Advertisements
Advertisements
प्रश्न
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: DP : PL = DC : BL.
उत्तर
In ∆DPC and ∆BPL, we have
∠DPC = ∠BPL ...[Vertically opposite angles are equal]
∠DCP = ∠PBL ...[Alternate angles (as AB || DC) are equal]
∴ ∆DPC ~ ∆BPL ...[By A.A.]
Since the corresponding sides of similar triangles are proportional.
`(DP)/(PL) = (DC)/(BL)`
i.e., DP : PL = DC : BL
APPEARS IN
संबंधित प्रश्न
In quadrilateral ABCD, diagonals AC and BD intersect at point E such that
AE : EC = BE : ED. Show that: ABCD is a trapezium.
P is a point on side BC of a parallelogram ABCD. If DP produced meets AB produced at point L, prove that: DL : DP = AL : DC.
In the given figure, DE || BC, AE = 15 cm, EC = 9 cm, NC = 6 cm and BN = 24 cm.
- Write all possible pairs of similar triangles.
- Find lengths of ME and DM.
In ΔABC, angle ABC is equal to twice the angle ACB, and bisector of angle ABC meets the opposite side at point P. Show that: AB × BC = BP × CA
In the following figure, XY is parallel to BC, AX = 9 cm, XB = 4.5 cm and BC = 18 cm.
Find : XY
In the given figure, AB and DE are perpendiculars to BC.
Prove that : ΔABC ~ ΔDEC
Triangles ABC and DEF are similar.
If area (ΔABC) = 9 cm2, area (ΔDEF) = 64 cm2 and DE = 5.1 cm, find AB.
Triangles ABC and DEF are similar.
If area (ΔABC) = 36 cm2, area (ΔDEF) = 64 cm2 and DE = 6.2 cm, find AB.
In ΔABC, and E are the mid-points of AB and AC respectively. Find the ratio of the areas of ΔADE and ΔABC.
In the given figure ABC is a triangle with ∠EDB = ∠ACB.
(i) Prove that ΔABC ∼ ΔEBD.
(ii) If BE = 6 cm, EC = 4 cm, BD = 5 cm and area of ΔBED = 9 cm2. Calculate the length of AB and area of ΔABC.
