Review: Constructions And Tilings — Ganita Prakash: Class 7 Mathematics, Part 2 (NCERT)

What You Can Do Now

Tick what you can now construct and explain.

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After this chapter, I can…

Chapter in One Card

The key facts of the chapter.

Constructions and tilings (Textbook p. 163)

Bisection: dividing something into two identical parts.

Any point equally far from X and Y lies on the perpendicular bisector of XY. This gives the ruler-and-compass construction.

The same method gives 90° at any point on a line.

Angles can be bisected and copied using congruent triangles (SSS).

60° comes from constructing an equilateral triangle.

Tiling: covering a region with shapes, without gaps or overlaps. A domino tiling needs equal black and white squares.

Key Terms From This Chapter

Flip through the key constructions and reasons.

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Questions From the Whole Chapter

Eight questions from quick recall to harder reasoning.

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Which tools are used for the constructions in this chapter?

Step-by-Step Construction Challenges

Three constructions with guided steps.

Plan, construct and justify

Construct a 75° angle.
Construct a regular hexagon of side 3.5 cm, and a six-pointed star on it.
Draw a line and a point P about 4 cm from it. Construct the line through P parallel to the first line, and then the perpendicular from P to it.

75°: your plan and steps

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Which angles can you combine?

Hexagon and star: your steps

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Parallel and perpendicular through P: your steps

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Solve It Yourself

Four problems from the chapter, no hints.

Solve each problem

When constructing the perpendicular bisector, must the radius be the same above and below XY? Explain. (Textbook p. 140, Q1)
Around a point there are angles of 40°, 60°, 50°, 30°, 40° and 90°. Find the gap angle. Will a 70° angle fit? (p. 152)
Can a 5 × 3 grid with one corner removed be tiled with dominoes? Show a tiling. (p. 158)
Prove that a chessboard with two opposite corners removed can't be tiled with dominoes. (p. 160, Q2)

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Talk it through: construction doubts

Stuck on a construction step or a tiling puzzle? Ask here.

Learners can ask follow-up questions and keep the thread going.

Ask me anything from this chapter: why the arcs must be wider than half of XY, which radii must match, why SSS and SAS prove the constructions, how to get 30°, 15° or 75°, why 65.5° can't be made by bisecting, the chessboard colouring trick, or why only three regular polygons tile the plane. Tell me what you're constructing and where you're stuck.

almost 3 years ago