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3 years ago

Which of the following statements is true if m∠E = m∠Y and m∠F = m∠X?

Mathematics

2 answers:

babymother [125]3 years ago

5 0

Answer:

We always apreciate an explination, but the simple answer is: ΔEFG ~ ΔYXZ

Step-by-step explanation:

I'm taking the test.

mars1129 [50]3 years ago

3 0

Answer:

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX

Step-by-step explanation:

see the attached figure to better understand the problem

we know that

If m∠E = m∠Y and m∠F = m∠X

then

Triangles EFG and YXZ are similar by AA Similarity Theorem

Remember that

If two figures are similar, then the ratio of its corresponding sides is proportional and its corresponding angles are congruent

In this problem

The corresponding sides are

FE and XY

EG and YZ

GF and ZX

so therefore

segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX Firstly , let us learn about trigonometry in mathematics.

Suppose the ΔABC is a right triangle and ∠A is 90°.

sin ∠A = opposite / hypotenuse

cos ∠A = adjacent / hypotenuse

tan ∠A = opposite / adjacent

Let us now tackle the problem!

A similar triangle has the same angle, in other words the triangle has the same shape but different sizes.

From the figure in the attachment , we can conclude that:

m∠E = m∠Y

m∠F= m∠X

m∠G = m∠Z

∴ ΔEFG ~ ΔYXZ ( ΔEFG is similar to ΔYXZ )

Because of the similarity , then:

FE : XY = EG : YZ = GF : ZX

Conclusion:

ΔFG is similar to ΔYXZ.

Segment FE over segment XY equals segment EG over segment YZ equals segment GF over segment ZX , i.e:

Keywords: Sine , Cosine , Tangent , Opposite , Adjacent , Hypotenuse , Triangle , Fraction , Lowest , Function , Angle

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The least common multiple of two numbers is 3780, and the greatest common divisor is 18. given that one of the numbers is 180, w

garri49 [273]

To solve these GCF and LCM problems, factor the numbers you're working with into primes:
3780 = 2*2*3*3*3*5*7
180 = 2*2*3*3*5
We know that the LCM of the two numbers, call them A and B, = 3780 and that A = 180. The greatest common factor of 180 and B = 18 so B has factors 2*3*3 in common with 180 but no other factors in common with 180. So, B has no more 2's and no 5's
Now, LCM(180,B) = 3780. So, A or B must have each of the factors of 3780. B needs another factor of 3 and a factor of 7 since LCM(A,B) needs for either A or B to have a factor of 2*2, which A has, and a factor of 3*3*3, which B will have with another factor of 3, and a factor of 7, which B will have.
So, B = 2*3*3*3*7 = 378.

8 0

3 years ago

I will mark you brainliest for the right answer and you must HURRY to get it! 15 points!

DENIUS [597]

A triangles three angles always sum up to 180 degrees. We must find angle B.

We already have angle A and C, so it's quite simple.

Angle A is 28*, and angle C is 36*

We add these two together

28 + 36 = 64

Now we subtract

180 - 64 = 116

Angle B = 116*

Hope this helps you! (:

-Hamilton1757

3 0

3 years ago

Am I right?? * Show examples & details if I am wrong!! *

baherus [9]

Yes, you are correct.

From the image, we can see 3 triangles, the large triangle and the two triangles that make the larger triangle.

All 3 of these triangles are similar since they're angle measurements are the same (can be proven by geometry).

We can gather the following information from the given information.

The largest triangle (the one made up of two triangles) has a hypotenuse of 3+9=12, and a leg length of x. The hypotenuse to leg ratio is 12/x

The second largest triangle has a hypotenuse length x and leg length 9. The hypotenuse to leg ratio is x/9

We know the hypotenuse to corresponding leg ratio must be equal since these two triangles are similar. Thus, we have the equation:

12/x = x/9

Using the cross product property gives us:

x² = 9 × 12

x² = 108

Taking the square root of both sides gives us:

x = √108

= 6 √3

Thus, your answer is correct. Great job!

Let me know if you need any clarifications, thanks!

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3 years ago

A square pool has a side length of x feet.A uniform border around pool is 1 footwide.The total area of the pool and the border o

lions [1.4K]

The total area of pool and border = 361 square feet.

Length of square pool = x

Length of square pool plus border = (x + 1 +1 ) = x + 2

There is 1 foot length on each side on the x length.

The other length of the square pool and border = (x + 2)

Area = (x+2)(x+2)

   (x + 2)(x +2) = 361.    Let A = x +2

A*A = 361
    A² = 361    Take square root of both sides
   A = √361
   A = 19

A = x + 2 = 19
   x = 19 - 2
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Area of square pool = x*x = 17*17 = 289

Area of the pool = 289 square feet.

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maria [59]

Answer:

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