SHORT QUESTIONS
1. What is a quadrilateral?
Answer: A quadrilateral is a figure with four sides because “quadri” means four and “latus” means sides.
2. What is the sum of angles in a quadrilateral?
Answer: A quadrilateral can be divided into 2 triangles → each triangle has 180° → 180° + 180° = 360°.
3. What are the angles of a rectangle?
Answer: All angles in a rectangle are right angles → each angle = 90°.
4. What is special about diagonals of a rectangle?
Answer: The diagonals are equal in length and they cut each other into two equal parts (bisect each other).
5. Define a square.
Answer: A square has all sides equal and all angles equal to 90°.
6. What is a parallelogram?
Answer: A parallelogram is a quadrilateral in which opposite sides are parallel.
7. What is the sum of adjacent angles in a parallelogram?
Answer: Adjacent angles lie on the same side of a transversal → they add up to 180°.
8. What is a rhombus?
Answer: A rhombus is a quadrilateral in which all sides are equal.
9. What is a trapezium?
Answer: A trapezium is a quadrilateral with at least one pair of parallel sides.
10. What is a kite?
Answer: A kite is a quadrilateral with two pairs of adjacent equal sides.
LONG QUESTIONS
1. Prove diagonals of a rectangle are equal
Solution:
In rectangle ABCD:
AB = CD
∠BAD = ∠CDA = 90°
AD is common
So, triangles ADC and DAB are congruent (SAS)
Therefore, AC = BD
2. Find missing angle (90°, 80°, 100°)
Solution:
Sum of angles of quadrilateral = 360°
Add given angles: 90 + 80 + 100 = 270°
Remaining angle = 360 – 270 = 90°
3. Prove opposite angles of parallelogram are equal
Solution:
Let one angle = x
Adjacent angle = 180 – x
Next angle = x
Fourth angle = 180 – x
So, opposite angles are equal
4. Find all angles of rhombus if one angle is 50°
Solution:
Opposite angles are equal
Adjacent angles = 180°
So next angle = 180 – 50 = 130°
Thus angles are 50°, 130°, 50°, 130°
5. Prove diagonals of parallelogram bisect each other
Solution:
In parallelogram ABCD, diagonals intersect at O
AB = CD
Alternate angles equal
Vertical angles equal
So triangles AOB and COD are congrent (ASA)
Therefore AO = OC and BO = OD
Leave a Reply