Advertisements
Advertisements
प्रश्न
In the given figure, G is the point of concurrence of medians of ΔDEF. Take point H on ray DG such that D-G-H and DG = GH, then prove that `square`GEHF is a parallelogram.
Advertisements
उत्तर
Let, the median side drawn from point D intersects EF at point M.
Point G is the concurrence point.
The concurrence point divides each median in the ratio 2:1.
∴ DG : GM = 2 : 1
∴ `("DG")/("GM") = 2/1`
∴ DG = 2GM ...(i)
∴ DG = GM + MH ...(G-M-H)
∴ 2GM = GM + MH ...[from (i)]
∴ 2GM – GM = MH
∴ GM = MH ...(ii)
In `square`GEHF,
Line GM ≅ Line MH ...[From (ii)]
Line EM ≅ Line MF ...(Point M is the midpoint of line EF)
A quadrilateral is a parallelogram if its diagonals bisect each other.
`square`GEHF is a parallelogram.
APPEARS IN
संबंधित प्रश्न
Consider the given parallelogram. Find the values of the unknowns x, y, z.
Consider the given parallelograms. Find the values of the unknowns x, y, z.
Can a quadrilateral ABCD be a parallelogram if ∠A = 70° and ∠C = 65°?
In the above figure both RISK and CLUE are parallelograms. Find the value of x.
In the given figure, `square`ABCD is a parallelogram. Point E is on the ray AB such that BE = AB then prove that line ED bisects seg BC at point F.
In the adjacent figure, if seg AB || seg PQ, seg AB ≅ seg PQ, seg AC || seg PR, seg AC ≅ seg PR then prove that, seg BC || seg QR and seg BC ≅ seg QR.
In parallelogram ABCD, ∠A = 3 times ∠B. Find all the angles of the parallelogram. In the same parallelogram, if AB = 5x – 7 and CD = 3x +1 ; find the length of CD.
In parallelogram ABCD, E is the mid-point of side AB and CE bisects angle BCD. Prove that:
- AE = AD,
- DE bisects and ∠ADC and
- Angle DEC is a right angle.
In the following diagram, the bisectors of interior angles of the parallelogram PQRS enclose a quadrilateral ABCD.
Show that:
(i) ∠PSB + ∠SPB = 90°
(ii) ∠PBS = 90°
(iii) ∠ABC = 90°
(iv) ∠ADC = 90°
(v) ∠A = 90°
(vi) ABCD is a rectangle
Thus, the bisectors of the angles of a parallelogram enclose a rectangle.
In parallelogram ABCD, X and Y are midpoints of opposite sides AB and DC respectively. Prove that:
(i) AX = YC
(ii) AX is parallel to YC
(iii) AXCY is a parallelogram.
Use the information given in the alongside diagram to find the value of x, y, and z.
Iron rods a, b, c, d, e, and f are making a design in a bridge as shown in the figure. If a || b, c || d, e || f, find the marked angles between c and f
Which of the following figures satisfy the following properties?
- All sides are congruent.
- All angles are right angles.
- Opposite sides are parallel.
Which of the following is a property of a parallelogram?
Two angles of a quadrilateral are each of measure 75° and the other two angles are equal. What is the measure of these two angles? Name the possible figures so formed.
ABCD is a parallelogram. The bisector of angle A intersects CD at X and bisector of angle C intersects AB at Y. Is AXCY a parallelogram? Give reason.
In parallelogram ABCD, the angle bisector of ∠A bisects BC. Will angle bisector of B also bisect AD? Give reason.
Construct a parallelogram HOME with HO = 6 cm, HE = 4 cm and OE = 3 cm.
Draw a rough figure of a quadrilateral that is not a parallelogram but has exactly two opposite angles of equal measure.
