Abcd in rectangle -Maths 9th

Abcd in rectangle -Maths 9th
by

1 Answer

Answer :

This answer was deleted by our moderators...
by

Related questions

3. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. -Maths 9th

Description : 3. ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rhombus. -Maths 9th

Last Answer : Solution: Given in the question, ABCD is a rectangle and P, Q, R and S are mid-points of the sides AB, BC, CD and DA respectively. Construction, Join AC and BD. To Prove, PQRS is a rhombus. Proof: In ΔABC P and Q ... (ii), (iii), (iv) and (v), PQ = QR = SR = PS So, PQRS is a rhombus. Hence Proved

2. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. -Maths 9th

Description : 2. ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. Show that the quadrilateral PQRS is a rectangle. -Maths 9th

Last Answer : Solution: Given in the question, ABCD is a rhombus and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively. To Prove, PQRS is a rectangle. Construction, Join AC and BD. Proof: In ΔDRS and ... , In PQRS, RS = PQ and RQ = SP from (i) and (ii) ∠Q = 90° , PQRS is a rectangle.

ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) Diagonal BD bisects ∠B as well as ∠D. -Maths 9th

Description : ABCD is a rectangle in which diagonal AC bisects ∠A as well as ∠C. Show that: (i) ABCD is a square (ii) Diagonal BD bisects ∠B as well as ∠D. -Maths 9th

Last Answer : Solution: (i) ∠DAC = ∠DCA (AC bisects ∠A as well as ∠C) ⇒ AD = CD (Sides opposite to equal angles of a triangle are equal) also, CD = AB (Opposite sides of a rectangle) ,AB = BC = CD = AD Thus ... interior angles) ⇒ ∠CBD = ∠ABD Thus, BD bisects ∠B Now, ∠CBD = ∠ADB ⇒ ∠CDB = ∠ADB Thus, BD bisects ∠D

In figure, if parallelogram ABCD and rectangle ABEM are of equal area, then -Maths 9th

Description : In figure, if parallelogram ABCD and rectangle ABEM are of equal area, then -Maths 9th

Last Answer : (c) In rectangle ABEM, AB = EM [sides of rectangle] and in parallelogram ABCD, CD = AB On adding, both equations, we get AB + CD = EM + AB (i) We know that, the perpendicular distance between two ... AB+BE + EM+ AM [∴ CD = AB = EM] Perimeter of parallelogram ABCD > perimeter of rectangle ABEM

In figure, if parallelogram ABCD and rectangle ABEM are of equal area, then -Maths 9th

Description : In figure, if parallelogram ABCD and rectangle ABEM are of equal area, then -Maths 9th

Last Answer : (c) In rectangle ABEM, AB = EM [sides of rectangle] and in parallelogram ABCD, CD = AB On adding, both equations, we get AB + CD = EM + AB (i) We know that, the perpendicular distance between two ... AB+BE + EM+ AM [∴ CD = AB = EM] Perimeter of parallelogram ABCD > perimeter of rectangle ABEM

The dimensions of a rectangle ABCD are 51 cm x 25 cm. -Maths 9th

Description : The dimensions of a rectangle ABCD are 51 cm x 25 cm. -Maths 9th

Last Answer : According to question find the lengths QC and PD.

The dimensions of a rectangle ABCD are 51 cm x 25 cm. -Maths 9th

Description : The dimensions of a rectangle ABCD are 51 cm x 25 cm. -Maths 9th

Last Answer : According to question find the lengths QC and PD.

AC and BD are chords of a circle that bisect each other. Prove that AC and BD are diameters and ABCD is a rectangle. -Maths 9th

Description : AC and BD are chords of a circle that bisect each other. Prove that AC and BD are diameters and ABCD is a rectangle. -Maths 9th

Last Answer : Solution :- Let AC and BD bisect each other at point 0. Then, OA = OC and OB = OD In triangles AOB and COD, we have OA = OC OB = OD and ∠ AOB = ∠ COD (Vertically opposite angles) ∴ △ AOB ... ∠ADC Also, ∠BAD = 90° = ∠BCD Also, AB = CD and BC = DA (Proved above) Hence, ABCD is a rectangle.

