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3 years ago

How can you prove that corresponding parts of congruent triangles are congruent?

Mathematics

1 answer:

maksim [4K]3 years ago

4 0

Answer:

You can tell by using the degrees of the angles and the lengths of the sides, congruent triangles will have the same angle measures and same side lengths where as similar triangles will have the same angle measures but different side lengths.

Step-by-step explanation:

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Type the correct answer for each.

xxTIMURxx [149]

If point $\left(x,\ \frac{\sqrt{7}}{3}\right)$ is on the unit ircle, then:

$x^2+\left( \frac{ \sqrt{7} }{3} \right)^2=1 \\ \\ \Rightarrow x^2+ \frac{7}{9} =1 \\ \\ \Rightarrow x^2=1- \frac{7}{9} = \frac{2}{9} \\ \\ \Rightarrow x= \sqrt{ \frac{2}{9} } = \frac{ \sqrt{2} }{3}$

Since, the point is in the second quadrant, x is negative.

Thus, $(x,\ y)=\left(x,\ \frac{\sqrt{7}}{3}\right)=\left(-\frac{ \sqrt{2} }{3},\ \frac{\sqrt{7}}{3}\right)$

Part A:

$3 \sqrt{7} =6\left( \frac{ \sqrt{7} }{2} \right) \\ \\ =6\left( \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \right) \\ \\ =6\left( \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } \right)=-6\left( \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } \right) \\ \\ =-6\left( \frac{y}{x} \right)=-6\tan\theta$

Therefore, $-6\tan\theta=3\sqrt{7}$ .

Part B:

$- \frac{ \sqrt{7} }{2} =- \frac{ \sqrt{7} }{3} \cdot \frac{3}{ \sqrt{2} } \\ \\ =- \frac{ \frac{ \sqrt{7} }{3} }{ \frac{ \sqrt{2} }{3} } = \frac{ \frac{ \sqrt{7} }{3} }{ -\frac{ \sqrt{2} }{3} } = \frac{y}{x} \\ \\ =\tan\theta$

Therefore, $\tan\theta=- \frac{ \sqrt{7} }{2}$

8 0

3 years ago

If f(x)=7x+4x and g(x) =1/2x what is the value of (f/g)(5)

Aliun [14]

Answer:

(f/g)(5) = 22

Step-by-step explanation:

All we need to do is plug in 5 for x in both f(x) and g(x) then divide the result of f(x) and g(x) to find our final answer.

Step 1: Plug in 5 for x

f(x) = 7(5) + 4(5) = 55

g(x) = 1/2(5) = 2.5

Step 2: Divide f(x) by g(x)

f(5)/g(5) = 55/2.5 = 22

And we have our final answer!

4 0

3 years ago

Find the values of x and y for the isosceles trapezoid

butalik [34]

<h3>Answer:</h3>

x = 15
y = 3

<h3>Step-by-step explanation:</h3>

If the trapezoid is isosceles, angles A and C are supplementary, so ...

... (4x+4) +(7x+11) = 180

... 11x +15 = 180 . . . . . . collect terms

... 11x = 165 . . . . . . . . . subtract 15

... x = 15 . . . . . . . . . . . . divide by the coefficient of x

And angles C and E are congruent.

... 4·15 +4 = 21y +1

... 63 = 21y . . . . . subtract 1

... 3 = y . . . . . . . . divide by the coefficient of y

4 0

3 years ago

2m=-6n-5 literal equation

Bingel [31]

Answer:

read below

Step-by-step explanation:

Alright, archtan /

tan

−

(

)

is the inverse of tangent. Tan is

sin

cos

. Like the inverse of sin, the inverse of tan is also restricted to quadrants 1 and 4.

Knowing this we are solving for the inverse of tan -1. We are basically being asked the question what angle/radian does tan(-1) equal. Using the unit circle we can see that tan(1)= pi/4.

Since the "Odds and Evens Identity" states that tan(-x) = -tan(x). Tan(-1)= -pi/4.

Knowing that tan is negative in quadrants 2 and 4. the answer is in either of those two quadrants. BUT!!! since inverse of tan is restricted to quadrants 1 and 4 we are left with the only answer -pi/4.

the answer is m=-3n-5/2 or n=2m+5/6

8 0

3 years ago

A builder needed to buy four hundred fourteen boards for his latest project. If the boards he

allochka39001 [22]

Answer:

Step-by-step explanation:

3 0

3 years ago

Read 2 more answers