Question

Use the diagram, which is not drawn to scale, to decide which proportions are true.

Answer 1

I think of these in terms of "short side", "long side" and "hypotenuse." The proportions will be true that equate the ratios of corresponding sides.

I is (long side of CDB)/(short side of CDB) = (long side of BDA)/(short side of BDA)

These are corresponding sides, so the proportion is true.

II is (hypotenuse of CBA)/(long side of CBA) = (long side of CBA)/(hypotenuse of CBA)

This proportion equates a value to its inverse, so is false (since the triangle has non-zero area)

III is (long side of CBA)/(short side of CBA) = (hypotenuse of CBD)/(long side of CBD)

The sides involved here are not corresponding, so this is false.

IV is (long side of CDB)/(hypotenuse of CDB)/(long side of BDA)/(hypotenuse of BDA)

These are corresponding sides, so the proportion is true.

The appropriate choice is ...

... a. I and IV only