Question

Which of the following must be given to prove that ΔABC is similar to ΔDBA?

a. Segment AD is an altitude of ΔABC.
b. Segment CB is a hypotenuse.
c. Segment CA is shorter than segment BA.
d. Angle C is congruent to itself.

Answer 1

this answer is a (A) segment AD is an altitude at angle ABC

Answer 2

The correct answer is option A.

Explanation:

For the given triangles to be similar the segment AD must be an altitude of ΔABC.

We can provide a theorem for the same:

If we draw an altitude from the right angle of any right triangle, then the two triangles formed are similar to the original triangle.

Also all the three triangles are similar to each other.

Like here, in the triangle ABC, we draw an altitude from A to the side BC, thus forming 2 triangles; ΔDBA and ΔDAC. These both will be similar to ΔABC.

So, by the theorem it is proven that ΔABC is similar to ΔDBA.

Therefore, option A is correct.