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
Viefleur [7K]
2 years ago
13

Prove that if two lines intersect each other then the vertically opposite angles are equal.

Mathematics
1 answer:
Svetradugi [14.3K]2 years ago
7 0

If two lines intersect each other then the vertically opposite angles are equal.

<h3>What is a line?</h3>

A line is a one-dimensional figure, which has length but no width. A line is made of a set of points which is extended in opposite directions infinitely.

To prove, two lines intersect each other then the vertically opposite angles are equal.

Suppose there are two lines AB and CD intersecting at a point O.

So, the angles a and c ; b and d are vertically opposite.

Now taking line AB,

Since sum of angles made on a straight line is 180°.

Thus ∠a + ∠b = 180°    ...(i)

Similarly taking line CD,

∠b + ∠c = 180°            ....(ii)

Comparing eq (i)  and (ii) we get,

∠a + ∠b = ∠b + ∠c

Therefore, we get

∠a = ∠c

which are vertically opposite angles.

Taking line CD,

Since sum of angles made on a straight line is 180°.

Thus ∠c + ∠b = 180°    ...(iii)

Similarly taking line CD,

∠c + ∠d = 180°            ....(iv)

Comparing eq (iii)  and (iv) we get,

∠c + ∠b = ∠c + ∠d

Therefore, we get

∠b = ∠d

which are vertically opposite angles.

Thus, if two lines intersect each other then the vertically opposite angles are equal.

To learn more about angles:

brainly.com/question/11337367

#SPJ4

You might be interested in
how to find the volume of a cylinder with a radius of 8 and a height of 23 rounding to the 10th place
alisha [4.7K]

Answer:

V≈4624.42

Step-by-step explanation:

4 0
3 years ago
During a solar eclipse, what is causing the earth’s view of the sun to be darkened?
Serggg [28]

Answer:

the moon blocks light from the sun by coming between the earth and the sun

7 0
3 years ago
Read 2 more answers
What is 9 divided by 2.70 <br> and explain
shusha [124]
3.33 repeating. if you look at it it's 2.70 what I would do is take away the zero for a minute and see how many times 9 goes into 27
8 0
3 years ago
Read 2 more answers
A trapezoid of 15 square feet. if the bases are 4 feet and 6 feet what is the height of a trapezoid? Answer ASAP with workout.
gavmur [86]

Answer:

Trapezoid Area = [(sum of bases) / (2)] * height)

Trapezoid Area = (10) / (2)  * height

15 = 5 * height

height = 3 feet

Step-by-step explanation:

8 0
3 years ago
PLZ HELP ITS DUE RN BRAINIEST TO WHOEVER RIGHT!
lyudmila [28]

Answer:

The zeros are -1, 0, and 2

Step-by-step explanation:

The zeroes of f are the points where the graph f crosses the x-axis, which occur at x = -2, x = 0, x = 2.

Have a great day :)

3 0
2 years ago
Read 2 more answers
Other questions:
  • Amoeba dapat membelah diri menjadi 2 setiap 20 menit . Jika mula mula terdapat 15 amoeba maka setelah dua jam banyaknya amoeba a
    8·1 answer
  • Circle A has a diameter of 9 inches, a circumference of 28.26 inches, and an area of 63.585 square inches. The diameter of circl
    5·1 answer
  • Find the distance between the two points in simplest radical form.<br> (-1, -5) and (4,7)
    6·1 answer
  • What is the slope of the linear function represented in<br> the table?<br> -7
    13·1 answer
  • What is the area of the triangle on the flag of Bosnia and Herzegovina
    9·1 answer
  • Which of the following best describes the equation below?
    12·1 answer
  • 1) How is unit rate related to slope or rise over run?
    12·1 answer
  • If there are 45 boys and 60 girls in a room, fill out all of the possible ratios of boys to girls that could be made.
    15·1 answer
  • How much money should be deposited today in an account that earns 6% compounded monthly so that it will accumulate to $1000000 (
    13·1 answer
  • Help please <br><br><br><br><br><br><br><br><br><br><br> !!!!!!!!!!!!!!!!!!
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!