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3 years ago

12

URGENT HELPP!!!

2 answers:

tatuchka [14]3 years ago

6 0

All three sides are parallel to the corresponding sides, and all corresponding angles are congruent.

Aleonysh [2.5K]3 years ago

3 0

<span>All three sides of triangle X'Y'Z' must be parallel to the corresponding sides in triangle XYZ and the corresponding angles are congruent .

The dilated triangle will be similar to the original triangle, which means all angles will be the same.

</span><span>The sides of the two triangles will also be parallel. You can test this by observing the slopes:
Line XY has a slope of 2/3, moving from -4,2 and passing through -1,4.
Line X'Y' has the same slope, moving from (-6,3) to (-3,5)

You can see that this is the case for all corresponding sides' slopes. </span>

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StartFraction StartRoot 3 EndRoot Over 3 EndFraction

Step-by-step explanation:

see the attached figure to better understand the problem

step 1

we know that

In the right triangle XYZ

$cos(Y)=\frac{ZY}{XY}$ ---> adjacent side divided by the hypotenuse

substitute the values

$cos(30\°)=\frac{ZY}{4}$

Remember that

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so

substitute

$\frac{\sqrt{3}}{2}=\frac{ZY}{4}$

$ZY=(4)\frac{\sqrt{3}}{2}$

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step 2

$sin(Y)=\frac{XZ}{XY}$ --> opposite side divided by the hypotenuse

substitute the values

$sin(30\°)=\frac{XZ}{4}$

Remember that

$sin(30\°)=\frac{1}{2}$

so

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step 3

$tan(Y)=\frac{XZ}{ZY}$ --> opposite side divided by adjacent side

substitute the values

$tan(Y)=\frac{2}{2\sqrt{3}}$

$tan(Y)=\frac{1}{\sqrt{3}}$

Simplify

$tan(Y)=\frac{\sqrt{3}}{3}$

so

StartFraction StartRoot 3 EndRoot Over 3 EndFraction

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