Moderate Level Worksheet
Part A: Subjective Questions - Very Short Answer (1 Mark Each)
Note: Answer with proper reasoning and geometric principles. Draw accurate diagrams where needed.
In this moderate level, we'll explore detailed properties, angle relationships, and problem-solving with quadrilaterals.
Let's deepen our understanding of quadrilateral properties!
1. What is the angle sum property of a quadrilateral?
The sum of all
Perfect! This is a fundamental property of all quadrilaterals.
2. Define a parallelogram.
A parallelogram is a quadrilateral in which
Excellent! Parallelograms have both pairs of opposite sides parallel.
3. Define a trapezium.
A trapezium is a quadrilateral with
Correct! Trapezium has exactly one pair of parallel sides.
4. How many diagonals does a rectangle have?
A rectangle has
These diagonals are
Great! Rectangle has 2 equal diagonals.
5. Write the difference between a rhombus and a kite.
Rhombus: All
Kite: Only
Perfect! Rhombus has all sides equal, kite has adjacent pairs equal.
6. Write the property of opposite angles in a parallelogram.
Opposite angles are
Excellent! In a parallelogram, opposite angles are always equal.
7. In a rectangle, opposite sides are
Opposite sides are
Correct! Rectangle is a special parallelogram with all angles 90°.
8. Write one example of a real-life quadrilateral.
Example:
Great! Many everyday objects are quadrilaterals.
9. Write the property of diagonals of a square.
Diagonals are
Diagonals are
Diagonals
Perfect! Square diagonals have all three properties.
10. Write the name of the quadrilateral having diagonals equal but not perpendicular.
Name:
Excellent! Rectangle has equal diagonals that are not perpendicular.
Drag each property to the correct quadrilateral:
Part A: Section B – Short Answer Questions (2 Marks Each)
1. Find the fourth angle of a quadrilateral if the other three are 70°, 90°, and 80°.
Sum of all angles =
Sum of three angles = 70 + 90 + 80 =
Fourth angle = 360 - 240 =
Perfect! The fourth angle is 120°.
2. Prove that the sum of all angles in a quadrilateral is 360°.
A quadrilateral can be divided into
Sum of angles in each triangle =
Total sum = 2 × 180 =
Excellent! This proves the angle sum property.
3. The angles of a quadrilateral are in the ratio 2 : 3 : 5 : 8. Find all angles.
Let angles be 2x, 3x, 5x, 8x
Sum = 2x + 3x + 5x + 8x =
18x =
x =
Angles are: 2×20 =
Perfect! The angles are 40°, 60°, 100°, and 160°.
4. Find the missing angle in a quadrilateral if three angles are 85°, 75°, and 95°.
Sum of three angles = 85 + 75 + 95 =
Missing angle = 360 - 255 =
Great! The missing angle is 105°.
5. Write two properties of a kite.
Property 1: Two pairs of
Property 2: One diagonal
Excellent! Kite has these special diagonal properties.
6. Write any three properties of a parallelogram.
Property 1: Opposite sides are
Property 2: Opposite angles are
Property 3: Diagonals
Perfect! These are fundamental parallelogram properties.
7. In a parallelogram ABCD, ∠A = 70°. Find ∠C.
In a parallelogram, opposite angles are
∠A and ∠C are
Therefore, ∠C =
Excellent! Opposite angles in a parallelogram are equal.
8. Write two properties of a rectangle.
Property 1: All angles are
Property 2: Diagonals are
Great! Rectangle has right angles and equal diagonals.
9. Write two similarities between a rhombus and a square.
Similarity 1: All
Similarity 2: Diagonals are
Perfect! Both have equal sides and perpendicular diagonals.
10. Write two differences between a square and a rectangle.
Square: All sides
Rectangle: Opposite sides
Square: Diagonals
Rectangle: Diagonals
Excellent! Side lengths and diagonal angles differ.
Part A: Section C – Long Answer Questions (4 Marks Each)
1. ABCD is a quadrilateral. ∠A = 80°, ∠B = 90°, ∠C = 100°. Find ∠D and verify the angle sum property.
Step 1: Find ∠D
Sum of all angles =
∠A + ∠B + ∠C + ∠D = 360°
80 + 90 + 100 + ∠D =
∠D = 360 - 270 =
Step 2: Verify
80 + 90 + 100 + 90 =
Perfect! Angle sum property verified.
