B and B' are congruent" is not sufficient to prove similarity nor congruence because SSA is not generally sufficient.

To conclude, the first option is sufficient to prove similarity (AAA)

Hence

"Angles B and B' are congruent, and angles C and C' are congruent." is sufficient to prove similarity of two triangles.

"Segments AC and A'C' are congruent, and segments BC and B'C' are congruent." does not prove anything because we know nothing about the angles.

"Angle C=C', angle B=B', and segments BC and B'C' are congruent." would prove ABC is congruent to A'B'C' if and only if AB is congruent to A'B' (not just proportional).

"Segment BC=B'C', segment AC=A'C', and angles B and B' are congruent" is not sufficient to prove similarity nor congruence because SSA is not generally sufficient.

To conclude, the first option is sufficient to prove similarity (AAA)