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
Alex73 [517]
3 years ago
12

Two parallel lines are intersected by a transversal. Prove: Angle bisectors of the same side interior angles are perpendicular.

Mathematics
1 answer:
n200080 [17]3 years ago
3 0

Answer:

The answer is given below

Step-by-step explanation:

From the diagram below,Let the line AB and CD be parallel line. Let transversal line EF cut AB at Y and transversal line EF cut CD at Z.

The bisector of ∠BYZ and ∠DZY meet at O. Therefore ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2

∠BYZ and ∠DZY are interior angles.

∠BYZ + ∠DZY = 180 (sum of consecutive interior angles)

∠BYZ/2 + ∠DZY/2 = 180/2

∠BYZ/2 + ∠DZY/2 = 90°

In ΔOYZ:

∠YZO + ∠ZYO + ∠YOZ = 180 (sum of angles on a straight line).

But  ∠YZO = ∠DZY/2 and ∠ZYO = ∠BYZ/2

∠DZY/2 + ∠BYZ/2 + ∠YOZ = 180

90 + ∠YOZ = 180

∠YOZ = 180 - 90

∠YOZ = 90°

Therefore Angle bisectors of the same side interior angles are perpendicular.

You might be interested in
A woman bought some large frames for $10 each and some small frames for $5 each add a closeout sale if she bought 20 frames for
vampirchik [111]

Answer:

The quantity of large frames is 7

The quantity of small frames is 13

Step-by-step explanation:

Given as :

The price of each large frames = $ 10

The price of each small frames = $ 5

The total number of both frames bought = 20

The price for both the frames = $ 135

Now,

Let the quantity of large frames = L

And The quantity of small frames = S

So , According to question

The total number of both frames bought = 20

Or, The quantity of large frames + the quantity of small frame = 135

Or, L + S = 20         ......A

And $ 10 L + $ 5 S = $ 135                         ................B

Or, $ 10× ( L + S ) = $ 10× 20

Or, $ 10 L + $ 10 S = $ 200

(  $ 10 L + $ 10 S ) - ( $ 10 L + $ 5 S ) = $ 200 - $ 135

Or , ( $ 10 L - $ 10 L ) + ( $ 10 S - $ 5 S ) = $ 65

Or, 0 + 5 S = 65

∴  S = \frac{65}{5}

I.e S = 13

So, The quantity of small frames = S = 13

Put the Value of S in eq A

So , L + S = 20

Or, L = 20 - S

Or, L = 20 - 13

∴   L = 7

So, The quantity of large frames = L = 7

Hence The quantity of large frames is 7

And   The quantity of small frames is 13   Answer

7 0
3 years ago
I'm not good at math so Imma leave this here :))
Elodia [21]

Answer:

1. a/2b 2. 5/6 3. x-1/2 4. y-5/y+5 5. x+5/x-1

Step-by-step explanation:

5 0
3 years ago
the sum of three consecutive natural numbers is 156 find the number which is the multiple of 13 out of these numbers​
vichka [17]

Answer:

52 is the multiple of 13

Step-by-step explanation:

3x+3=156

3x=153

x=52

8 0
3 years ago
Read 2 more answers
What is the simplified form of 5 square root x • 5 square root x • 5 square root x • 5 square root x?
Lina20 [59]

Answer:

D

Step-by-step explanation:

The expression \sqrt[5]{x} *\sqrt[5]{x}* \sqrt[5]{x} *\sqrt[5]{x} simplifies to \sqrt[5]{x*x*x*x} = \sqrt[5]{x^4}

A radical can be written as a fractional exponent. The index of a radical is the denominator of its fractional exponent.

x^\frac{4}{5}

5 0
3 years ago
Encuentra el área total de la superficie del prisma cuadrangular??​
Alex787 [66]

Superficie total de un prisma

La fórmula general para el área de superficie total de un prisma recto es T. S. A. = ph + 2B donde p representa el perímetro de la base, h la altura del prisma y B el área de la base.

¡Espero que esto ayude!

8 0
2 years ago
Other questions:
  • The U.S department of Agriculture reported that 45 out of every 115 milk drinkers drink skim milk. If a store owner orders 23 ga
    10·1 answer
  • Use the graph.
    6·2 answers
  • my son had his 18 months visit to the doctor last week.the nurse took several measurement while we were there.his length(height)
    5·1 answer
  • This soda can is going to be made from aluminum. How many square centimeters of aluminum are needed if the radius r = 3.5 cm and
    5·1 answer
  • Analyze the diagram below and complete the instructions that follow.
    5·1 answer
  • Help... ;( ASAP PLZZZZZZZ
    13·2 answers
  • Please help I need to do this ASAP!!
    6·1 answer
  • Find an ordered pair (x, y) that is a solution to the equation. <br><br> -x+2y=3
    11·1 answer
  • Find the slope of the line that passes through (-70, 84) and ( 69, -1).​
    8·2 answers
  • PLEASE HELP
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!