Constructions and Tilings — Class 7 Mathematics NCERT Solutions (Free)
Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Constructions and Tilings" — 6 important questions with detailed answers for CBSE board exam preparation.
TL;DR: Free step-by-step NCERT solutions for Class 7 Mathematics chapter "Constructions and Tilings" — 6 important questions with detailed answers for CBSE b…
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Key Questions Covered:
- What are the basic tools used in geometric constructions? List them and expla…
- Construct a perpendicular to a line AB at a point P on the line.
- Define line symmetry and rotational symmetry. Give examples of each.
- What are tilings (tessellations)? How do regular triangles tile a plane? Show…
- Construct an angle of 60° using compass and ruler. Explain why this construct…
- Identify and name all lines of symmetry in a square ABCD.
Solutions Summary:
| Question | Status |
|---|---|
| What are the basic tools used in geometric constructions?… | ✓ Solved |
| Construct a perpendicular to a line AB at a point P on th… | ✓ Solved |
| Define line symmetry and rotational symmetry. Give exampl… | ✓ Solved |
| What are tilings (tessellations)? How do regular triangle… | ✓ Solved |
| Construct an angle of 60° using compass and ruler. Explai… | ✓ Solved |
| Identify and name all lines of symmetry in a square ABCD. | ✓ Solved |
Showing 6 of 6 questions
Q1: What are the basic tools used in geometric constructions? List them and explain one tool's use.
Basic Tools for Geometric Constructions:
1. Ruler (Straight Edge)
Used to: Draw straight lines and measure lengths
2. Compass
Used to: Draw circles and arcs of specific radii
3. Set Square / Triangle (30-60-90 or 45-45-90)
Used to: Draw perpendicular lines and angles of 30°, 45°, 60°, 90°
4. Protractor
Used to: Measure and draw angles in degrees
5. Divider
Used to: Transfer distances and mark equal segments on lines
6. Pencil
Used to: Mark points and draw construction lines
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Detailed ...
Q2: Construct a perpendicular to a line AB at a point P on the line.
Constructing a Perpendicular to Line AB at Point P:
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Steps:
Step 1: Draw the base line
Draw a straight line AB with point P marked on it.
A ____________P____________ B
Step 2: Mark equal arcs on either side of P
Using a compass with any suitable radius:
• Place the compass needle at P
• Draw arcs on both sides of P on line AB
• Mark these intersection points as X and Y
• Now PX = PY (equidistant from P)
A ___X___P___Y___ B
Step 3: Draw arcs above and below the line
Using a compass with...
Q3: Define line symmetry and rotational symmetry. Give examples of each.
Line Symmetry (Reflection Symmetry):
Definition: A shape has line symmetry if it can be folded along a line so that both halves match exactly.
The line is called the line of symmetry or axis of symmetry.
Properties:
• The line divides the shape into two identical halves
• Each point on one side has a corresponding point on the other side
• The corresponding points are equidistant from the line of symmetry
Examples of Line Symmetry:
1. Isosceles triangle: 1 line of symmetry (vertical)
2. Recta...
Q4: What are tilings (tessellations)? How do regular triangles tile a plane? Show the arrangement.
Tilings (Tessellations):
Definition: A tiling or tessellation is a pattern of shapes that completely covers a plane without gaps or overlaps.
The shapes fit together perfectly to create a continuous pattern.
Requirements for Tiling:
1. The shapes must cover the entire plane
2. There should be no gaps between shapes
3. There should be no overlapping shapes
4. The pattern can repeat infinitely
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Regular Tilings:
Only three regular polygons can tile a plane alone:
1. Equilateral triangles
2. ...
Q5: Construct an angle of 60° using compass and ruler. Explain why this construction works.
Constructing a 60° Angle using Compass and Ruler:
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Steps of Construction:
Step 1: Draw the base ray
Draw a ray OA starting from point O.
O_____________A
Step 2: Mark an arc from point O
Using a compass with any suitable radius (say 3 cm):
• Place the compass needle at O
• Draw an arc intersecting ray OA
• Mark the intersection point as B
O___B___________A
Step 3: Draw an arc from point B
Using the SAME radius as Step 2:
• Place the compass needle at B
• Draw an arc intersecting the arc...
Q6: Identify and name all lines of symmetry in a square ABCD.
Identifying Lines of Symmetry in a Square ABCD:
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Square Setup:
Let the square have vertices:
A _______ B
| |
| |
| |
D _______ C
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Total Lines of Symmetry: A square has 4 lines of symmetry
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Line 1: Horizontal Line of Symmetry
Line through the midpoint of AB and midpoint of DC
A ___M1__ B
| | |
|____|____|
D ___M2__ C
Line: M1M2 (horizontal midline)
This line folds the square so that:
• Top half (A-B-M1-M2) matches...
Showing 6 of 6 questions. Visit the full page for complete solutions.
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