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triangles ABD and ACE are similar right triangles. which ratio best explains why the slope of AB is the same as the slope of AC

a. BD/BA = CE/CA
b. AC/EA = AB/DA
c. BD/DA = EA/CE
d. BD/DA = CE/EA

triangles ABD and ACE are similar right triangles which ratio best explains why the slope of AB is the same as the slope of AC a BDBA CECA b ACEA ABDA c BDDA EA class=

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Answer:

The correct option is d.

Step-by-step explanation:

The slope of a line is

[tex]Slope=\frac{Rise}{Run}[/tex]

Slope of line AB is

[tex]m_{AB}=\frac{BD}{DA}[/tex]

Slope of line AC is

[tex]m_{AC}=\frac{CE}{EA}[/tex]

Triangles ABD and ACE are similar right triangles, therefore the corresponding sides are proportional.

[tex]\frac{AB}{AC}=\frac{BD}{CE}=\frac{AD}{AE}[/tex]

Using last two ratios, we get

[tex]\frac{BD}{CE}=\frac{AD}{AE}[/tex]

The required ratio is

[tex]\frac{BD}{DA}=\frac{CE}{EA}[/tex]

Therefore the correct option is d.

The ratio best explains why the slope of AB is the same as the slope of AC [tex]\rm \dfrac{BD}{BA}=\dfrac{CE}{CA}[/tex].

Given

Triangles ABD and ACE are similar right triangles.

What are similar triangles?

If the two triangles are similar then their angles and side length ratios are equal to each other.

The slope of the line AB is given by;

[tex]\rm Slope =\dfrac{BD}{DA}[/tex]

And the slope of the line AC is;

[tex]\rm Slope =\dfrac{CE}{EA}[/tex]

The triangles are similar their side ratio equal to each other, therefore, the slope of both triangles is also equal to each other.

[tex]\rm \dfrac{BD}{BA}=\dfrac{CE}{CA}[/tex]

Hence, the ratio best explains why the slope of AB is the same as the slope of AC [tex]\rm \dfrac{BD}{BA}=\dfrac{CE}{CA}[/tex].

To know more about a Similar triangle click the link given below.

https://brainly.com/question/4770091

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