The diagonal of the parallelogram made by two vectors as adjacent sides is not passing through common point of two vectors. What does it represent?

The diagonal of the parallelogram made by two vectors as adjacent sides is not passing through common point of two vectors. What does it represent?
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The diagonal of the parallelogram made by two vectors as adjacent sides is not passing through common point of two vectors. What does it represent?
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If A = i + 2j + 3k and B = 3i - 2j + k, then the area of parallelogram formed from these vectors as the adjacent sides will be

Description : If A = i + 2j + 3k and B = 3i - 2j + k, then the area of parallelogram formed from these vectors as the adjacent sides will be

Last Answer : If A = i + 2j + 3k and B = 3i - 2j + k, then the area of parallelogram formed from these ... units (C) 6√3 square units (D) 8√3 square units

5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD. -Maths 9th

Description : 5. In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively (see Fig. 8.31). Show that the line segments AF and EC trisect the diagonal BD. -Maths 9th

Last Answer : . Solution: Given that, ABCD is a parallelogram. E and F are the mid-points of sides AB and CD respectively. To show, AF and EC trisect the diagonal BD. Proof, ABCD is a parallelogram , AB || CD also, ... (i), DP = PQ = BQ Hence, the line segments AF and EC trisect the diagonal BD. Hence Proved.

ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram. -Maths 9th

Description : ABCD is a quadrilateral in which P, Q, R and S are mid-points of the sides AB, BC, CD and DA (see Fig 8.29). AC is a diagonal. Show that: (i) SR || AC and SR = 1/2 AC (ii) PQ = SR (iii) PQRS is a parallelogram. -Maths 9th

Last Answer : . Solution: (i) In ΔDAC, R is the mid point of DC and S is the mid point of DA. Thus by mid point theorem, SR || AC and SR = ½ AC (ii) In ΔBAC, P is the mid point of AB and Q is the mid point of BC. ... ----- from question (ii) ⇒ SR || PQ - from (i) and (ii) also, PQ = SR , PQRS is a parallelogram.

The middle points of the parallel sides AB and CD of a parallelogram ABCD are P and Q respectively. If AQ and CP divide the diagonal BD -Maths 9th

Description : The middle points of the parallel sides AB and CD of a parallelogram ABCD are P and Q respectively. If AQ and CP divide the diagonal BD -Maths 9th

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The lengths of two adjacent sides of a parallelogram are 17 cm and 12 cm. -Maths 9th

Description : The lengths of two adjacent sides of a parallelogram are 17 cm and 12 cm. -Maths 9th

Last Answer : For △BCD: Let a = 17 cm, b = 12 cm, c = 25 cm So its semi-perimeter, s = (a + b + c)/2 = (17 + 12 + 25)/2 = 27 cm ∴ Area of △BCD = root under(√(s -a)(s - b)(s - c)) = ... △BCD = 2 x 90 = 180 cm2 Also, area of parallelogram ABCD = DC x AE ∴ 180 = 12 x AE ⇒ AE = 180/12 = 15 cm

Prove that the figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a parallelogram. -Maths 9th

Description : Prove that the figure formed by joining the mid-points of the adjacent sides of a quadrilateral is a parallelogram. -Maths 9th

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A cyclic parallelogram having unequal adjacent sides is necessarily a: -Maths 9th

Description : A cyclic parallelogram having unequal adjacent sides is necessarily a: -Maths 9th

Last Answer : answer:

The adjacent sides of a parallelogram are 2a and a. If the angle between them is 60°, then one of the diagonals of the parallelogram is -Maths 9th

Description : The adjacent sides of a parallelogram are 2a and a. If the angle between them is 60°, then one of the diagonals of the parallelogram is -Maths 9th

Last Answer : answer:

O is any point on the diagonal PR of a parallelogram PQRS. -Maths 9th

Description : O is any point on the diagonal PR of a parallelogram PQRS. -Maths 9th

Last Answer : Join QS. Let diagonals PR and QS intersect each other at T. We know, that diagonals of a parallelogram bisect each other . ∴ T is the mid - point of QS. Since a median of a triangle divides it into two triangles of equal ... ar(△PTS) + ar( △STO) = ar(△PQT) = ar( △ QTO ) ⇒ ar(△PSO) = ar(△PQO)

O is any point on the diagonal PR of a parallelogram PQRS (figure). -Maths 9th

Description : O is any point on the diagonal PR of a parallelogram PQRS (figure). -Maths 9th

Last Answer : According to question prove that ar(ΔPSO) = ar(ΔPQO).

