In Fig. 8.11, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.
Solution:
Given, AB || DE and AB = DE
AC || DF and AC = DF
We have to prove that BC || EF and BC = EF.
Considering quadrilateral ABED,
Given, AB || DE
AB = DE
So, ABED is a parallelogram
Now, AD || BE
AD = BE ------------------------- (1)
Considering quadrilateral ACFD,
AC || FD
AC = FD
So, ACFD is a parallelogram
Now, AD || FC
AD = FC -------------------------- (2)
From (1) and (2),
AD = BE = FC
CF || BE
So, BCFE is a parallelogram.
We know that the opposite sides of a parallelogram are parallel and equal.
Now, BC = EF
BC || EF
Therefore, it is proven that BC = EF and BC || EF.
✦ Try This: In the given fig. AB ∣∣ CD, ∠BDC = 40° and ∠BAD = 75. Find x,y,z.
☛ Also Check: NCERT Solutions for Class 9 Maths Chapter 8
NCERT Exemplar Class 9 Maths Exercise 8.4 Problem 9
In Fig. 8.11, AB || DE, AB = DE, AC || DF and AC = DF. Prove that BC || EF and BC = EF.
Summary:
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure. In Fig. 8.11, AB || DE, AB = DE, AC || DF and AC = DF. It is proven that BC || EF and BC = EF
☛ Related Questions:
- E is the mid-point of a median AD of ∆ABC and BE is produced to meet AC at F. Show that AF = 1/3 AC
- Show that the quadrilateral formed by joining the mid-points of the consecutive sides of a square is . . . .
- E and F are respectively the mid-points of the non-parallel sides AD and BC of a trapezium ABCD. Pro . . . .