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Semenov [28]
3 years ago
9

Which method is valid for proving that two circles are similar?

Mathematics
1 answer:
tatuchka [14]3 years ago
4 0

'a',  'c', and  'd'  are true for any two circles.  That's because
ALL circles are similar.  You don't need to prove it.  The question
is weird.


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Answer:

Part A: Angle R is not a right angle.

Part B; Angle GRT' is a right angle.

Step-by-step explanation:

Part A:

From the given figure it is noticed that the vertices of the triangle are G(-6,5), R(-3,1) and T(2,6).

Slope formula

m=\frac{y_2-y_1}{x_2-x_1}

The product of slopes of two perpendicular lines is -1.

Slope of GR is

\text{Slope of GR}=\frac{1-5}{-3-(-6)}=\frac{-4}{3}

Slope of RT is

\text{Slope of RT}=\frac{6-1}{2-(-3)}=\frac{5}{5}=1

Product of slopes of GR and RT is

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Therefore lines GR and RT are not perpendicular to each other and angle R is not a right angle.

Part B:

If vertex T translated by rule

(x,y)\rightarrow(x-1,y-2)

Then the coordinates of T' are

(2,6)\rightarrow(2-1,6-2)

(2,6)\rightarrow(1,4)

Slope of RT' is

\text{Slope of RT'}=\frac{4-1}{1-(-3)}=\frac{3}{4}

Product of slopes of GR and RT' is

\frac{-4}{3}\times \frac{3}{4}=-1

Since the product of slopes is -1, therefore the lines GR and RT' are perpendicular to each other and angle GRT' is a right angle.

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Step-by-step explanation:

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