Theorem 5: One Pair of Opposite Sides Parallel and Equal

Q. Question 9
In figure , AB ∥ DE, AB = DE, AC ∥ DF and AC = DF . Prove that BC ∥ EF and BC = EF.

Q. Question 11 (ii)
In $\Delta ABC$ and $\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral BEFC is a parallelogram.

Q. Question 9
In figure , AB ∥ DE, AB = DE, AC ∥ DF and AC = DF . Prove that BC ∥ EF and BC = EF.

Q. Question 3
Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q. Question 11 (iv)
In $\Delta ABCand\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ACFD is a parallelogram.

Q.

Prove that if the diagonals of a parallelogram are perpendicular, then it is a rhombus. [3 MARKS]

Q. Question 11 (iv)
In $\Delta ABCand\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ACFD is a parallelogram.

Q. Question 11 (v)
In $\Delta ABCand\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC ⃦EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that AC = DF .

Q. Question 11 (i)
In $\Delta ABC$ and $\Delta DEF$ , AB=DE, AB || DE, BC =EF and BC || EF. Vertices A, B and C are joined to vertices D, E and F respectively ( see the given figure). Show that Quadrilateral ABED is a parallelogram.

Q. In figure, AB ∥ DE, AB = DE, AC ∥ DF and AC = DF. Then, BC ∥ EF and BC = EF.

1. True
2. False

Q.

In figure, AB ∥ DE, AB = DE, AC ∥ DF and AC = DF. Then, BC ∥ EF and BC = ___ .

1. EF
2. BE
3. CF
4. AD

Q. In $\Delta ABCand\Delta DEF$, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B, and C are joined to vertices D, E and F respectively ( see the given figure). Then, quadrilateral ACFD:

1. $isarhombus$
2. $isaparallelogram$
3. $isarectangle$
4. $Noneoftheabove$

Q.

In $\Delta ABCand\Delta DEF$, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B, and C are joined to vertices D, E and F respectively ( see the given figure).

1. $AC||DF$

2. $AC=DF$

3. The relation between AB and DF can't be determined

4. None of these

Q. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q.

In $\Delta ABCand\Delta DEF$, AB = DE, AB || DE, BC = EF and BC || EF. Vertices A, B, and C are joined to vertices D, E and F respectively ( see the given figure). Then, quadrilateral ACFD:

1. is a rectangle

2. is a rhombus

3. is a parallelogram

4. None of the above

Q. Question 4
The quadrilateral formed by joining the mid – points of the sides of a quadrilateral PQRS, taken in order, is a rectangle, if
(A) PQRS is a rectangle
(B) PQRS is a parallelogram
(C) diagonals of PQRS are perpendicular
(D) diagonals of PQRS are equal

Q. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q. Show that if the diagonals of a quadrilateral bisect each other at right angles, then it is a rhombus.

Q.

$ \mathrm{ABCD}$ is a trapezium in which $ \mathrm{AB} \left|\right| \mathrm{DC}, \mathrm{BD}$ is a diagonal and $ \mathrm{E}$ is the mid-point of $ \mathrm{AD}$. A line is drawn through $ \mathrm{E} $parallel to $ \mathrm{AB}$ intersecting $ \mathrm{BC}$ at $ \mathrm{F}$ (see Fig.) . Show that $ \mathrm{F} $is the mid-point of $ \mathrm{BC}.$