1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Varvara68 [4.7K]
4 years ago
8

Given: ABCD is a trapezoid, m∠1=m∠2, m∠3=m∠4, AB = CD, AC ∩ BD = O Prove: m∠AOD = m∠BCD

Mathematics
1 answer:
LiRa [457]4 years ago
6 0
Since AB = CD the trapezoid is isosceles, which means that ∡A = ∡D

Therefore also ∡2 = ∡3 (they are half of the congruent angles)

For the properties of parallel lines (BD and AD) crossed by a transversal (BD) we have ∡3 = ∡CBD.

Now consider triangles AOD and BCD:
∡OAD (2) = ∡ADO (3) = ∡CBD (3) = ∡CDB (4)

T<span>he sum of the angles of a triangle must be 180°, t</span>herefore:
∡AOD = 180 - ∡2 - ∡3
∡BCD = 180 - ∡3 - ∡4

∡AOD = ∡BCD because their measure is the difference of congruent angles.

You might be interested in
-x + 2y=10<br> -3x+6y=11
Licemer1 [7]

Answer:

There is no solution.

Hope this helps!

PLEASE let me know if this is correct.

4 0
3 years ago
Read 2 more answers
I am not sure how to solve this could anyone help???
faltersainse [42]

Answer:

about 137 degrees

Step-by-step explanation:

see attached picture

6 0
3 years ago
Find the missing length
olga55 [171]

Answer:

θ ≈ 36.03°

Step-by-step explanation:

We can use tangent (opposite side / adjacent side) for this question:

tan (θ) = 8 / 11

θ = tan⁻¹ (8/11)

θ = 36.02737339

θ ≈ 36.03°

4 0
3 years ago
What is the median of the following string of values?<br> 55, 18, 58, 49, 8, 77, 62, 26, 7.11
LuckyWell [14K]

Answer:

The answer is 49 if we are to assume you meant 7.11 and not 7,11.

If you meant 7,11 - the answer is 28.5.

Step-by-step explanation:

If we are assuming you meant "7,11" and not "7.11", then we would start by removing the lowest and highest numbers from the list respectively, and repeating the process until you only have 1 or 2 numbers left.

Here are the pairs of numbers removed if we are assuming you meant 7.11;

7.11 / 77

8 / 62

18 / 58

26 / 55

We are left with 49, and that would be your median.

However, if we were to assume you meant 7,11, then we'd have to start over and repeat the process.

7 / 77

8 / 62

11 / 58

18 / 55

26 / 49 is our final answer; however we are not to assume this as we need a definite number. To resolve this, we would need to average the two numbers. To do this, we add them together and divide by how many numbers we added.

26 + 49 = 75.

75 / 2 = 28.5

Your median for this would be 28.5.

Hope this helps! Have a great rest of your day. :)

3 0
2 years ago
Read 2 more answers
Which shows the graph of the solution set of 2x + y &lt; 4?
insens350 [35]

Answer:

my answer is in the graph. hope i am right!

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • A car is traveling at a rate of 44 feet per second. what is the car's rate in miles per hour? how many miles will the car travel
    6·1 answer
  • PLEASE HELP ME WITH THESE SET OF QUESTIONS! WORTH 15 POINTS IF YOU SOLVE IT CORRECTLY!!!
    14·1 answer
  • (7) (10) = (x) (4) I need help with this please anyone?
    10·1 answer
  • You randomly select one card from a​ 52-card deck. find the probability of selecting a jack of club or the two of diamonds
    11·2 answers
  • 3 x 16 divided by 2-1
    7·1 answer
  • HELP ME PLEASE! 30 points
    5·2 answers
  • What is the value of x
    5·1 answer
  • Give three examples of equations where there will be no solution.
    15·1 answer
  • Please help me I will give you extra points and the brain thing. (image below) 3/5
    9·1 answer
  • Rephrase verbally in equivalent only if, sufficient, necessary, contrapositive and unless form: ”if we had an FTL drive, then we
    9·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!