2. The angles of a quadrilateral are in the ratio 1 : 2 : 3 : 4. Find all the angles.
Let angles be x, 2x, 3x, 4x
Sum = x + 2x + 3x + 4x =
10x =
x =
Angles are:
1×36 =
2×36 =
3×36 =
4×36 =
Excellent! The angles are 36°, 72°, 108°, and 144°.
3. List four properties of a parallelogram and draw a neat labeled figure.
Draw on your answer sheet with vertices A, B, C, D
Property 1: Opposite sides are
Property 2: Opposite angles are
Property 3: Adjacent angles are
Property 4: Diagonals
Perfect! These are the main parallelogram properties.
4. Compare the properties of a rectangle, rhombus, and square in a table.
Create a table with the following comparisons:
All sides equal: Rectangle -
All angles 90°: Rectangle -
Diagonals equal: Rectangle -
Diagonals perpendicular: Rectangle -
Excellent! You've compared all key properties.
5. The angles of a quadrilateral are 90°, 120°, 70°, and x°. Find x and name the possible type of quadrilateral.
Find x:
90 + 120 + 70 + x =
x =
Type: This is an
Perfect! The fourth angle is 80°, and it's an irregular quadrilateral.
Part B: Objective Questions - Test Your Knowledge!
Answer these multiple choice questions:
6. The figure with one pair of parallel sides is:
(a) Rectangle (b) Rhombus (c) Trapezium (d) Kite
Correct! Trapezium has exactly one pair of parallel sides.
7. A parallelogram with all sides equal is called:
(a) Square (b) Rectangle (c) Rhombus (d) Kite
Perfect! Rhombus is a parallelogram with all sides equal (but not all angles 90°).
8. The number of diagonals in a parallelogram is:
(a) 1 (b) 2 (c) 3 (d) 4
Correct! All quadrilaterals have exactly 2 diagonals.
9. In a square, diagonals bisect each other at:
(a) 45° (b) 60° (c) 90° (d) 120°
Excellent! Square diagonals bisect each other at right angles (90°).
10. The opposite sides of a parallelogram are:
(a) Equal (b) Perpendicular (c) Unequal (d) Parallel only
Perfect! Opposite sides are both equal AND parallel (choose "Equal" as the best answer).
🌟 Excellent Progress! You've Mastered Intermediate Quadrilaterals!
Here's what you've learned:
Angle Sum Property - Proof:
- Any quadrilateral can be divided into 2 triangles
- Each triangle has angle sum = 180°
- Total: 2 × 180° = 360°
- This proves why all quadrilaterals have angle sum 360°
Ratio Problems:
- When angles are in ratio a : b : c : d
- Let angles be ax, bx, cx, dx
- Sum: (a+b+c+d)x = 360°
- Solve for x, then find each angle
- Example: 1
3:4 → 10x = 360° → x = 36°
Detailed Properties:
Parallelogram:
- Opposite sides: equal and parallel
- Opposite angles: equal
- Adjacent angles: supplementary (sum = 180°)
- Diagonals: bisect each other
Rectangle:
- All properties of parallelogram
- All angles = 90°
- Diagonals: equal and bisect each other
Rhombus:
- All properties of parallelogram
- All sides equal
- Diagonals: perpendicular and bisect each other
Square:
- All properties of rectangle AND rhombus
- All sides equal
- All angles = 90°
- Diagonals: equal, perpendicular, bisect each other
Trapezium:
- Exactly one pair of parallel sides
- No other special properties
Kite:
- Two pairs of adjacent sides equal
- One diagonal bisects the other at 90°
Relationship Between Quadrilaterals:
- Square is a special rectangle (all sides equal)
- Square is a special rhombus (all angles 90°)
- Rectangle and Rhombus are special parallelograms
- All these are special quadrilaterals
Diagonal Properties:
- Rectangle: Equal, bisect each other
- Rhombus: Perpendicular, bisect each other
- Square: Equal, perpendicular, bisect each other
- Parallelogram: Bisect each other
- Kite: One bisects the other at 90°
Adjacent vs Opposite:
- Adjacent: Next to each other
- Opposite: Across from each other
- In parallelogram: Adjacent angles are supplementary
- In parallelogram: Opposite angles are equal
Problem-Solving Strategy:
- Identify type of quadrilateral
- List known properties
- Apply angle sum property if needed
- Use special properties of that type
- Verify answer makes sense
Real-World Applications:
- Architecture: Building design
- Engineering: Bridge structures
- Art: Tile patterns
- Sports: Court markings
- Furniture: Table tops
Mastering quadrilateral properties is essential for geometry, design, and spatial reasoning!