(a) चतुर्भुज LOVE मा कुन-कुन भुजाहरू बराबर भए यो समानान्तर चतुर्भुज हुन्छ ?
In quadrilateral LOVE, which sides should be equal to be a parallelogram?
[1]
(b) दिइएको समानान्तर चतुर्भुज ABCD मा BC को कुनै बिन्दु E छ । यदि DE = DC, 4 DEC = 2x° र
4 EDC = x ° भए 4 BAD को मान निकाल्नुहोस् ।
In the given parallelogram ABCD, E is any point on BC. If DE = DC, x EDC = x °, find the value of 4 BAD.
[1] Ans: 72°
(c) AB = 6.5cm ₹4ABC = 60° भएको समबाहु चतुर्भुज ABCD को रचना गर्नुहोस् ।
Construct the rhombus ABCD with AB = 6.5 cm and xABC = 60°
[2]
B
E
2xº
In quadrilateral LOVE, which sides should be equal to be a parallelogram?
[1]
(b) दिइएको समानान्तर चतुर्भुज ABCD मा BC को कुनै बिन्दु E छ । यदि DE = DC, 4 DEC = 2x° र
4 EDC = x ° भए 4 BAD को मान निकाल्नुहोस् ।
In the given parallelogram ABCD, E is any point on BC. If DE = DC, x EDC = x °, find the value of 4 BAD.
[1] Ans: 72°
(c) AB = 6.5cm ₹4ABC = 60° भएको समबाहु चतुर्भुज ABCD को रचना गर्नुहोस् ।
Construct the rhombus ABCD with AB = 6.5 cm and xABC = 60°
[2]
B
E
2xº
Answers & Comments
Answer:
In the quadrilateral LOVE, for it to be a parallelogram, the opposite sides should be equal. So, in this case, LO should be equal to VE, and OV should be equal to EL.
For part (b), in parallelogram ABCD, since DE = DC and angles 4 DEC = 2x° and 4 EDC = x°, it implies that the opposite angles in a parallelogram are equal. Therefore, 4 BAD is also equal to 2x°. Given that 4 EDC = x°, you can find the value of 4 BAD by substituting the given angle measure.
For part (c), to construct a rhombus ABCD with AB = 6.5 cm and 4 ABC = 60°, you would create a parallelogram with these given conditions. A rhombus is a type of parallelogram where all sides are equal. Therefore, construct a parallelogram with AB = 6.5 cm, and then adjust the angles to make it a rhombus by setting 4 ABC = 60°.