Line segment df intersect the side ac of a triangle

Asked by admin @ in Math viewed by 285 People

In the given figure, line segment DF intersect the side AC of a triangle ΔABC at the

point E such that E is the mid–point of CA and ∠AEF = ∠AFE. Prove that:
BD/CD= BF/CE
[Hint: Take point G on AB such that CG || DF.]

Answered by admin @


Given that E is the mid point of AC ,then
CE=AE...............................1
also given that ,
angle AEF=angle AFE................2
then, AE=AF........................3
by eq1 and eq2 we get ,
CE=AE=AF........................4
now draw CG parallel DF
we know that corresponding angles are equal,
therefore,angleAEF=angle ACG........5
also, angle AFE=angle AGC...............6
by eq2,5,6, we get
angleAEF=AFE=ACG=angleAGC
Then,AC=AG.......................7. as sides opposite to equal angles
AE+CE=AF+GF
By eq4,7 we get,
AE=AF=GF=CE
CE=AF=GF.............................8
By Thales theorem we get,
BC/CD=BG/GF
By adding 1 on both sides we get,
BC/CD+1=BG/GF+1
(BC+CD)/CD=(BG+GF)/GF
BD/CD=BF/GF
by eq 8 we get
BD/CD=BF/CE
Hence proved




Similar Questions

If a line divides two sides of a triangle

Asked by admin @ in Math viewed by 400 persons

If a line divides any two sides of a triangle in the same ratio,then the line is parallel to the third side prove it

Sides ab and ac of triangle abc are extended

Asked by admin @ in Math viewed by 338 persons

"Question 2 In the given figure sides AB and AC of ΔABC are extended to points P and Q respectively. Also, ∠PBC < ∠QCB. Show that AC > AB. Class …

What is the longest side of a right triangle called

Asked by admin @ in Mathematics viewed by 355 persons

What is the longest side of a right triangle called?

A triangle with 3 different sides in length is called

Asked by admin @ in Health viewed by 363 persons

A triangle with three different side lengths is called A. scalene. B. equilateral. C. isosceles. D. equiangular.

Find the length of side x in the right triangle

Asked by admin @ in Mathematics viewed by 368 persons

Which expression finds the length of side x in this right triangle?

What is the difference between intersecting lines and perpendicular lines

Asked by admin @ in Mathematics viewed by 265 persons

What is the difference between intersecting and perpendicular lines? Can two lines exist that are not intersecting or parallel? Explain your answer.

What is the definition of a line segment in geometry

Asked by admin @ in Mathematics viewed by 299 persons

Which is the definition of a line segment

How to find sides of a 30 60 90 triangle

Asked by admin @ in Mathematics viewed by 303 persons

In a 30-60-90 triangle, the length of the side opposite the 30 degree angle is 8. Find the length of the side opposite the 60 degree angle.

How to find the 3rd side of a right triangle

Asked by admin @ in Mathematics viewed by 455 persons

Two sides of a right triangle are equal to 3m and 4m. Find the length of the third side. (Two cases)If the two given sides are both legs, then the …

Find two sides of a right triangle given the hypotenuse

Asked by admin @ in Mathematics viewed by 324 persons

To solve for the hypotenuse of a right triangle, what information do you need? A. just the measure of one of the acute angles and the length of one side …

How do you find the side length of a triangle

Asked by admin @ in Mathematics viewed by 287 persons

Given the three side lengths, how can you tell if a triangle is a right triangle? Answer: Square all side lengths. If the longest side length squared is equal to …

How to find angles of a triangle with 2 sides

Asked by admin @ in Mathematics viewed by 345 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

Geometry find the missing side of each triangle worksheet answers

Asked by admin @ in Mathematics viewed by 388 persons

Special right triangles find the missing side lengths. Leave your answers as radicals in simplest form. Need help ASAP due tomorrow and don’t understand how to do it

How to find angle in right triangle with 3 sides

Asked by admin @ in Mathematics viewed by 367 persons

Explain how to find the measures of the angles in a right triangle, given the lengths of two sides.

How to find 2 unknown sides of a right triangle

Asked by admin @ in Mathematics viewed by 277 persons

Solve for the unknown side in the right triangle if b=24 and c=26 find a A.8 B.9 C.10 D.11

Most viewed questions in Math

What is the value of x in the expression

Asked by admin @ in Math viewed by 15141 persons

Shubham is facing south and moves 30 km

Asked by admin @ in Math viewed by 12986 persons

Prachi excellence in mathematics class 7 solutions pdf free download

Asked by admin @ in Math viewed by 12033 persons

Oxford new enjoying mathematics class 7 solutions chapter 1

Asked by admin @ in Math viewed by 11516 persons

Survey of various types of bank accounts icse project

Asked by admin @ in Math viewed by 11505 persons

The town of p is located at point x

Asked by admin @ in Math viewed by 11358 persons

A clock gains 4 minutes after every 4 minutes

Asked by admin @ in Math viewed by 10164 persons

Running a tuck shop or canteen maths project pdf

Asked by admin @ in Math viewed by 9377 persons

Paul is sixteenth from the front of the row

Asked by admin @ in Math viewed by 9348 persons

The average weight of 20 teachers is 80 kg

Asked by admin @ in Math viewed by 7522 persons

The number 567 xy is completely divisible by 30

Asked by admin @ in Math viewed by 7395 persons

In a row of friends tiya occupies fifteenth place

Asked by admin @ in Math viewed by 7203 persons

What would $ mean if fat is coded as

Asked by admin @ in Math viewed by 5274 persons

Consider a 3 digit integer x with distinct digits

Asked by admin @ in Math viewed by 4801 persons

Rahul went to his mother's mother in law

Asked by admin @ in Math viewed by 4177 persons