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
Mrrafil [7]
2 years ago
14

One of the legs of the obtuse isosceles △ABC and △DBE lie on the same line sharing vertex B without overlapping. The sides DE an

d AC intersect at point F, DC = 12 in, m∠BDF=m∠BCF=30°. Find AE and CE.
GIVE FULL EXPLANATION

PLZ HELP ILL GIVE 100 POINTS

Mathematics
2 answers:
Vladimir79 [104]2 years ago
8 0

9514 1404 393

Answer:

  AE = CE = 12 in

Step-by-step explanation:

Angles BDF and BCF are base angles of their respective isosceles triangles. That means the a.pex angle of each, DBF and ABC respectively is ...

  180° -2×30° = 120°

In your diagram, BC is 120° from the -x axis, so is 60° from the +x axis. It bisects the angle DBE. Similarly, BE is 120° from the +x axis, so is 60° from the -x axis. It bisects angle ABC. In an isosceles triangle, the a.pex angle bisector is an altitude and is the perpendicular bisector of the base segment. Any point on that line is equidistant from the base vertices.

Point C lies on the perpendicular bisector of DE, so CD ≅ CE = 12 in.

Point E lies on the perpendicular bisector of AC, so EC ≅ EA = 12 in.

The measurements of interest are ...

  AE = CE = 12 in.

_____

<em>Additional comment</em>

Point F serves no purpose except to confuse the issue. Each of the angles that reference point F could be described equally well using a different point:

  ∠BDF = ∠BDE

  ∠BCF = ∠BCA

This makes it more obvious that the triangles of interest are similar.

Yuri [45]2 years ago
7 0

Answer:

12

12

Step-by-step explanation:

see the below figure

i got that both triangles are similar

we get that in triangle ABC angle BCF is 30

so angle A is also 30 (isosceles)

so the remaining angle ABC is 120

and angle CBD becomes 180 - 120 = 60

now in triangle BDE angle BDF is 30

so angle BED is also 30

now angle EBC becomes 120 - angle CBD = 120 - 60

and got angles ABE EBC CBD as 60 each

so three 60 degree angles are formed at vertex B as shown in the figure

 tw0 30 30 120 degree triangles are similar

BC becomes perpendicular angular bisector of ED

C is a point on that line which is at equal distance from the base vertices

so CD = CE = 12

here BE is perpendicular bisector of AC

so AE = EC = 12    

You might be interested in
What's the probability of obtaining a 3 digit number at random which is DIVISIBLE by 7 ​
pochemuha

Answer:

  32/225 ≈ 0.1422

Step-by-step explanation:

If you consider "3-digit" numbers to be between 100 and 999, inclusive, there are 128 such numbers divisible by 7. The probability of choosing one at random is ...

  128/900 = 32/225 = 0.1422...(repeating)

__

If you consider all non-negative integers less than 1000 to be "3-digit numbers," then the probability is ...

  142/1000 = 0.142 (exactly)

6 0
3 years ago
Carrie has a stamp collection she is very proud of. She buys a frame to display her favorite stamps. The frame is 6 inches wide,
olga55 [171]
The stamps should be .85 inches each
7 0
2 years ago
The table shows the price for different numbers of board games:
zlopas [31]

Answer:

We conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

Step-by-step explanation:

We know that when y varies directly with x, the equation is

y ∝ x

y = kx

k = y/x

where 'k' is called the proportionality constant.

From the table,

For the point (2, 7)

k = y/x

  = 7/2

  = 3.5

For the point (4, 14)

k = y/x

   = 14 / 4

   = 7/2

    = 3.5

For the point (5, 17.50)

k  = y/x

   = 17.5 / 5

   = 3.5

For the point (9, 31.50)

k  = y/x

   = 31.50 / 9

   = 3.5

From the above calculations, we computed that the value of the proportionality constant remains the same.

Thus, the table of numbers represents a proportional relationship.

Therefore, the equation becomes

y = kx

The price of 2 board game

y = 3.5 (2)

  = 7

The price of 4 board game

y = 3.5 (4)

  = 14

Therefore, we conclude that the price is 3.5 times the number of board games.

Hence, option B is true.

6 0
2 years ago
What are same-side interior angles
REY [17]

Step-by-step explanation:

same side interior angles are formed when a transversal line intersects two or more lines

6 0
2 years ago
Read 2 more answers
Claire has 15 green beads 8 blue beads and 4 yellow beads. If she puts them onto 3 strings equally how many beads are on each st
Katyanochek1 [597]
There are 9 beads on each string
4 0
3 years ago
Read 2 more answers
Other questions:
  • What is the result when 4x4 + 6x3 – 19x2 – 8x – 10 is divided by x + 3? If
    13·1 answer
  • Graph these two equations.<br> y= 2x - 3<br> x + 2y = 4
    13·1 answer
  • In a jumping contest marcus jumped 1.02 meters gustavo jumped 1.29 meters and lorena jumped 1.202 meters.who won the jumping con
    14·1 answer
  • you need to hire a catering company to serve meals to guests at a wedding reception. Company A charges $500 plus $20 per guest.
    5·1 answer
  • Helllllppppppp plzzzzzzzz
    9·2 answers
  • 2<br> Which of these shapes is congruent to the given shape?
    8·1 answer
  • Kala must choose a shirt, a pair of pants, and a cap for today's outfit. She has 3 shirts, 3 pairs of pants, and 1 cap to choose
    15·1 answer
  • If bob had 4 apples and tim had 6 oranges but john had 4 times more oranges then tim but stephaine had 6 times more apples then
    11·1 answer
  • The distance between Franklin City and Williamsville on a map is 3.2 inches. If the scale of the map is 1 inch = 15 miles, how m
    5·1 answer
  • 74.37 rounded to the nearest ten
    6·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!