# mathematics

posted by .

ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpindicular AC

• mathematics -

let AB = x
then BC = 2x

then CE = 4x

angle B and angle C are right
AB/BC = BC/CE = 1/2
triangle ABC similar to triangle BCE
Call F intersection of BE and AC
Now angle EBC = FAB (similar triasngles)
Angle FCB = BEC (also same similar triangles)
BUT those angles add to 90 degrees (two angles in right triangle)
so
angle BFC = 90 degrees

• mathematics -

thanks for ur help..

## Similar Questions

1. ### geometry (maths)

ABCD is a rectangle, in which BC=2AB. A point E lies on ray CD, such that CE=2BC. Prove that BE perpendicular AC.
2. ### trig

I need to prove parallelogram law using the law of cosines. 2AB^2 + 2BC^2 = AC^2 + BD^2 Please, help me to do this.
3. ### maths --plse help me..

ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT 1) ar(EGB) = 1/6 ar(ABCD) 2)ar(EFC) = 1/2 ar(EBF) 3) ar(EBG) = ar(EFC) …
4. ### maths --plse help me..

ABCD IS A PARALLELOGRAM, G IS THE POINT ON AB SUCH THAT AG = 2GB, E IS A POINT OF CD SUCH THAT CE = 2DE AND AND F IS A POINT OF BC SUCH THAT BF = 2FC. PROVE THAT 1) ar(EGB) = 1/6 ar(ABCD) 2)ar(EFC) = 1/2 ar(EBF) 3) ar(EBG) = ar(EFC) …
5. ### maths

Given is a quadrilateral ABCD,diagonals AC and BDare such that AO=BO=CO=DO=3cm,where Ois point of intersection of AC and BD then quadrilateral ABCD is a rectangle State true or false with reason
6. ### Math (Geometry)

ABCD is a rectangle with AC=20 and AB=2BC. What is the area of rectangle ABCD?
7. ### Extended mathematics

In the diagram ,N lies on a side of the square ABCD,AM and LC are perpendicular to DN,prove that ADN=LCD.
8. ### math

Rectangle WXYZ is drawn on triangle ABC, such that point W lies on segment AB, point X lies on segment AC, and points Y and Z lies on segment BC, as shown. If <BWZ=26 degrees and <CXY=64 degrees, what is<BAC, in degrees?
9. ### Geometry

Determine the vertices of rectangle ABCD, where AB = 2BC. a) rectangle ABCD A) (0,0) B) (8,2) C (_,_) D (_,_) So far I just found the midpoint of A and B and got (4,1) but i don't know what to do after that. THe slope is 1/4, so i …
10. ### Algebra

1.The coordinates of rectangle ABCD are A(2, 2), B(2, 5), C(6, 5), and D(6, 2). Using rectangle ABCD, find the coordinates of the rectangle that results when the center of dilation is the origin and ABCD is dilated by a scale factor …

More Similar Questions