O is any point on the diagonal PR of a parallelogram PQRS. -Maths 9th

Description : O is any point on the diagonal PR of a parallelogram PQRS. -Maths 9th

Last Answer : Join QS. Let diagonals PR and QS intersect each other at T. We know, that diagonals of a parallelogram bisect each other . ∴ T is the mid - point of QS. Since a median of a triangle divides it into two triangles of equal ... ar(△PTS) + ar( △STO) = ar(△PQT) = ar( △ QTO ) ⇒ ar(△PSO) = ar(△PQO)

O is any point on the diagonal PR of a parallelogram PQRS (figure). -Maths 9th

Description : O is any point on the diagonal PR of a parallelogram PQRS (figure). -Maths 9th

Last Answer : According to question prove that ar(ΔPSO) = ar(ΔPQO).

PQRS is a parallelogram whose area is 180 cm2 and A is any point on the diagonal QS. The area of △ASR = 90 cm2. Find this statement is true or false. -Maths 9th

Description : PQRS is a parallelogram whose area is 180 cm2 and A is any point on the diagonal QS. The area of △ASR = 90 cm2. Find this statement is true or false. -Maths 9th

Last Answer : Solution :- As diagonal of the parallelogram divides it into two triangles of equal area. Since, area (△SRQ ) = 1/2 area(PQRS) area (△SRQ ) = 1/2 x 180 ... = 90 cm2 (Given) This is not possible unless area (△SRQ ) = area (△ASR ) So, the given statement is false.

P and O 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. -Maths 9th

Description : P and O 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. -Maths 9th

Last Answer : According to question PQ passes through the point of intersection O of its diagonals AC and BD.

P and O 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. -Maths 9th

Description : P and O 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. -Maths 9th

Last Answer : According to question PQ passes through the point of intersection O of its diagonals AC and BD.

Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two vectors.

Description : Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two vectors.

Last Answer : Show that magnitude of vector product of two vectors is numerically equal to the area of a parallelogram formed by the two vectors.

The vector product of two vectors is given by area of the parallelogram. State True/False. a) True b) False

Description : The vector product of two vectors is given by area of the parallelogram. State True/False. a) True b) False

Last Answer : a) True

Prove that a diagonal of a parallelogram divide it into two congruent triangles. -Maths 9th

Description : Prove that a diagonal of a parallelogram divide it into two congruent triangles. -Maths 9th

Last Answer : Given: A parallelogram ABCD and AC is its diagonal . To prove : △ABC ≅ △CDA Proof : In △ABC and △CDA, we have ∠DAC = ∠BCA [alt. int. angles, since AD | | BC] AC = AC [common side] and ∠BAC = ∠DAC [alt. int. angles, since AB | | DC] ∴ By ASA congruence axiom, we have △ABC ≅ △CDA

Prove that a diagonal of a parallelogram divide it into two congruent triangles. -Maths 9th

Description : Prove that a diagonal of a parallelogram divide it into two congruent triangles. -Maths 9th

Last Answer : Given: A parallelogram ABCD and AC is its diagonal . To prove : △ABC ≅ △CDA Proof : In △ABC and △CDA, we have ∠DAC = ∠BCA [alt. int. angles, since AD | | BC] AC = AC [common side] and ∠BAC = ∠DAC [alt. int. angles, since AB | | DC] ∴ By ASA congruence axiom, we have △ABC ≅ △CDA

Prove that the diagonal divides a parallelogram into two congruent triangles. -Maths 9th

Description : Prove that the diagonal divides a parallelogram into two congruent triangles. -Maths 9th

Last Answer : Solution :-

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ -Maths 9th

Description : ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD (see Fig. 8.21). Show that (i) ΔAPB ≅ ΔCQD (ii) AP = CQ -Maths 9th

Last Answer : Q Solution: (i) In ΔAPB and ΔCQD, ∠ABP = ∠CDQ (Alternate interior angles) ∠APB = ∠CQD (= 90o as AP and CQ are perpendiculars) AB = CD (ABCD is a parallelogram) , ΔAPB ≅ ΔCQD [AAS congruency] (ii) As ΔAPB ≅ ΔCQD. , AP = CQ [CPCT]

Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus. -Maths 9th

Description : Diagonal AC of a parallelogram ABCD bisects ∠A (see Fig. 8.19). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus. -Maths 9th

Last Answer : . Solution: (i) In ΔADC and ΔCBA, AD = CB (Opposite sides of a parallelogram) DC = BA (Opposite sides of a parallelogram) AC = CA (Common Side) , ΔADC ≅ ΔCBA [SSS congruency] Thus, ∠ACD = ∠CAB by ... are equal) Also, AB = BC = CD = DA (Opposite sides of a parallelogram) Thus, ABCD is a rhombus.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . -Maths 9th

Description : ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . -Maths 9th

Last Answer : In gm ABCD , AP and CQ are perpendicular from the vertices A and C on diagonal BD. Show that : (i) AAPB ≅ ACQD (ii) AP = CQ .

