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Elis [28]
3 years ago
12

Which of the following is true about a parallelogram? A. Opposite angles of a parallelogram are not congruent. B. Parallelograms

always have four congruent sides. C. Only two sides of a parallelogram are parallel. D. The diagonals of a parallelogram always bisect each other.
Mathematics
1 answer:
mafiozo [28]3 years ago
5 0

Answer: The option is D.

Step-by-step explanation:

A line that intersects another line segment and separates it into two equal parts is called a bisector.

In a quadrangle, the line connecting two opposite corners is called a diagonal. We will show that in a parallelogram, each diagonal bisects the other diagonal.

Problem

ABCD is a parallelogram, and AC and BD are its two diagonals.  Show that AO = OC and that BO = OD

Strategy

Once again, since we are trying to show line segments are equal, we will use congruent triangles. And here, the triangles practically present themselves. Let’s start with showing that AO is equal in length to OC, by using the two triangles in which AO and OC are sides: ΔAOD and  ΔCOB.

There are all sorts of equal angles here that we can use. Several pairs of (equal) vertical angles, and several pairs of alternating angles created by a transversal line intersecting two parallel lines. So finding equal angles is not a problem. But we need at least one side, in addition to the angles, to show congruency.

As we have already proven, the opposite sides of a parallelogram are equal in size, giving us our needed side.

Once we show that ΔAOD and  ΔCOB are congruent, we will have the proof needed, not just for AO=OC, but for both diagonals, since BO and OD are alsocorresponding sides of these same congruent triangles.

ABCD is a parallelogram    

Given

AD || BC                                

From the definition of a parallelogram

AD = BC                                 Opposite sides of a parallelogram are equal in size

∠OBC ≅ ∠ODA                      Alternate Interior Angles Theorem, ∠OCB ≅ ∠OAD                      Alternate Interior Angles Theorem,

ΔOBC ≅ ΔODA                     

Angle-Side-Angle

BO=OD                                Corresponding sides in congruent triangles AO=OC                             Corresponding sides in congruent triangles.

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erica [24]

Answer:

a = 5

Step-by-step explanation:

If it's easier for you, you can replace n(a) with y and put a as x.

Now the equation is y = 7x + 4.

It asks you to put in 39 as y.

39 = 7x + 4.

To solve this, the goal is to isolate the variable on one side. The first step I see is to subtract the 4 from both sides.

35 = 7x

Now divide both sides by 7 and we're done!

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7 0
3 years ago
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Find an equivalent fraction with the lowest common denominator. <br> 9/10+2/3
mafiozo [28]

Answer: 1-17/30, or 47/30

Step-by-step explanation:

Find the common denominator. In this case, it’s 30. Multiply the numerators to fit the new denominator. (10•3=30, so 9•3=27, and 2•10=20.)

Your new fractions are 27/30 and 20/30. Now add the numerators.

27+20=47.

Your new fraction is 47/30.

Now check if you can simplify. Since 47 is a prime number, this fraction is in its simplest form. However, it is an improper fraction, so you can simplify it to 1-17/30.

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A small diner has one employee and a counter with seating for 8 customers. The diner does not package food for takeout. Customer
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Answer:

Step-by-step explanation:

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3 years ago
Please please please help me!
OleMash [197]

Answer:

<76

Step-by-step explanation:

Remark

You can't do this problem unless CD and E are all on the same line. If they are, then you can use || line properties.

Properties

<ABG = x                       Given

<ABG = <BGF               Alternate interior angles are equal.

<BGF = x                       Substitute

x + 2x - 9 = 180             Consecutive angles in a ||gram equal 180 degrees.

3x - 9 = 180                    Add 9 to both sides

3x - 9 +9 = 180 +9

3x = 189                         Divide by 3

x = 63

<DHG = 2x - 50            Given

<DHG = 2*63 - 50         Substitute for x

<DHG = 76

<IDC  = 76

<DHG and <IDC are corresponding angles and are equal; it is a property of parallel lines.

6 0
3 years ago
True Or False?
natali 33 [55]
Electromagnets are devices that create a magnetic field through the application of electricity. Strong electromagnets are used to lift, move and drop heavy objects, such as vehicles. Electromagnets have advantages over permanent magnets. When the current is switched off, the electromagnet will lose its magnetism. The car will fall back to earth and we need that when we move cars in a junkyard. With a regular ( permanent ) magnet it would be much harder to do.
Answer: A. True

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