All categories

3 years ago

When lines are parallel...

Mathematics

1 answer:

Otrada [13]3 years ago

3 0

Answer:

1) Congruent

2) Supplementary

3) Congruent

4) Congruent

Step-by-step explanation:

1) The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate interior angles are congruent .

2) Formally, we can say that if two lines are parallel, then consecutive interior angles are supplementary. We refer to this as the consecutive interior angles postulate.

3) When the lines are parallel, the corresponding angles are congruent . When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles.

4) The Alternate Exterior Angles Theorem states that, when two parallel lines are cut by a transversal , the resulting alternate exterior angles are congruent.

You might be interested in

Which are the possible side lengths of a triangle

Scorpion4ik [409]

Answer:

The sum of the lengths of any two sides of a triangle is greater than the length of the third side.

Step-by-step explanation:

3 0

4 years ago

Mona has 400 yards of fencing to enclose a rectangular area. Find the dimensions of the rectangle that maximize the enclosed are

olganol [36]

Answer:

10,000 yd

Step-by-step explanation:

8 0

3 years ago

Y = 2x <br> x + y = −6<br> the answer should be like this (x,y) or ( , )

melisa1 [442]

Answer:

(-2, -4)

Step-by-step explanation:

Given:

The system of equations to solve is given as:

$y=2x\\\\x+y=-6$

In order to solve this system of linear equations, we use substitution method.

In substitution method, we substitute the value of any one variable in the other equation.

So, we substitute the value of 'y' from first equation in the second equation.

This gives,

$x+2x=-6\\\\3x=-6$

Dividing both sides by 3, we get:

$\frac{3x}{3}=\frac{-6}{3}\\\\x=-2$

Now, $y=2x=2\times -2=-4$

Therefore, the solution is (-2, -4)

6 0

4 years ago

John is parasailing 350 ft away from the boat that pulls him. suppose he is lifted 400 feet into the air. Find the length of the

ohaa [14]

John
| \
| \
|. \
|. \
(a)400ft
|. \
|. \
|. \(c) length of rope
|. \
|. \
|____________________Boat
350 ft (b)

Pythagorean theorem
a-squared + b-squared = c-squared
400-squared + 350-squared = c-squared
160,000 + 122,500 = c- squared
282,500 = c-squared
Now take the square root of each side of the equation
531.5 = c
The length of the rope is 531.5 feet

7 0

3 years ago

Complete the following:

Svetlanka [38]

1) A mathematical ratio is known as the golden ratio. It is frequently found in nature, and when employed in a design, it encourages compositions that look organic and natural and are visually appealing.

2) The algebraic form of golden ratio is root of x2-x-1 = 0

3) The golden ratio number is approximately equal to 1.618

4) When a line is split into two equal sections, the sum of the two parts, (a) + (b), divided by (a), equals 1.618, and this is known as the Golden Ratio

5) When designing forms, logos, layouts, and other things, this formula might be useful. By dividing each number in the Fibonacci series by its direct predecessor, the golden ratio is obtained. Mathematically speaking, the quotient F(n)/F(n-1) will become closer to the limit 1.618 for rising values of n if F(n) describes the nth Fibonacci number. The golden ratio is a more popular name for this restriction.

Learn more about golden ratio here: brainly.com/question/2263789

#SPJ4

5 0

1 year ago