Advertisements
Advertisements
प्रश्न
In Quadrilateral ABCD, side AD || BC, diagonal AC and BD intersect in point P, then prove that `"AP"/"PD" = "PC"/"BP"`
उत्तर
Proof: seg AD || seg BC and BD is their transversal. ...[Given]
∴ ∠DBC ≅ ∠BDA ...[Alternate angles]
∴ ∠PBC ≅ ∠PDA ...(i)[D−P−B]
In ΔPBC and ΔPDA,
∠PBC ≅ ∠PDA ...[From (i)]
∠BPC ≅ ∠DPA ...[Vertically opposite angles]
∴ ΔPBC ∼ ΔPDA ...[AA test of similarity]
∴ `"BP"/"PD" = "PC"/"AP"` ...[Corresponding sides of similar triangles]
∴ `"AP"/"PD" = "PC"/"BP"` ...[By alternendo]
संबंधित प्रश्न
ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that :
- ΔADE ∼ ΔACB.
- If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.
- Find, area of ΔADE : area of quadrilateral BCED.
A line PQ is drawn parallel to the base BC of ∆ABC which meets sides AB and AC at points P and Q respectively. If AP = `1/3` PB; find the value of:
- `"Area of ΔABC"/"Area of ΔAPQ"`
- `"Area of ΔAPQ"/"Area of trapezium PBCQ"`
The corresponding sides of two similar triangles ABC and DEF are BC = 9.1cm and EF = 6.5cm. If the perimeter of ΔDEF is 25cm, find the perimeter of ΔABC.
In the given figure, DB⊥BC, DE⊥AB and AC⊥BC.
Prove that `(BE)/(DE)=(AC)/(BC)`
In the given figure, DE║BC and DE: BC = 3:5. Calculate the ratio of the areas of ΔADE and the trapezium BCED.
In the figure, parts of the two triangles bearing identical marks are
congruent. State the test by which the triangles are congruent.
ΔABC ∼ ΔDEF and A(ΔABC) : A Δ(DEF) = 1 : 2 If AB = 4 find DE.
Figure shows Δ PQR in which ST || QR and SR and QT intersect each other at M. If `"PT"/"TR" = 5/3` find `("Ar" (triangle "MTS"))/("Ar" (triangle "MQR"))`
A model of a ship is made with a scale factor of 1 : 500. Find
The length of the ship, if the model length is 60 cm.
In the following figure, point D divides AB in the ratio 3 : 5. Find :
DE = 2.4 cm, find the length of BC.
A line PQ is drawn parallel to the side BC of ΔABC which cuts side AB at P and side AC at Q. If AB = 9.0 cm, CA = 6.0 cm and AQ = 4.2 cm, find the length of AP.
In fig.DE || BC ,AD = 1 cm and BD = 2 cm. what is the ratio of the ar(ΔABC) to the ar (ΔADE)?
Let ∆ ABC ∽ ∆ DEF and their areas be respectively, 64 cm2 and 121 cm2. If EF = 15⋅4 cm, find BC.
ABCD is a parallelogram whose sides AB and BC are 18cm and 12cm respectively. G is a point on AC such that CG : GA = 3 : 5 BG is produced to meet CD at Q and AD produced at P. Prove that ΔCGB ∼ ΔAGP. Hence, fi AP.
The scale of a map is 1 : 50000. The area of a city is 40 sq km which is to be represented on the map. Find: The area of land represented on the map.
If ∆ABC is an isosceles triangle with ∠C = 90° and AC = 5 cm, then AB is
Write the test of similarity for triangles given in figure.
The ratio of the corresponding altitudes of two similar triangles is `3/5`. Is it correct to say that ratio of their areas is `6/5`? Why?
In ΔPQR, S and T are points on PQ and PR respectively. `(PS)/(SQ) = (PT)/(TR)` and ∠PST = ∠PRQ. Prove that PQR is an isosceles triangle.
In the adjoining diagram the length of PR is ______.
