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2 years ago

The triangles are congruent by the SSS congruence theorem.

Mathematics

1 answer:

Likurg_2 [28]2 years ago

6 0

Translation then Rotation or Rotation then Translation

We know that,

1. Rotation turns the figure around a point to a certain degree

2. Translation slides the figure in any direction

Now, it is given that the triangles BCD and WXY are congruent by the SSS Theorem.

<h3>What is the SSS Theorem?</h3>

The corresponding three sides of both triangles are equal.

So, the only possible ways for the triangles to be congruent are

I. If we first translate the figure BCD to the right and then rotate it counter-clockwise. i.e. Translation, then rotation.

II. If we first rotate the figure counter-clockwise and then translate the figure BCD to the right. i.e. Rotation, then translation.

Hence, either Translation then Rotation or Rotation then Translation maps BCD onto WXY.

To learn more about the rotation visit:

brainly.com/question/26249005

#SPJ1

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2 years ago

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Vsevolod [243]

Answer:

Step-by-step explanation:

$\bold{METHOD\ 1:}$

The slope-intercept form of an equation of a line:

$y=mx+b$

m - slope

b - y-intercept

Let $k:y=m_1x+b_1,\ l:y=m_2x+b_2$

then

$l\ \parallel\ k\iff m_1=m_2\\\\l\ \perp\ k\iff m_1m_2=-1\to m_2=-\dfrac{1}{m_1}$

We have the equation of a line:

$2x+3y=6$

Convert to the slope-intercept form:

$2x+3y=6$ subtract 2x from both sides

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$y=-\dfrac{2}{3}x+2\to m_1=-\dfrac{2}{3}$

therefore the slope is $m_2=-\dfrac{2}{3}$

Put the value of the slope and the coordinates of the point (-2, 3) to the equation of a line:

$3=-\dfrac{2}{3}(-2)+b$

$3=\dfrac{4}{3}+b$ subtract 4/3 from both sides

$\dfrac{9}{3}-\dfrac{4}{3}=b\to b=\dfrac{5}{3}$

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Convert to the standard form (Ax + By = C):

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$3y=-2x+5$ add 2x to both sides

$2x+3y=5$

$\bold{METHOD\ 2:}$

Let $k:A_1x+B_1y=C_1,\ l:A_2x+B_2y=C_2$ .

Lines k and l are parallel iff

$A_1=A_2\ \wedge\ B_1=B_2\to\dfrac{A_2}{A_1}=\dfrac{B_2}{B_1}$

We have the equation:

$2x+3y=6\to A_1=2,\ B_1=3$

then the equation of a line parallel to given lines has the equation:

$2x+3y=C$

Put the coordinates of the point (-2, 3) to the equation:

$C=2(-2)+3(3)\\\\C=-4+9\\\\C=5$

Finally:

$2x+3y=5$

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see the attached figure to better understand the problem

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