In quadrilateral ABCD of the given figure, X and Y are points on diagonal AC such that AX = CY and BXDY ls a parallelogram. -Maths 9th

Description : In quadrilateral ABCD of the given figure, X and Y are points on diagonal AC such that AX = CY and BXDY ls a parallelogram. -Maths 9th

Last Answer : This answer was deleted by our moderators...

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. -Maths 9th

Description : E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. -Maths 9th

Last Answer : According to question diagonal AC of a parallelogram ABCD such that AE = CF.

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus. -Maths 9th

Description : A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus. -Maths 9th

Last Answer : According to question parallelogram bisects one of its angles.

ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . -Maths 9th

Description : ABCD is a parallelogram and AP and CQ are perpendiculars from vertices A and C on diagonal BD . -Maths 9th

Last Answer : In gm ABCD , AP and CQ are perpendicular from the vertices A and C on diagonal BD. Show that : (i) AAPB ≅ ACQD (ii) AP = CQ .

In quadrilateral ABCD of the given figure, X and Y are points on diagonal AC such that AX = CY and BXDY ls a parallelogram. -Maths 9th

Description : In quadrilateral ABCD of the given figure, X and Y are points on diagonal AC such that AX = CY and BXDY ls a parallelogram. -Maths 9th

Last Answer : This answer was deleted by our moderators...

E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. -Maths 9th

Description : E and F are points on diagonal AC of a parallelogram ABCD such that AE = CF. -Maths 9th

Last Answer : According to question diagonal AC of a parallelogram ABCD such that AE = CF.

A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus. -Maths 9th

Description : A diagonal of a parallelogram bisects one of its angles. Show that it is a rhombus. -Maths 9th

Last Answer : According to question parallelogram bisects one of its angles.

In Fig. 8.37, ABCD is a parallelogram and P, Q are the points on the diagonal BD such that BQ = DP. Show what APCQ is a parallelogram. -Maths 9th

Description : In Fig. 8.37, ABCD is a parallelogram and P, Q are the points on the diagonal BD such that BQ = DP. Show what APCQ is a parallelogram. -Maths 9th

Last Answer : Solution :-

Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus -Maths 9th

Description : Diagonal AC of a parallelogram ABCD bisects ∠A (see figure). Show that (i) it bisects ∠C also, (ii) ABCD is a rhombus -Maths 9th

Last Answer : (i) Here, ABCD is a parallelogram and diagonal AC bisects ∠A. ∴ ∠DAC=∠BAC ---- ( 1 ) Now, AB∥DC and AC as traversal, ∴ ∠BAC=∠DCA [ Alternate angles ] --- ( 2 ) AD∥BC and AAC as traversal, ∴ ∠DAC= ... ---- ( 2 ) From ( 1 ) and ( 2 ), ⇒ AB=BC=CD=DA Hence, ABCD is a rhombus.

ABCD is a parallelogram with diagonal AC If a line XZ is drawn such that XZ ∥ AB, then BX/XC = ? (a) (AY/AC) (b) DZ/AZ (c) AZ/ZD (d) AC/AY Answer: (c) AZ/ZD 13. In the given figure, value of x (in cm) is (a) 5cm (b) 3.6 cm (c) 3.2 cm (d) 10 cm

Description : ABCD is a parallelogram with diagonal AC If a line XZ is drawn such that XZ ∥ AB, then BX/XC = ? (a) (AY/AC) (b) DZ/AZ (c) AZ/ZD (d) AC/AY Answer: (c) AZ/ZD 13. In the given figure, value of x (in cm) is (a) 5cm (b) 3.6 cm (c) 3.2 cm (d) 10 cm

Last Answer : (a) 5cm

A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. -Maths 9th

Description : A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in figure. -Maths 9th

Last Answer : Each shade of paper is divided into 3 triangles i.e., I, II, III 8 cm For triangle I: ABCD is a square [Given] ∵ Diagonals of a square are equal and bisect each other. ∴ AC = BD = 32 cm Height of AABD ... are: Area of shade I = 256 cm2 Area of shade II = 256 cm2 and area of shade III = 17.92 cm2

If an angle of a parallelogram is two - third of its adjacent angle , then find the smallest angle of the parallelogram . -Maths 9th

Description : If an angle of a parallelogram is two - third of its adjacent angle , then find the smallest angle of the parallelogram . -Maths 9th

Last Answer : In a parallelogram ABCD, Let ∠A be x and ∠B be 2x / 3 ∴ ∠A + ∠B = 180° ⇒ x + 2x / 3 = 180° ⇒ 5x / 3 = 180° ⇒ x° = 180° × 3 / 5 = 108° ∠A = 108° , ∠B = 2 / 3 × 108° = 72°

In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. -Maths 9th

Description : In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. -Maths 9th

