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Chapter Analysis
Beginner32 pages • EnglishQuick Summary
The chapter 'Playing with Constructions' explores the art of geometric constructions using a ruler and compass. It covers the construction of basic shapes such as squares and rectangles, emphasizing their properties and measurements. The chapter also tackles various problem-solving strategies related to constructing figures and the use of diagonals to divide angles equally.
Key Topics
- •Construction of squares and rectangles
- •Use of compass and ruler in geometry
- •Dividing angles and understanding diagonals
- •Geometric transformations and properties
- •Practical applications of geometric constructions
Learning Objectives
- ✓Learn to use basic geometric tools for constructions.
- ✓Understand properties and construction methods of squares and rectangles.
- ✓Develop techniques to solve practical geometric problems.
- ✓Explore the relationship between angles and side lengths in geometric figures.
- ✓Gain skills in visualizing and constructing 3D objects on a 2D plane.
Questions in Chapter
Draw a rectangle with sides of length 4 cm and 6 cm. After drawing, check if it satisfies both the rectangle properties.
Answer: ∠A = ∠B = ∠C = ∠D = 90°, AB = CD = 4 cm and AD = BC = 6 cm.
Page 197
Draw a rectangle of sides 2 cm and 10 cm. After drawing, check if it satisfies both the rectangle properties.
Answer: ∠P = ∠Q = ∠R = ∠S = 90°
Page 197
Is it possible to construct a 4-sided figure in which all the angles are equal to 90º but opposite sides are not equal?
Answer: No.
Page 197
Construct a rectangle where one of its sides is 5 cm and the length of a diagonal is 7 cm.
Page 208
Construct a rectangle one of whose sides is 4 cm and the diagonal is of length 8 cm.
Page 211
Additional Practice Questions
How do you ensure that a constructed rectangle has equal diagonals?
mediumAnswer: To ensure equal diagonals in a constructed rectangle, use the property that opposite sides must be parallel and equal. By constructing perpendiculars at corners and confirming all angles are 90°, reinforce that both diagonals bisect each other at their midpoint, ensuring they are equal.
Explain how to bisect a given angle using a compass and straightedge?
hardAnswer: To bisect a given angle, place the compass point on the angle's vertex and draw an arc that intersects both rays of the angle. Without adjusting the compass width, draw arcs from both intersection points that intersect each other. Draw a line from the vertex to the intersection of these arcs, and this line will bisect the angle.
What steps are involved in constructing a square when the length of the diagonal is known?
mediumAnswer: To construct a square when the diagonal length is known, first draw the diagonal. Using the midpoint of the diagonal, draw perpendicular bisectors to create right angles. Measure the length of half the diagonal using a compass, then place arcs from each endpoint of the diagonal along the perpendicular bisectors to form the square.
How can you construct an equilateral triangle inside a given rectangle?
mediumAnswer: To construct an equilateral triangle inside a given rectangle, ensure the side of the triangle equals the shorter side of the rectangle. Mark this side length at one corner, use the compass from each endpoint to create arcs across the rectangle, and the intersection point of arcs with equal compass width ensures the equilateral triangle.
Discuss the method of constructing a circle that passes through three non-collinear points.
hardAnswer: To construct a circle through three non-collinear points, draw two segments connecting the points. Construct perpendicular bisectors of these segments, which intersect at the circle's center. Use a compass set to the distance from the center to any of the original points to draw the circle.