The dimensions of a rectangle ABCD are 51 cm × 25 cm. -Maths 9th

Description : The dimensions of a rectangle ABCD are 51 cm × 25 cm. -Maths 9th

Last Answer : Area of rectangle ABCD = AB x BC = 51 x 25 = 1275 cm2 Area of trapezium PBCQ = 5/6 x 1275 = 6375/6 cm2 Let QC = 9x cm and PB = 8x cm ∴ Area of trapezium PBCQ = 1/2(QC + PB) x BC ⇒ 6375/6 = 1/2(9x + 8x) x 25 ⇒ 17x ... 6375/6 x 2/17 x 25 ⇒ x = 5 ∴ QC = 9 x 5 cm = 45 cm and PB = 8 x 5 cm = 40 cm

ABCD is a rectangle and p q r s are the mid points of the side AB BC CD AND DA respectively. Show that the quadrilateral PQRS is a rhombus -Maths 9th

Description : ABCD is a rectangle and p q r s are the mid points of the side AB BC CD AND DA respectively. Show that the quadrilateral PQRS is a rhombus -Maths 9th

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

abcd is a rectangle and bd is one of its diagonals if area of triangle abd is 8cm^2 find are of triangle bcd -Maths 9th

Description : abcd is a rectangle and bd is one of its diagonals if area of triangle abd is 8cm^2 find are of triangle bcd -Maths 9th

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

If ABCD is a rectangle and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively, then quadrilateral PQRS is a rhombus. -Maths 9th

Description : If ABCD is a rectangle and P, Q, R and S are the mid-points of the sides AB, BC, CD and DA respectively, then quadrilateral PQRS is a rhombus. -Maths 9th

Last Answer : Here, we are joining A and C. In ΔABC P is the mid point of AB Q is the mid point of BC PQ∣∣AC [Line segments joining the mid points of two sides of a triangle is parallel to AC(third side) and ... RS=PS=RQ[All sides are equal] ∴ PQRS is a parallelogram with all sides equal ∴ So PQRS is a rhombus.

A point O in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Then, show that OA^2 + OC^2 = OB^2 + OD^2. -Maths 9th

Description : A point O in the interior of a rectangle ABCD is joined with each of the vertices A, B, C and D. Then, show that OA^2 + OC^2 = OB^2 + OD^2. -Maths 9th

Last Answer : answer:

Let ABCD be a cyclic quadrilateral. Show that the incentres of the triangles ABC, BCD, CDA and DAB form a rectangle. -Maths 9th

Description : Let ABCD be a cyclic quadrilateral. Show that the incentres of the triangles ABC, BCD, CDA and DAB form a rectangle. -Maths 9th

Last Answer : answer:

In the given figure, O is the centre of the circle. The radius OP bisects a rectangle ABCD at right angles. -Maths 9th

Description : In the given figure, O is the centre of the circle. The radius OP bisects a rectangle ABCD at right angles. -Maths 9th

Last Answer : answer:

ABCD is a rectangle formed by the points A(–1, –1), B(–1, 4), C(5, 4) and D(5, –1). P, Q, R and S are mid-points -Maths 9th

Description : ABCD is a rectangle formed by the points A(–1, –1), B(–1, 4), C(5, 4) and D(5, –1). P, Q, R and S are mid-points -Maths 9th

Last Answer : (b) RhombusAB = \(\sqrt{(3-1)^2+(5-1)^2}\) = \(\sqrt{4+16}\) = \(\sqrt{20}\) = \(2\sqrt5\)BC = \(\sqrt{(1-5)^2+(1-3)^2}\) = \(\sqrt{16+4}\) = \(\sqrt{20}\) = \(2\sqrt5\)CD = \ ... = \(6\sqrt2\)Now, AB = BC = CD = AD ⇒ All sides are equal Also, AC ≠ BD ⇒ Diagonals are not equal. ⇒ ABCD is a rhombus.