Last Answer : Given : A parallelogram ABCD such that the bisectors of adjacent angles A and B intersect at P. To prove : ∠APB = 90° Proof : Since ABCD is a | | gm ∴ AD | | BC ⇒ ∠A + ∠B = 180° [sum of consecutive interior ... 90° + ∠APB + ∠2 = 180° [ ∵ ∠1 + ∠2 = 90° from (i)] Hence, ∠APB = 90°

If an angle of a parallelogram is two - third of its adjacent angle , then find the smallest angle of the parallelogram . -Maths 9th

Description : If an angle of a parallelogram is two - third of its adjacent angle , then find the smallest angle of the parallelogram . -Maths 9th

Last Answer : In a parallelogram ABCD, Let ∠A be x and ∠B be 2x / 3 ∴ ∠A + ∠B = 180° ⇒ x + 2x / 3 = 180° ⇒ 5x / 3 = 180° ⇒ x° = 180° × 3 / 5 = 108° ∠A = 108° , ∠B = 2 / 3 × 108° = 72°

In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. -Maths 9th

Description : In a parallelogram, show that the angle bisectors of two adjacent angles intersect at right angles. -Maths 9th

Last Answer : Given : A parallelogram ABCD such that the bisectors of adjacent angles A and B intersect at P. To prove : ∠APB = 90° Proof : Since ABCD is a | | gm ∴ AD | | BC ⇒ ∠A + ∠B = 180° [sum of consecutive interior ... 90° + ∠APB + ∠2 = 180° [ ∵ ∠1 + ∠2 = 90° from (i)] Hence, ∠APB = 90°

Two adjacent angles of a ||gm are in the ratio 2:3. Find all the four angles of the parallelogram. -Maths 9th

Description : Two adjacent angles of a ||gm are in the ratio 2:3. Find all the four angles of the parallelogram. -Maths 9th

Last Answer : Solution :-

If one of a parallelogram is twice of its adjacent angle , find the angles of the parallelogram . -Maths 9th

Description : If one of a parallelogram is twice of its adjacent angle , find the angles of the parallelogram . -Maths 9th

Last Answer : Let the two adjacent angles be x° and 2x° . In a parallelogram, sum of the adjacent angles are 180°. ∴ x + 2x = 180° ⇒ 3x = 180° ⇒ x = 60° Thus , the two adjacent angles are 120° and 60°. Hence, the angles of the parallelogram are 120°, 60°, 120° and 60°.

If one of a parallelogram is twice of its adjacent angle , find the angles of the parallelogram . -Maths 9th

Description : If one of a parallelogram is twice of its adjacent angle , find the angles of the parallelogram . -Maths 9th

Last Answer : Let the two adjacent angles be x° and 2x° . In a parallelogram, sum of the adjacent angles are 180°. ∴ x + 2x = 180° ⇒ 3x = 180° ⇒ x = 60° Thus , the two adjacent angles are 120° and 60°. Hence, the angles of the parallelogram are 120°, 60°, 120° and 60°.

The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to -Maths 9th

Description : The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to -Maths 9th

Last Answer : Solution of this question

The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to -Maths 9th

Description : The mid-point of the sides of a triangle along with any of the vertices as the fourth point make a parallelogram of area equal to -Maths 9th

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What is the volume of a parallelepiped whose sides are given by the vectors a 3i plus wj plus k b -i plus 3j and c 2i plus 2j plus 5k?

Description : What is the volume of a parallelepiped whose sides are given by the vectors a 3i plus wj plus k b -i plus 3j and c 2i plus 2j plus 5k?

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A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. -Maths 9th

Description : A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. -Maths 9th

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A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. -Maths 9th

Description : A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs. -Maths 9th

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All electric cables passing through watertight bulkheads must be _____________. A. installed with watertight stuffing tubes B. grounded on both sides of the bulkhead C. fitted with unions on each side of the bulkhead D. welded on both sides of the bulkhead

Description : All electric cables passing through watertight bulkheads must be _____________. A. installed with watertight stuffing tubes B. grounded on both sides of the bulkhead C. fitted with unions on each side of the bulkhead D. welded on both sides of the bulkhead

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If two adjacent sides of a kite are 5cm and 7cm, find its perimeter. -Maths 9th

Description : If two adjacent sides of a kite are 5cm and 7cm, find its perimeter. -Maths 9th

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A rhombus has sides of length 1 and area 1/2 Find the angle between the two adjacent sides of the rhombus -Maths 9th

Description : A rhombus has sides of length 1 and area 1/2 Find the angle between the two adjacent sides of the rhombus -Maths 9th

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The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is -Maths 9th

Description : The figure obtained by joining the mid-points of the adjacent sides of a rectangle of sides 8 cm and 6 cm, is -Maths 9th

Last Answer : Here, length of rectangle ABCD = 8 cm and breadth of rectangle ABCD = 6.cm Let E, F, G and H are the mid-points of the sides of rectangle ABCD, then EFGH is a rhombus.