Question

16 Which of the following conditions would make triangle ADB similar to triangle ABC? A. Angle B is a right angle. B. Angle A is congruent to angle C. C. AD = AB D. AD BC = DB AB

Answer 1

The condition that would make triangle ADB similar to triangle ABC is D. AD/DB = AC/AB, which follows the Side-Splitter Theorem needed for establishing similarity between triangles. Therefore correct option is D

Step-by-step explanation:

To determine which condition would make triangle ADB similar to triangle ABC, we apply the concept of similar triangles, which requires that corresponding angles are congruent and corresponding sides are in proportion. Reviewing the choices given

• A. Angle B is a right angle: This alone doesn't ensure similarity.
• B. Angle A is congruent to angle C: This suggests that the two triangles share one identical angle, which is a step towards similarity if the other angles are also congruent or the sides are in proportion.
• C. AD = AB: Equal lengths alone do not guarantee similarity.
• D. AD/DB = AC/AB: This proportion represents the Side-Splitter Theorem, which indicates that if the sides of two triangles are in proportion, the triangles are similar.

The correct answer is: D. AD/DB = AC/AB, as this is the condition that satisfies the criteria for similarity of triangles.