Question

Is triangle ADC similar to triangle CDB? *Explain or show your reasoning.*​

Answer 1

Yes, they are both acute angles.

Answer 2

No, triangle ADC is not similar to triangle CDB because the corresponding side lengths are not proportional.

The Right Triangles Similarity Theorem states that when the altitude of a triangle is drawn to the hypotenuse of a right angled triangle, then, the two triangles that are formed would be similar to each other, as well as the original triangle.

Pythagorean theorem is an Euclidean postulate that can be modeled or represented by the following mathematical equation:

`c^2=a^2+b^2`

Where:

• a is the opposite side of a right-angled triangle.
• b is the adjacent side of a right-angled triangle.
• c is the hypotenuse of a right-angled triangle.

By applying Pythagorean's theorem to right-angled triangle ADC and CDB, we can logically that the lengths of the hypotenuse (AC and BC) are not the same. Therefore, the side lengths are not proportional;

9/5.4 ≠ 12/9.6