Advertisements
Advertisements
प्रश्न
In a triangle ABC, AD is a median and E is mid-point of median AD. A line through B and E meets AC at point F.
Prove that: AC = 3AF.
Advertisements
उत्तर
The required figure is shown below
For help, we draw a line DG || BF
Now from triangle ADG, DG || BF and E is the midpoint of AD
Therefore, F is the midpoint of AG, i.e; AF = FG ...(1)
From triangle BCF, DG || BF and D is the midpoint of BC
Therefore, G is the midpoint of CF, i.e; FG = GC …(2)
AC = AF + FG + GC
= AF + AF + AF
AC = 3AF ...(From (1) and (2))
Hence, proved.
APPEARS IN
संबंधित प्रश्न
In Fig. below, BE ⊥ AC. AD is any line from A to BC intersecting BE in H. P, Q and R are
respectively the mid-points of AH, AB and BC. Prove that ∠PQR = 90°.
Fill in the blank to make the following statement correct
The triangle formed by joining the mid-points of the sides of an isosceles triangle is
Fill in the blank to make the following statement correct:
The triangle formed by joining the mid-points of the sides of a right triangle is
In the given figure, `square`PQRS and `square`MNRL are rectangles. If point M is the midpoint of side PR then prove that,
- SL = LR
- LN = `1/2`SQ
The diagonals of a quadrilateral intersect at right angles. Prove that the figure obtained by joining the mid-points of the adjacent sides of the quadrilateral is rectangle.
D and F are midpoints of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E.
- Prove that BDFE is a parallelogram
- Find AB, if EF = 4.8 cm.
ΔABC is an isosceles triangle with AB = AC. D, E and F are the mid-points of BC, AB and AC respectively. Prove that the line segment AD is perpendicular to EF and is bisected by it.
In the given figure, PS = 3RS. M is the midpoint of QR. If TR || MN || QP, then prove that:
ST = `(1)/(3)"LS"`
P, Q, R and S are respectively the mid-points of the sides AB, BC, CD and DA of a quadrilateral ABCD such that AC ⊥ BD. Prove that PQRS is a rectangle.
P and Q are the mid-points of the opposite sides AB and CD of a parallelogram ABCD. AQ intersects DP at S and BQ intersects CP at R. Show that PRQS is a parallelogram.