If the diagonals of a parallelogram are equal, then show that it is a rectangle. -Maths 9th

Description : If the diagonals of a parallelogram are equal, then show that it is a rectangle. -Maths 9th

Last Answer : Given : A parallelogram ABCD , in which AC = BD TO Prove : ABCD is a rectangle . Proof : In △ABC and △ABD AB = AB [common] AC = BD [given] BC = AD [opp . sides of a | | gm] ⇒ △ABC ≅ △BAD [ ... ∵ ∠ABC = ∠BAD] ⇒ 2∠ABC = 180° ⇒ ∠ABC = 1 /2 180° = 90° Hence, parallelogram ABCD is a rectangle.

Give possible expression for the length and breadth of the rectangle whose area is given by 4a2 +4a - 3. -Maths 9th

Description : Give possible expression for the length and breadth of the rectangle whose area is given by 4a2 +4a - 3. -Maths 9th

Last Answer : Given, area of rectangle = 4a2 + 6a-2a-3 = 4a2 + 4a – 3 [by splitting middle term] = 2a(2a + 3) -1 (2a + 3) = (2a – 1)(2a + 3) Hence, possible length = 2a -1 and breadth = 2a + 3

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, -Maths 9th

Description : Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, -Maths 9th

Last Answer : Given, length of a rectangle = 5 units and breadth of a rectangle = 3 units One vertex is at origin i.e., (0, 0) and one of the other vertices lies in III quadrant. So, the length of the rectangle is 5 ... negative,direction of y-axis and then vertex is C(0, -3). The fourth vertex B is (-5, - 3).

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is -Maths 9th

Description : A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is -Maths 9th

Last Answer : The acute angle between the diagonals is given below.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if -Maths 9th

Description : The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if -Maths 9th

Last Answer : According to question the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle,

Diagonals of a rectangle are equal and perpendicular. Is this statement true ? -Maths 9th

Description : Diagonals of a rectangle are equal and perpendicular. Is this statement true ? -Maths 9th

Last Answer : No, diagonals of a rectangle are equal but need not be perpendicular.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. -Maths 9th

Description : Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. -Maths 9th

Last Answer : Given Let ABCD be a parallelogram and AP, BR, CR, be are the bisectors of ∠A, ∠B, ∠C and ∠D, respectively. To prove Quadrilateral PQRS is a rectangle. Proof Since, ABCD is a parallelogram, then DC ... and ∠PSR = 90° Thus, PQRS is a quadrilateral whose each angle is 90°. Hence, PQRS is a rectangle.

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.

If the diagonals of a parallelogram are equal, then show that it is a rectangle. -Maths 9th

Description : If the diagonals of a parallelogram are equal, then show that it is a rectangle. -Maths 9th

Last Answer : Given : A parallelogram ABCD , in which AC = BD TO Prove : ABCD is a rectangle . Proof : In △ABC and △ABD AB = AB [common] AC = BD [given] BC = AD [opp . sides of a | | gm] ⇒ △ABC ≅ △BAD [ ... ∵ ∠ABC = ∠BAD] ⇒ 2∠ABC = 180° ⇒ ∠ABC = 1 /2 180° = 90° Hence, parallelogram ABCD is a rectangle.

