Advertisements
Advertisements
प्रश्न
In a parallelogram ABCD, AB = 10 cm and AD = 6 cm. The bisector of ∠A meets DC in E. AE and BC produced meet at F. Find the length of CF.
Advertisements
उत्तर
Given, AB = 10 cm, AD = 6 cm
DC = AB = 10 cm and AD = BC = 6 cm
Given, bisector of ∠A intersects DE at E and BC produced at F.
Now, drawing PF || CD.
From the figure,
CD || FP and CF || DP
PDCF is a parallelogram.
And AB || FP and AP || BF
ABFP is also a parallelogram
In ΔAPF and ΔABF
∠APF = ∠ABF ...(Opposite angles of a parallelogram are equal)
AF = AF ...(Common side)
∠PAF = ∠AFB ...(Alternate angles)
ΔAPF ≅ ΔABF ...(By ASA congruence criterion)
AB = AP ...(CPCT)
AB = AD + DP
= AD + CF ...(Since DCFP is a parallelogram)
∴ CF = AB – AD
= (10 – 6) cm
= 4 cm
APPEARS IN
संबंधित प्रश्न
The diagonals AC and BD of a parallelogram ABCD intersect each other at the point O. If ∠DAC = 32º and ∠AOB = 70º, then ∠DBC is equal to ______.
Diagonals of a parallelogram are perpendicular to each other. Is this statement true? Give reason for your answer.
Diagonals of a quadrilateral ABCD bisect each other. If ∠A = 35º, determine ∠B.
In the following figure, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.
P and Q are points on opposite sides AD and BC of a parallelogram ABCD such that PQ passes through the point of intersection O of its diagonals AC and BD. Show that PQ is bisected at O.
ABCD is a rectangle in which diagonal BD bisects ∠B. Show that ABCD is a square.
P is the mid-point of the side CD of a parallelogram ABCD. A line through C parallel to PA intersects AB at Q and DA produced at R. Prove that DA = AR and CQ = QR.
If diagonals of a quadrilateral bisect each other, it must be a parallelogram.
The point of intersection of diagonals of a quadrilateral divides one diagonal in the ratio 1:2. Can it be a parallelogram? Why or why not?
