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solong [7]
2 years ago
5

Mei draws three pairs of parallel lines that are each intersected by a third line. In each figure, she measures a pair of angles

.
What is a reasonable conjecture for Mei to make by recognizing a pattern and using inductive reasoning?


When a pair of parallel lines are intersected by a third line, the alternate interior angles are acute.

When a pair of parallel lines are intersected by a third line, all of the angles formed are obtuse.

When a pair of parallel lines are intersected by a third line, all of the angles formed are congruent.

When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.
Mathematics
1 answer:
alisha [4.7K]2 years ago
6 0

Answer:

The correct answer is When a pair of parallel lines are intersected by a third line, the alternate interior angles are congruent.


Step-by-step explanation:

I just took the test.

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Answer:

let

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tp=24

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24÷3=8

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A spiral staircase turns as it rises 10 feet. The radius of the staircase is 3 feet. What is the number of feet in the length of
jenyasd209 [6]

The number of feet in the length of the handrail is 17.3 feet.

<h3>What is a Pythagorean Theorem?</h3>

Pythagorean theorem, is a geometric theorem that the total of a squares on the sides of a right triangle equals the square upon that hypotenuse (a side opposite its right angle)—or, using familiar algebraic notation, the sum of squared on the hypotenuse equals the square also on hypotenuse.

H² = B² + P²

A spiral would be a shape that wraps around and around with each curve being higher or lower than the one before it.

Now, according to the question;

The simplest way to understand this is to assume that we may "unfold" this spiral to form a rectangle.

Its bottom part of rectangle is simply an arc length of a 3 ft radius circle spun around 270°= (3/4) of a full revolution.

Thus,

= (3/4)× (2\pi) ×(3)  

=  (9/2)×\pi ft

=   4.5×\pi  ft

The height of the staircase will be the side of rectangle = 10ft.

And the rectangle's diagonal will correspond to the length of a railing.

To solve this, we can apply the Pythagorean Theorem.

Handrail length = √ [ (4.5 ×\pi)² + 10² ]  

Handrail length ≈  17.3 ft

Therefore, the the number of feet in the length of the handrail is 17.3 feet.

To know more about Pythagorean Theorem, here

brainly.com/question/343682

#SPJ4

The complete question is-

A spiral staircase turns 270° as it rises 10 feet. The radius of the staircase is 3 feet. What is the number of feet in the length of the handrail?

7 0
1 year ago
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