Give possible expression for the length and breadth of the rectangle whose area is given by 4a2 +4a - 3. -Maths 9th

Description : Give possible expression for the length and breadth of the rectangle whose area is given by 4a2 +4a - 3. -Maths 9th

Last Answer : Given, area of rectangle = 4a2 + 6a-2a-3 = 4a2 + 4a – 3 [by splitting middle term] = 2a(2a + 3) -1 (2a + 3) = (2a – 1)(2a + 3) Hence, possible length = 2a -1 and breadth = 2a + 3

Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, -Maths 9th

Description : Write the coordinates of the vertices of a rectangle whose length and breadth are 5 and 3 units respectively, -Maths 9th

Last Answer : Given, length of a rectangle = 5 units and breadth of a rectangle = 3 units One vertex is at origin i.e., (0, 0) and one of the other vertices lies in III quadrant. So, the length of the rectangle is 5 ... negative,direction of y-axis and then vertex is C(0, -3). The fourth vertex B is (-5, - 3).

A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is -Maths 9th

Description : A diagonal of a rectangle is inclined to one side of the rectangle at 25°. The acute angle between the diagonals is -Maths 9th

Last Answer : The acute angle between the diagonals is given below.

The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if -Maths 9th

Description : The quadrilateral formed by joining the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if -Maths 9th

Last Answer : According to question the mid-points of the sides of a quadrilateral PQRS, taken in order, is a rectangle,

Diagonals of a rectangle are equal and perpendicular. Is this statement true ? -Maths 9th

Description : Diagonals of a rectangle are equal and perpendicular. Is this statement true ? -Maths 9th

Last Answer : No, diagonals of a rectangle are equal but need not be perpendicular.

Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. -Maths 9th

Description : Prove that the quadrilateral formed by the bisectors of the angles of a parallelogram is a rectangle. -Maths 9th

Last Answer : Given Let ABCD be a parallelogram and AP, BR, CR, be are the bisectors of ∠A, ∠B, ∠C and ∠D, respectively. To prove Quadrilateral PQRS is a rectangle. Proof Since, ABCD is a parallelogram, then DC ... and ∠PSR = 90° Thus, PQRS is a quadrilateral whose each angle is 90°. Hence, PQRS is a rectangle.

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.

Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm. -Maths 9th

Description : Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm. -Maths 9th

Last Answer : We know that, each angle of a rectangle is right angle (i.e., 90°) and its opposite sides are equal and parallel. To construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm, use the ... AD and CD. Thus, ABCD is the required rectangle with adjacent sides of length 5 cm and 3.5 cm.

Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement. -Maths 9th

Description : Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement. -Maths 9th

Last Answer : It is not correct. Because in a histogram, the area of each rectangle is proportional to the corresponding frequency of its class.

Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm. -Maths 9th

Description : Construct a rectangle whose adjacent sides are of lengths 5 cm and 3.5 cm. -Maths 9th

Last Answer : To construct a triangle ABC in which AB = 3.6 cm, AC = 3.0 cm and BC = 4. 8 cm, use the following steps. 1.Draw a line segment BC of length 4.8 cm. 2.From B, point A is at a distance of 3.6 ... 3.Joining BP, we obtain angle bisector of ∠B. 4.Flere, ∠ABC=39° Thus, ∠ABD = ∠DBC = 1/2 x 139° = 19.5°

Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement. -Maths 9th

Description : Is it correct to say that in a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement. -Maths 9th

Last Answer : It is not correct. Because in a histogram, the area of each rectangle is proportional to the corresponding frequency of its class.

If the length of a rectangle is decreased by 3 units and breadth increased by 4 unit, then the area will increase by 9 sq. units. Represent this situation as a linear equation in two variables. -Maths 9th

Description : If the length of a rectangle is decreased by 3 units and breadth increased by 4 unit, then the area will increase by 9 sq. units. Represent this situation as a linear equation in two variables. -Maths 9th

Last Answer : Solution :-

Write the coordinates of the vertices of a rectangle whose lenght and breadth are 7 and 4 units respectively,one vertex atthe the origin,the longer side lies on the x-axis and one of the vertices lies in the third quadrant. -Maths 9th

Description : Write the coordinates of the vertices of a rectangle whose lenght and breadth are 7 and 4 units respectively,one vertex atthe the origin,the longer side lies on the x-axis and one of the vertices lies in the third quadrant. -Maths 9th

