Question

What can we conclude about the triangles on the line shown below?

The triangles are congruent and therefore have the same slope.

The triangles are similar and therefore have the same slope.

The triangles are similar but do not have the same slope.

The triangles are unrelated to one another.

Answer 1

B

Explanation:

My teacher just told us in class

Answer 2

The triangles are similar and therefore have the same slope.

Explanation:

see the attached figure with letters to better understand the problem

we know that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem triangles ABC and DEC are similar by AA Similarity Theorem

Because

∠CAB=∠CDE =90°

∠ACB=∠ECD ----> by vertical angles

so

The ratio of its corresponding sides is proportional

`(AB)/(DE)=(AC)/(DC)` ----> equation A

Remember that the slope is the change in the y-value by the change in the x-value

so

The slope BC is equal to

`m_B_C=(AB)/(AC)`

The slope EC is equal to

`m_E_C=(CD)/(ED)`

Rewrite the equation A

`(AB)/(DE)=(AC)/(DC)`

`(AB)/(AC)=(DE)/(DC)`

therefore

`m_B_C=m_E_C`

The triangles are similar and therefore have the same slope.