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3 years ago

Find the shape resulting from the cross section of the cylinder

Mathematics

1 answer:

Lesechka [4]3 years ago

4 0

Answer: Second option.

Step-by-step explanation:

For this exercise it is important to remember that, by definition, a "Cross section" is the two-dimensional shape obtained by the intersection of a three-dimensional body with a plane.

In this case you can observe in the figure given in the exercise, that the the cylinder (which is the three dimensional body) is sliced perpendicular to its base.

By definition , when a plane intersects a cylinder perpendicular to its base, the resulting shape obtained is a Rectangle.

A Rectangle is defined as a quadrilateral whose opposite sides are parallel and have equal lengt. And each angle measures 90 degrees (Angles that measure 90 degrees are also called "Right angles").

To see this better, you can see the picture attached.

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Prove ΔPAB is isosceles.

Licemer1 [7]

Answer:

See explanation

Step-by-step explanation:

If $PX\cong PY,$ then triangle PXY is isosceles triangle. Angles adjacent to the base XY of an isosceles triangle PXY are congruent, so

$\angle 1\cong \angle 2$

and

$m\angle 1=m\angle 2$

Angles 1 and 3 are supplementary, so

$m\angle 3=180^{\circ}-m\angle 1$

Angles 2 and 4 are supplementary, so

$m\angle 4=180^{\circ}-m\angle 2$

By substitution property,

$m\angle 4=180^{\circ}-m\angle 2=180^{\circ}-m\angle 1=m\angle 3$

Hence,

$\angle 3\cong \angle 4$

Consider triangles APX and BPY. In these triangles:

$PX\cong PY$ - given;
$\angle 5\cong \angle 6$ - given;
$\angle 3\cong \angle 4$ - proven,

so $\triangle APX\cong \triangle BPY$ by ASA postulate.

Congruent triangles have congruent corresponding sides, then

$AP\cong BP$

Therefore, triangle APB is isosceles triangle (by definition).

6 0

3 years ago

A cooler contains 5 bottles of lemonade, 4 bottles of water, and 3 bottles of juice. Each type is equally likely to be chosen. B

-BARSIC- [3]

You need to find a number that all three of those numbers go into. They all go into 60. Then, divide 60 by three because there are three items. 60 divided by 3 is 20, which is the answer.

6 0

4 years ago

How to simplify : <br><br> √(1+√(1-x^2 )) - √(1-√(1-x^2 ))

muminat

√(1 + √(1 - x²)) - √(1 - √(1 - x²))
√(1 + 1 - x) - √(1 - 1 - x)
√(2 - x) - √(0 - x)
(1.414 - x^1/2) - (0 - x^1/2)
1.414 - 0 - x^1/2 + x^1/2
1.414

4 0

4 years ago

If a = 12, b = 30, and c = 22, find the area of triangle ABC to the nearest tenth.

UNO [17]

7900 should be the answer, is there any options?

4 0

3 years ago

The division of whole numbers is commutative. true or false?

AURORKA [14]

'Commutative' means you can work it in the other direction without changing it.
But 1/2 is not the same number as 2/1 . So I guess division is NOT commutative.

3 0

3 years ago