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If two adjacent angles of a parallelogram are in the ratio 2:4 then the measure of the angles are.
(adjacent angles are supplementary)
In a rhombus ABCD, the diagonals bisect at o. what kind of a triangle AOB is?
The triangle AOB is a right angled triangle but not an isosceles triangle
In the quadrilateral ABCD, AO and DO are the bisectors of \(\angle A \) and \(\angle D \) respectively.
If \(\angle B=90^o \) and \(\angle C=99^o \) then \(\angle AOD \) is
In a parallelogram ABCD find \(\angle CDB \) if \(\angle DAB=64^o \) and \( \angle DBC=50^o\)
(opposite angles)
In a parallelogram ABCD, \(\angle A\angle C \) is
(Opposite angles of a parallelogram are equal)
In a parallelogram ABCD if \(AB= 2x+5,\ CD=y+1,\ AD=y+5,\ BC=3x4 \)
What is the ratio of AB and BC?
Subtracting eqn (1) from (2) we get
In quadrilateral ABCD if diagonals AC and BD are equal and perpendicular to each other what is ABCD?
In square diagonals are equal and perpendicular to each other
D and E are the midpoint of AB and AC respectively of \(\triangle \)ABC. DE is produced to F. To prove that CF is equal and parallel to DA, we need an additional information which is
(given)
(V.O.A)
(SAS)
(Cpct)
So, the additional information is
The diagonals AC and BD of a parallelogram ABCD intersect each other at O. If \(\angle DAC=32^o \) and \(\angle AOB=70^o \) then \(\angle DBC \) is equal to
(alternate angle)
(Cointerior angle)
The figure obtained by joining the midpoints of the sides of a quadrilateral ABCD taken in order is a square only if
In square diagonals are equal and perpendicular.
Three angles of a quadrilateral are \( 75^o\ 90^o,75\). The fourth angle is
Let the fourth angle be x.
A diagonal of a rectangle is inclined to one side of the rectangle at \( 25^o\). The acute angle between the diagonals is
ABCD is a rhombus such that \(\angle ACB=40^o \) Then \(\angle ADB \) is
Diagonal bisect each other at right angles
(Alternate angle)
If angles A, B, C, D of quadrilateral ABCD taken in order are in the ratio \( 3:7:6:4 \) then ABCD is a
angles are
ABCD is a trapezium.
If PQ and RS are two perpendicular diameters of a circle what is PQRS?
As in square diagonals are equal and bisect at right angles.
If an angle of a parallelogram is fourfifth of its adjacent angle. Find the angles of a parallelogram.
Let one angle be x
Other angle
Two opposite angles of a parallelogram are (3p – 4) and (48 – p) what is the value of p?
Opposite angles of a parallelogram are equal.
\(\triangle \)ABC and \(\triangle \)DEF are such that AB = DE, BC = EF, AB  DE, and BC  EF. What is ADFC?
AB = DE and AB  DE
ABED is a parallelogram
BEAD and BE = AD â€¦.(1)
Given BC= EF and BC  EF
BEFC is a parallelogram
BE  CF and BE = CF â€¦..(2)
From (1) and (2) we get
AD  CF and AD = CF
So, ADFC is a parallelogram.
In the parallelogram PQRS find the measurement of \(\angle \)PSQ and \(\angle \)PQS when \(\angle \)QPS is \(55^o \) and \(\angle \)QSR is \(70^o \)
(Opposite angles are equal)
If angles P, Q, R, S of the quadrilateral PQRS taken in order are in the ratio 9:11 : 12:8 then what kind of slope does PQRS represent?
Clearly adjacent angles are supplementary but opposite angles are not equal so, it is a trapezium.
ABCD is a square A line segment DX cuts the sides BC at x and diagonal AC at O such that \(\angle \text{COD}=110^o \) and \(\angle \text{OXC}=x^o\). Find the value of x
The diagonals of a rhombus ABCD intersect at o. if AB=10 cm, BD= 16 cm find AC
ABCD is a parallelogram. The angle bisectors of \(\angle \)A and \(\angle \)D meet at a O. What is the measure of \(\angle \)AOD?
The length and breadth of a rectangle is 5 cm and 12 cm. Find the radius of circumcircle of rectangle
ABCD is a rectangle. PA = 3 cm, PB = 5 cm, PC = 3 cm. Find the value of PD.
Diagonals are equal.
AC = AP + PC = 3 + 3 = 6 cm
PD = 6 – 5 = 1 cm
In a square ABCD, E, F, G, H are the midpoint of four side. What kind of shape is represented by EFGH.
AB = BC = CD = DA
( ABCD is a square)
AE = EB
BF= FC
CG = GD
DG = HA
ABCD is a parallelogram in which p is the midpoint of CD and PA bisect \(\angle \)DAB taken
(alt. angle)
Find the measurement of angles of a parallelogram if one of its angles is \(60^o \) less than the twice of the smallest angle.
Let the smallest angle be x
Another angle
PQ is the largest side and RS is the shortest side then:
Addingâ€¦. (1) and (2) we get
In quadrilateral PQRS, \(\angle P+\angle R=140^o \) and \(\angle Q:\angle S=5:6 \). Find \(\angle Q \)
Another angle