Last Answer : Solution :-

Write the coordinates of the vertices of a rectangle whose length and breadth are 6 and 3 units respectively, one vertex at the origin, the longer side lies on the y-axis and one of the vertices lies in the second quadrant. -Maths 9th

Description : Write the coordinates of the vertices of a rectangle whose length and breadth are 6 and 3 units respectively, one vertex at the origin, the longer side lies on the y-axis and one of the vertices lies in the second quadrant. -Maths 9th

Last Answer : Solution :-

Prove that each angle of a rectangle is a right angle. -Maths 9th

Description : Prove that each angle of a rectangle is a right angle. -Maths 9th

Last Answer : Solution :-

Prove that the bisector of the angles of a parallelogram enclose a rectangle. -Maths 9th

Description : Prove that the bisector of the angles of a parallelogram enclose a rectangle. -Maths 9th

Last Answer : Solution :-

Two parallel lines l and m are intersected by a transversal p (see Fig. 8.46). Show that the quadrilateral formed by the bisectors of interior angles is a rectangle. -Maths 9th

Description : Two parallel lines l and m are intersected by a transversal p (see Fig. 8.46). Show that the quadrilateral formed by the bisectors of interior angles is a rectangle. -Maths 9th

Last Answer : Solution :-

If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral,prove that it is a rectangle. -Maths 9th

Description : If diagonals of a cyclic quadrilateral are diameters of the circle through the vertices of the quadrilateral,prove that it is a rectangle. -Maths 9th

Last Answer : Solution :- Let, ABCD be a cyclic quadrilateral such that its diagonal AC and BD are the diameters of the circle though the vertices A,B,C and D. As angle in a semi-circle is 900 ∴ ∠ABC = 900 and ∠ADC = 900 ∠DAB = 900 ... Hence, ABCD is a rectangle.

Prove that if the opposire anles of a parallelogram are equal then it is a rectangle -Maths 9th

Description : Prove that if the opposire anles of a parallelogram are equal then it is a rectangle -Maths 9th

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

A rectangle inscribed in a triangle has its base coinciding with the base b of the triangle. If the altitude of the triangle is h, and the -Maths 9th

Description : A rectangle inscribed in a triangle has its base coinciding with the base b of the triangle. If the altitude of the triangle is h, and the -Maths 9th

Last Answer : answer:

Explain RECTANGLE: and their properties. -Maths 9th

Description : Explain RECTANGLE: and their properties. -Maths 9th

Last Answer : answer:

Prove that the angle bisectors of a parallelogram form a rectangle. -Maths 9th

Description : Prove that the angle bisectors of a parallelogram form a rectangle. -Maths 9th

Last Answer : answer:

If a rectangle and a parallelogram are equal in area and have the same base and are situated on the same side, and the ratio of the perimeter -Maths 9th

Description : If a rectangle and a parallelogram are equal in area and have the same base and are situated on the same side, and the ratio of the perimeter -Maths 9th

Last Answer : answer:

PQRS is a rectangle in which PQ = 2PS. T and U are the mid-points of PS and PQ respectively. QT and US intersect at V. -Maths 9th

Description : PQRS is a rectangle in which PQ = 2PS. T and U are the mid-points of PS and PQ respectively. QT and US intersect at V. -Maths 9th

Last Answer : answer:

Calculate the perimeter of a rectangle whose area is 25x2 – 35x + 12. -Maths 9th

Description : Calculate the perimeter of a rectangle whose area is 25x2 – 35x + 12. -Maths 9th

Last Answer : Given, Area of rectangle = 25x2 - 35x + 12 We know, area of rectangle = length breadth So, by factoring 25x2 - 35x + 12, the length and breadth can be obtained. 25x2 - 35x + 12 = 25x2 - 15x - 20x + 12 => 25x2 - 35x + ... )] = 2(5x - 3 + 5x - 4) = 2(10x - 7) = 20x - 14 So, the perimeter = 20x - 14