In triangle abc d is the midpoint of bc

Asked by admin @ 12/08/2021 in Math viewed by 269 People

in a triangle abc d is the midpoint of bc and e is the midpoint of ad. if be is produced meets ac in f, then prove that af=1/3ac

Answered by admin @ 12/08/2021

in triangle ABC,ADis the median .

in triangle ABC,ADis the median . E is themid point of AD. BE when produce meet ac at F. show that AF=1/3AC.

Given AD is the median of ΔABC.
E is the midpoint of AD, also BE meets AD at F after producing BE
Draw DG||BF
In ΔADG, E is the midpoint of AD and EF||DG.
By converse of midpoint theorem, we have
F is the midpoint of AG
That is AF = FG --- (1)
Similarly, in ΔBCF, D is the midpoint of BC and DG||BF
Therefore, G is the midpoint of CF
Hence FG = GC ---(2)
From equations (1) and (2), we get
AF = FG = GC --- (3)
From the figure we have, AF + FG + GC = AC
⇒ AF + AF + AF = AC [From (3)]
3AF = AC
Hence AF = (1/3) AC

In triangle abc d and e are the midpoints

Asked by maham237 @ 29/04/2021 in Mathematics viewed by 407 persons

In ABC, points D and E are the midpoints of and respectively. What are the slope and length of , if the slope and length of are 0.5 and 3.2 …

Side bc of triangle abc is produced to d

Asked by admin @ 20/08/2021 in Math viewed by 282 persons

the side of BC of triangle ABC is produced to D If the bisector of angle A meets BC in L. prove that angle abc + angle acd = 2 …

Abc is an isosceles triangle with ac bc

Asked by admin @ 29/08/2021 in Math viewed by 356 persons

ABC is an isosceles triangle with AC = BC . If AB2 = 2AC2 . Prove that abc is a right angle triangle

In triangle abc ad is perpendicular to bc

Asked by admin @ 25/08/2021 in Math viewed by 274 persons

In triangle ABC, AD is perpendicular to BC, AD^2=BD×CD. Prove that triangle is a right triangle.

Draw a triangle abc with side bc 7cm

Asked by admin @ 29/08/2021 in Math viewed by 353 persons

Draw a triangle ABC with side BC=7cm, angle B=45,angle A=105. Then construct a triangle whose sides are 4/3 times the corresponding sides of triangle abc

In triangle abc de is parallel to bc

Asked by admin @ 24/08/2021 in Math viewed by 327 persons

In a given triangle ABC,DE parallel to BC and AD/DB=3/5.If AC=5.6cm then the value of AE

In triangle abc prove that ab bc ca 2ab

Asked by admin @ 23/08/2021 in Math viewed by 346 persons

In triangle ABC prove that AB+BC+CA>2AB

In an equilateral triangle abc d is a point

Asked by admin @ 10/08/2021 in Math viewed by 312 persons

In an equilateral triangle ABC , D is a point on side BC, such that BD =1/3 BC. Prove that 9AD square = 7 AB square.

In triangle abc ad is perpendicular bisector of bc

Asked by admin @ 17/08/2021 in Math viewed by 289 persons

in angle ABC ,ad is the perpendicular bisector of BC show that angle abc is an isosceles triangle in which ab is equal to ac

Draw a triangle abc with side bc 6 cm

Asked by admin @ 13/08/2021 in Math viewed by 325 persons

Draw a triangle ABC with side BC= 6cm ,AB=5cm and <ABC=60° then construct a triangle whoss sides are 3/4 of the corresponding sides of the triangle ABC.