Question

Help asap please??????????????

Answer 1

The statement that best explains why the slopes of line AD and AB are equal is: the triangles are similar so the sides are proportional $\frac{DE}{AE}$ = $\frac{BC}{AC}$. Therefore slope of line AD is the same as slope of line AB.

what are similar triangles?

Similar triangles are triangles that have the same shape, but their sizes may vary. All equilateral triangles, squares of any side lengths are examples of similar objects. In other words, if two triangles are similar, then their corresponding angles are congruent and corresponding sides are in equal proportion.

since triangle ADE is similar to triangle ABC,

then $\frac{AE}{AC}$ = $\frac{DE}{BC}$

Cross multiply,

AE x BC =AC x DE

divide both sides by AC

$\frac{AE X BC}{AC}$ = DE

divide both sides by AE we have

$\frac{BC}{AC}$ = $\frac{DE}{AE}$

But slope for line AD = $\frac{DE}{AE}$

And slope for line AB = $\frac{BC}{AC}$

Therefore slope AD = slope AB

In conclusion the both slopes are equal because triangles are similar and  the sides are proportional $\frac{DE}{AE}$ = $\frac{BC}{AC}$

Learn more about similar triangles: brainly.com/question/11920446

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