One of the legs of the obtuse isosceles △ABC and △DBE lie on the same line sharing vertex B without overlapping. The sides DE and AC intersect at point F, DC = 12 in, m∠BDF=m∠BCF=30°. Find AE and CE.
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Answers
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.
_____
Additional comment
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.
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
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Answer:
[tex]\frac{19}{5}= 3\frac{4}{5}[/tex]
Step-by-step explanation:
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Answers
Answer:
Your GPA would be 1.5 If you have 6 periods.
Step-by-step explanation:
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Step-by-step explanation:
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Answers
Answer:
The cost of Ronny is $876, Dough is $1095 and Ronald is $1752.
Step-by-step explanation:
Firstly, make all ratios into units:
Let Ronny = 4 units, Doug = 5 units,
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Answer:
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Step-by-step explanation:
Answer:
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Step-by-step explanation:
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Step-by-step explanation:
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What is the equation in slope-intercept form of the line that passes through the points (-4, 6) and (-2,5) ?
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Answers
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Answer:
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Step-by-step explanation:
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Answer:
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Step-by-step explanation
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Answer:
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A little mermaid can swim 12 miles downstream in the same amount
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Find the argument of the complex number 2 = 4+ 3i to the nearest whole degree.
Answers
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since it’s being translated over the y axis the only coordinate that’s changing would be the x coordinate. when it’s translated over it would be the opposite to the original point. (positive original point would become a negative point after translated)
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Vertex form: y = -2(x-1)^2 + 8Standard form: y = -2x^2 + 4x + 6Pick whichever form you prefer.
=============================================================
Explanation:
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In general, the vertex is (h,k). So we have h = 1 and k = 8.
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Plug those four values mentioned into the equation below. Solve for 'a'.
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9514 1404 393
Answer:
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Step-by-step explanation:
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Silvia is planning to use a 4-year loan to purchase a car.
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• The amount of interest she will have to pay on the loan is $1,036
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A. $175
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Answers
Answer:
B
Step-by-step explanation:
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What to calculate net payable amount after interest is applied?The net payable amount is the sum of main amount to be paid + the amount of interest.
For this case, it is specified that:
The price of the car is $8,575.The amount of interest she will have to pay on the loan is $1,036Thus, we get:
Total payable amount by Silvia for car purchasing = $8575 + $1036 = $9,611
This payable amount is divided in 48 equal parts. The value of each part (the monthly payment amount by Silvia) is:
[tex]\dfrac{9611}{48} \approx 200 \: \rm dollars[/tex]
Thus, the best estimate of each monthly payment that Silvia will make is given by: Option B: $200
Learn more about division here:
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Answer:
Lemons ( 27 ) = Cups ( 9 )
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can someone heelp me plz
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Answer:
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Answer:
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Step-by-step explanation:
First you need to ____
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Is dis good
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Hope this helped!! :)
Step-by-step explanation:
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Answer:
0.85
Step-by-step explanation:
Answer:
first calculate the percenatge of the ammount and then either add this answer on to increase the qauntity
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(2,2)
Step-by-step explanation:
A new hotel was built with r rooms. The first weekend it was open, 3/5 of them were reserved. Which of the following expressions represents the number of rooms which were reserved?
A r-3/5
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D ÷3/5
PLEASE HELP ITS STUDY ISLAND
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i think
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Quadrant is a quarter of a coordinate plane
The location of angle t is in quadrant 3
The trigonometry equations are given as:
tan(t)>0 and cos(t)<0
The cosine of an angle is negative in the following quadrants
Quadrant 2Quadrant 3The cosine of an angle is positive in the following quadrants
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1)
Cupcakes Pastries
7 2
21 6
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2)
Cupcakes Pastries
7 2
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3)
Cupcakes Pastries
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4)
Cupcakes Pastries
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Answer:
I wish I could help but I don't know
Answer:
D is correct
Step-by-step explanation: