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deff fn [24]
2 years ago
9

Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel. please Show All Work! Thanks!!

Mathematics
2 answers:
katrin [286]2 years ago
8 0

Answer:

Step-by-step explanation:

To prove this we should first make a little representation to get an idea of how will proceed to work .

To solve it we should use vectors so the first step is to identify this vectors :

  • we have four points : A/B/C/D
  1. A(-2,-4)
  2. B(1,2)
  3. C(2,10)
  4. D(-1,4)
  • VECTOR AB WITH VECTOR DC
  • VECTOR AD WITH VECTOR BC

NOW LET'S IDENTIFY THEIR COORDINATES :

  • VECTOR AB (1-(-2),2-(-4)) VECTOR DC (2-(-1),10-4)
  • VECTOR AD (-1-(-2),4-(-4)) VECTOR BC (2-1,10-2)

We get :

  • VECTOR AB (3,6) VECTOR DC (3,6)
  • VECTOR AD (1,8) VECTOR BC  (1,8)

We notice that the opposite ones have the same coordinates so the edges are parallel .

If we want to check more we can calculate the lenghts :

  • AB=\sqrt{3^{2}+6^{2}  }     DC=\sqrt{3^{2}+6^{2}  }

So AB=DC

  • AD=\sqrt{1^{2}+8^{2}  }     BC=\sqrt{1^{2}+8^{2}  }

So AD=BC

SO ABCD IS A PARALLELOGRAM

nadezda [96]2 years ago
7 0

Answer:

Here You Go! I'm not really sure about this one but i tried.

Step-by-step explanation:

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Darla uses 3 pink roses and 4 yellow tulips to fill each vase.She fills 7 vases.How many flowers does she use?
lora16 [44]

Answer:

The answer to your question is 49

Step-by-step explanation

4+3=7 So she uses 7 Flowers per vase and she wants to fill 7 vases so just do 7*7 and the answer is 49!

8 0
3 years ago
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I know I need to use the change of base
Zinaida [17]
The change of base formula looks like this:
                                           log x
(log to the base b of ) x = -----------    (you could also use ln instead of log)
                                            log b

                                                       log 40       1.602
Then (log to the base 7 of) 40 = ------------ = ------------- = 1.896   (answer)
                                                        log 7         0.8451

check (on calculator):    7^1.896 = 40.023   (close enough to 40 to verify 
                                                                     that this method "worked")
7 0
3 years ago
Two towns that are 31.5 km apart are 3 cm apart on a map. What is the scale of the map?
Aloiza [94]

Each Cm is equal to 10.5 kilometers


8 0
2 years ago
Please Help.<br> Match the reasons to the statements given.
marishachu [46]

Answer:

1. Given

2. Diagonals of a parallelogram bisect each other.

3. Vertical angles are equal.

4. Definition of parallelogram.

5. If lines parallel, then alternate interior angles are equal.

6. ASA

7. CPCTE

Step-by-step explanation:

Statement 1:

The first statement is a parallelogram ABCD, which is already given in the question. So, reason 1 is: Given.

Statement 2:

BT and TD are equal because for a parallelogram, its diagonal bisect each other. Here, BD and AC are the diagonals of parallelogram ABCD. So, the diagonals bisect each other at T. Hence, BT = TD

Statement 3:

Angles 1 and 2 is a pair of vertical angles. A pair of vertical angles are always equal to each other.

Statement 4:

A parallelogram is a quadrilateral whose opposite sides are parallel and equal. Hence, BC ||AD is because of the definition of a parallelogram.

Statement 5:

Angles 3 and 4 is a pair of alternate interior angles. If two lines are parallel, then the alternate interior angles are always equal.

Statement 6:

The triangles BET and DFT are now congruent because:

i.Angle- \angle1=\angle2

ii. Side - BT = TD

iii. Angle - \angle3=\angle4

Therefore, by ASA postulate the two triangles are congruent.

Statement 7:

As the two triangles are congruent, then their corresponding parts are also equal.

So, by CPCTE, ET=FT

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2 years ago
Finding missing angles
Zolol [24]

Answer:

95

Step-by-step explanation:

x \degree = 95 \degree \\(vertical \: angles)  \\  \\ x = 95

8 0
3 years ago
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