Question

AADE and AABC are similar. Which best explains why the slope of the line between

points A and D is the same as the slope between points A and B?

The triangles are similar, so the sides are proportional:

AE = AC and DE = BC. Therefore, De = BC, so the slope of

AD is the same as the slope of AB.

Points A, D and B are on the hypotenuses of similar triangles.

Therefore, AD = AB, so the slope of AD is the same as the

slope of AB

The triangles are similar, so the sides are proportional:

DE = BC. Therefore, the slope of AD is the same as the slope

of AB

AE C

The triangles are similar, so the sides have equal lengths.

Therefore, AD = DB, so the slope of AD is the same as the

slope of AB

Answer 1

(c) The triangles are similar, so the sides are proportional: DE = BC. Therefore, the slope of AD is the same as the slope of AB

Explanation:

Given

See attachment for proper format of question

Required

Why is the slope between A and D the same

From the question, we understand that:

`\triangle ADE` and
`\triangle ABC` are similar

This implies that similar sides are proportional.

i.e.

`AD \to AB`

`AE \to AC`

`DE \to BC`

Slope (m) is calculated as:

`m = (Rise)/(Run)`

So, the slope of
`\triangle ADE` is:

`m = (DE)/(AE)`

Slope of
`\triangle ABC` is:

`m = (BC)/(AC)`

Since the triangles are similar, then:

`m = m`

i.e.

`(DE)/(AE) = (BC)/(AC)`

Hence, (c) is true