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
Trava [24]
3 years ago
7

*In ∆ABC, on the extension of the side BC , draw a line segment CD ≅ CA . Draw the segment AD . The line segment CE is the angle

bisector of ∠ACB. The line segment CF is the median towards AD in ∆ACD. Prove: CF ⊥ CE

Mathematics
1 answer:
Leya [2.2K]3 years ago
7 0

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Step-by-step explanation:

In ∆ABC

  • On the extension of the side BC , draw a line segment CD ≅ CA
  • Draw the segment AD
  • The line segment CE is the angle bisector of ∠ACB
  • The line segment CF is the median towards AD in ∆ ACD

We want to prove that CF ⊥ CE

Look to the attached figure

In Δ ABC

∵ CE is the bisector of angle ACB

∴ ∠ACE ≅ ∠BCE

In Δ ACD

∵ CA = CD

∴ Δ ACD is an isosceles triangle

∵ AD is the median towards AD

- In any isosceles triangle the median from a vertex to its opposite

  side bisects this vertex

∴ AD bisects ∠ACD

∴ ∠ACF ≅ ∠DCF

∵ BCD is a straight segment

∵ CE , CA , CF are drawn from point C

∴ m∠BCE + m∠ACE + m∠ACF + m∠DCF = 180°

∵ m∠ACE ≅ m∠BCE

∵ m∠ACF ≅ m∠DCF

- Replace m∠BCE by m∠ACE and m∠DCF by m∠ACF

∴ m∠ACE + m∠ACE + m∠ACF + m∠ACF = 180°

∴ 2 m∠ACE + 2 m∠ACF = 180°

- Divide all terms by 2

∴ m∠ACE + m∠ACF = 90°

∴ EC ⊥ CF

CE ⊥ CF because m∠ECA + m∠FCA = 90°

Learn more:

You can learn more about perpendicular lines in brainly.com/question/11223427

#LearnwithBrainly

You might be interested in
Which equation represents a linear function?
quester [9]

Answer:

Step-by-step explanation:

y = 9 - X   is a linear function; x is to the first power.

y = x2 + 1   does NOT represent a linear function; it's a quadratic function.

o            

y=x² + 5    does NOT represent a linear function; it's a quadratic function.

D)

y = [xl - 9  does NOT represent a linear function; it's an absolute value function.  This function has two halves, each of which is a linear function.

But the best answer here is that y = 9 - X   is a linear function; x is to the first power.

3 0
3 years ago
Sooo..... can anybody help.....
Margaret [11]
V= wlh so the answer is 56.25 or 56 1/4
4 0
3 years ago
Read 2 more answers
Find the inverse of each of the given functions.
Leona [35]

Answer:

The inverse of the function is (3x+4)/2

Step-by-step explanation:

To find the inverse, exchange x and y and then solve for y

y = (2x-4) /3

Exchange x and y

x = (2y-4)/3

Solve for y

Multiply each side by 3

3x = (2y-4)/3 *3

3x =2y-4

Ad 4 to each side

3x+4 = 2y-4+4

(3x+4) =2y

Divide each side by 2

(3x+4)/2 =2y/2

(3x+4)/2 = y

The inverse of the function is (3x+4)/2

6 0
2 years ago
Read 2 more answers
C=36x+200 R=76x break-even point
Leokris [45]

Answer:

x = 5.

Step-by-step explanation:

The break even point is when they are equal:

76x = 36x + 200

40x = 200

x = 200/40

x = 5.

6 0
3 years ago
Read 2 more answers
The area of a square is 50 meters. how long is each side? round your answer to the nearest meter.
DanielleElmas [232]
The closest would be 7
7x7 is 49 and that is the closest
8 0
3 years ago
Read 2 more answers
Other questions:
  • The numbered disks shown are placed in a box and one disk is selected at random. find the probability of selecting an oddodd ​nu
    8·1 answer
  • In circle O, RT and SU are diameters. If m = m, what is m? 47° 52° 64° 87°
    9·2 answers
  • Courtney hit the bullseye 3/5 of time when playing darts.Write 3/5as a decimal
    10·1 answer
  • FIRST RIGHT GETS BRAINLIEST
    15·1 answer
  • What is 2.24 rounded to the nearest tenth?
    8·2 answers
  • Match the correct letter
    15·1 answer
  • An experiment was designed to measure how long subjects could track a moving target on a computer screen. The target moved errat
    15·1 answer
  • I WILL GIVE BRAINLIEST IF ITS CORRECT
    12·1 answer
  • What is the equation of the given line?
    15·2 answers
  • If a right cylinder has the same volume as the oblique cylinder shown here, what is the base area of the right cylinder? Use 3.1
    12·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!