Question

A geometry student says; "I got lost in that lesson - I wrote down that AD/AB = AC/AB but I have no idea

where it comes from."
Which of the following should have been the proportion that the student wrote?
answer choices:
a) AD/AB=AB/AC
b) AD/AC=AB/AB
c) AB/AD=AB/AC
d) AB/AC=AB/AD

Answer 1

Therefore the choice is

a) AD/AB=AB/AC

Explanation:

In Δ ADB and Δ ABC

∠A ≅ ∠A …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC ..............{ measure of each angle is 90° given }

Δ ADB ~ Δ ABC ….{Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

Therefore the choice is

a) AD/AB=AB/AC

Answer 2

Therefore the choice is

a) AD/AB=AB/AC

Explanation:

In Δ ADB and Δ ABC

∠A ≅ ∠A …………..{Reflexive Property}

∠ ADB ≅ ∠ ABC ..............{ measure of each angle is 90° given }

Δ ADB ~ Δ ABC ….{Angle-Angle Similarity test}

If two triangles are similar then their sides are in proportion.

`(AD)/(AB) =(AB)/(AC)\ \textrm{corresponding sides of similar triangles are in proportion}\\`

Therefore the choice is

a) AD/AB=AB/AC