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In which of the following figures are the diagonals equal?
Rectangle has equal length of diagonals.
The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. What is the sum of largest and smallest angle of quadrilateral?
Let the angles be 3x, 5x, 9x and 13x
∴ Sum of largest and smallest angle = 3x + 13x = 16x
3x + 5x + 9x + 13x = 360°
⇒ 30x = 360° ⇒ x = 12
∴ 16x = 16 × 12° = 192°
ABCD is a parallelogram in which W, X, Y, Z are mid - points of sides AB, BC, CD and DA respectively. AC is the diagonal, then which of the following is correct?
ZY ∥ AC and YZ = 1/2 [Using mid-point theorem]
If consecutive sides of a parallelogram are equal then it is a (none of the angle ≠ 90°)
Rhombus is a parallelogram having consecutive sides equal and none of the angles equal a right angle.
The diagonals of a rectangle PQRS meet at O. If ∠QOR = 44° Then what is the measure of ∠OPS?
In ΔABC, AD is the median through A and E is the mid-point of AD. BE produced meets AC in F. Then which of the following is correct?
∵ AD is the median of ΔABC
∴ BD = DC
Through D, draw DR || BF
Now, in ΔBFC,
DR || BF and D is the mid-point of BC
∴ R should be the mid-point of FC (according to converse of mid-point theorem)
∴ FR = RC ...(i)
Similarly, in ΔADR
E is the mid-point of AD and EF || DR
∴ F should be the mid-point of AR
∴ FR = AF ...(ii)
Using (i) and (ii)
FR = RC = AF
⇒ AC = 3AF
The resulting figure obtained from joining the consecutive mid points of side of a square is
The resulting figure will be a square
Select the incorrect statement.
A kite is generally not considered a parallelogram because a kite is a quadrilateral whose four sides can be grouped into two pairs of sides of the same length that are adjacent to each other.
ABCD is a parallelogram and X, Y are the mid-points of sides AB and CD respectively, then
AB || CD, or AX || CY
∵ AX = CY and AX || CY
∴ AXCY is a parallelogram
(∴ one pair of sides are equal and parallel)
The line segment joining the mid -points of the diagonals of a trapezium is
P and Q are the mid-points of BD and AC respectively
Applying mid-point theorem
PQ ∥ AB ∥ DC, and