Triangles on the Same Base and between the Same Parallels
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This question consists of two statements, namely, Assertion (A) and Reason (R). For selecting the correct answer, use the following code:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
PQRS is a trapezium having PS and QR as parallel sides. A is any point on PQ and B is a point on SR such that AB || QR. If area of △PBQ is 17 cm^2, Find the ara of △ASR.
The point A(2, 7) lies on the perpendicular bisector of the lie segment joining the points P(6, 5) and Q(0, -4).
O is any point on the diagonal PR of a parallelogram PQRS (figure). Prove that ar (Δ PSO) = ar (Δ PQO).
Assertion: A circle is not a rectilinear figure.
Reason: A figure formed by straight lines only is called a rectilinear figure.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
(ii)
Assertion: All right angles are equal to one another.
Reason: A unique line passes through a single point.
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
In the figure X and Y are the mid points of AC and AB respectively, QP || BC and CYQ and BXP are straight lines. Prove that ar(△ABP)=ar(△ACQ).
A villager Itwaari has a plot of land of the shape of a quadrilateral. The Gram
Panchayat of the village decided to take over some portion of his plot from one of the corners to construct a Health Centre. Itwaari agrees to the above proposal with the condition that he should be given the equal amount of land in lieu of his land adjoining his plot so as to form a triangular plot. Explain how this proposal will be implemented.
The base and altitude of a triangle are 3 cm and 8 cm respectively.Find the area of the triangle.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 13 cm, 14 cm and 15 cm and the parallelogram stands on the base 14 cm, find the height of the parallelogram.
ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY).
In the adjoining figure, the diagonals AC and BD of a quadrilateral ABCD intersect at O.If BO=OD, prove that ar(△ABC)=ar(△ ADC).
ABCD is a parallelogram. P is any point on CD. If ar(△DPA)=15cm2 and ar(△APC)=20cm2, then ar(△APB) =
20cm2
15cm2
35cm2
30cm2
In the figure, ABCD is a trapezium in which AB || DC. Prove that ar(△AOD=ar(△BOC)
This question consists of two statements, namely, Assertion (A) and Reason (R).For selecting the correct answer, use the following code:
(a) Both Assertion (A) and Reason (R) are true and Reason (R) correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.
Assertion (A)Reason (R)If ABCD is a rhombus whose one Median of a triangle divides itangle is 60∘then the ratio of the into two triangles of equal area.lenghts of its diagonals is √3:1.
The correct answer is :(a) /(b)/(c)/(d).
Diagonal AC and BD of trapezium ABCD, in which AB ||DC, intersect each other at O. The triangle which is equal in area of △AOD is
△DOC
△BOC
△ADC
△AOB
Assertion: If a≠b, then (a, b)≠(b, a).
Reason: (4, −3) lies in Quadrant IV
(a) Both Assertion and Reason are true and Reason is a correct explanation of Assertion.
(b) Both Assertion and Reason are true but Reason is not a correct explanation of Assertion.
(c) Assertion is true and Reason is false.
(d) Assertion is false and Reason is true.
P, Q, R, S are respectively the midpoints of the sides AB, BC, CD and DA of ||gm ABCD.Show that PQRS is a parallelogram and also show that ar(||gm PQRS)=12ar(||gm ABCD).
The midpoints of the sides of a triangle along with any of the vertices as the fourth point makes a parallelogram of area equal to
(a) 12(ar△ ABC)
(b) 13(ar△ ABC)
(c) 14(ar△ ABC)
(d) (ar△ ABC)
In the given figure ABCD is a parallelogram. If area of parallelogram ABCD = 1728 square units, then area △ BEC = ____ square units.
- 1728 square units
- 864 square units
- 432 square units
- 400 square units
In the figure, CD || AE and CY || BA.
(i) Name a triangle equal in area of△CBX.
(ii) Prove that ar(△ZDE)=ar(△CZA).
(iii) Prove that ar (BCZY) = ar(△EDZ)
In the adjoining figure, △ ABC and △ DBC are on the same base BC with A and D on opposite sides of BC such that (△ ABC)=ar(△ DBC) Show that BC bisects AD.
The base and height of a parallelogram are 5 cm and 8 cm respectively. Find the area of the triangle formed by one of the diagonal with the adjacent sides of the parallelogram.
ABC is an isosceles triangle in which altitudes BE and CF are drawn to equal sides AC and AB respectively (see the given figure). Show that these altitudes are equal.
In the adjoining figure, ABCD is a trapezium in which AB||DC and its diagonals AC and BD intersect at O.
Prove that ar(△AOD)=ar(△ BOC).
In the adjoining figure, ABCD is a quadrilateral.A line through D, parallel to AC, meets BC produced in P.
Prove that ar(△ABP)=ar(quad. ABCD).
In the adjoining figure, BD||CA, E is the midpoint of CA and BD=12CA.Prove that ar(△ ABC)=2ar(△ DBC).
