SUMMARY: The chapter "Practical Geometry" in Class 7 Mathematics focuses on constructing various geometric shapes using a compass and ruler. KEY TOPICS: construction of parallel lines, construction of triangles, construction of perpendicular lines, angle bisectors, constructing angles, constructing a triangle given its base, constructing a triangle given its perimeter, constructing a triangle given its altitude, constructing a triangle given its median, constructing a triangle given its angle bisector.
When constructing a triangle with sides 6 cm, 8 cm, and 10 cm, what type of triangle will it be?
AAcute triangle.
BObtuse triangle.
CRight triangle.
DScalene triangle.
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Correct answer: Option 3 — Right triangle.
Short Answer Questions5 questions
Q63 Marks
What is the first step in constructing a triangle using a compass and ruler?
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The first step is to draw a base line segment using the ruler. This segment will serve as one side of the triangle.
Q73 Marks
How do you ensure that the angles of a triangle sum up to 180 degrees when constructing it?
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You can check the angles by measuring them with a protractor after construction. The sum of the three angles should equal 180 degrees, confirming the triangle's validity.
Q83 Marks
Describe the method to construct a perpendicular bisector of a line segment.
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To construct a perpendicular bisector, place the compass point on one endpoint of the segment and draw arcs above and below the line. Repeat from the other endpoint, then connect the intersection points of the arcs to form the bisector.
Q93 Marks
What is the significance of using a protractor in practical geometry?
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A protractor is significant as it allows for accurate measurement of angles, which is essential in constructing shapes and verifying geometric properties in practical geometry.
Q103 Marks
Explain how to construct a triangle given its three sides (SSS criterion).
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To construct a triangle using the SSS criterion, first draw one side using a ruler. Then, using a compass, mark the lengths of the other two sides from each endpoint of the drawn side. Finally, connect the points where the arcs intersect to complete the triangle.
Long Answer Questions5 questions
Q116 Marks
Construct a triangle ABC where AB = 6 cm, BC = 8 cm, and CA = 7 cm. After constructing the triangle, measure the angles A, B, and C using a protractor. Explain the steps you took to construct the triangle and how you verified the measurements of the angles.
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To construct triangle ABC with sides AB = 6 cm, BC = 8 cm, and CA = 7 cm, I started by drawing a line segment BC measuring 8 cm. Next, I used a compass to draw an arc with radius 7 cm from point B and another arc with radius 6 cm from point C. The intersection of these arcs gives point A. I then connected points A, B, and C to form triangle ABC. To verify the angles, I used a protractor to measure angles A, B, and C, ensuring they added up to 180 degrees, confirming the triangle's validity.
Q126 Marks
Using a ruler and compass, construct a perpendicular bisector of a line segment AB of length 10 cm. Describe the process and explain the significance of the perpendicular bisector in geometry.
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To construct the perpendicular bisector of line segment AB measuring 10 cm, I first marked points A and B on a straight line. Then, I set the compass to more than half the length of AB and drew arcs above and below the line from points A and B. The intersections of these arcs create points C and D. Finally, I drew a line through points C and D, which is the perpendicular bisector of AB. The significance of the perpendicular bisector lies in its property that any point on this line is equidistant from points A and B, which is fundamental in various geometric constructions.
Q136 Marks
Construct a rhombus using a compass and straightedge, given one side length of 5 cm. Explain each step of your construction and how you can verify that the figure is indeed a rhombus.
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To construct a rhombus with a side length of 5 cm, I began by drawing a line segment AB of 5 cm. Next, I used a compass to draw arcs from points A and B with a radius of 5 cm, creating points C and D where the arcs intersect. I then connected points A to C, B to C, A to D, and B to D. To verify that the figure is a rhombus, I checked that all sides are equal in length (5 cm each) and that the opposite angles are equal, confirming the properties of a rhombus.
Q146 Marks
Construct a triangle with given angles of 60°, 70°, and 50°. Explain the steps involved in the construction and how you can ensure that the angles are accurate.
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To construct a triangle with angles of 60°, 70°, and 50°, I began by drawing a base line segment. I then used a protractor to mark a 60° angle at one end of the segment, labeling the vertex as A. From point A, I drew a line segment to form the angle. Next, I marked a 70° angle at the other end of the base segment, labeling this vertex as B. The intersection of the two lines gives point C. To ensure accuracy, I measured each angle with the protractor after construction, confirming they sum to 180°.
Q156 Marks
Using a compass and straightedge, construct an equilateral triangle with a side length of 4 cm. Describe the steps taken in the construction and how you can prove that the triangle is equilateral.
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To construct an equilateral triangle with each side measuring 4 cm, I started by drawing a line segment AB of 4 cm. With the compass set to 4 cm, I drew arcs from points A and B. The intersection of these arcs gives point C. I then connected points A, B, and C to form triangle ABC. To prove that the triangle is equilateral, I measured each side with a ruler, confirming that all sides are equal to 4 cm, and checked that all angles are 60° using a protractor.
Assertion–Reason Questions5 questions
Q161 Mark
Assertion (A): A triangle can be constructed if the lengths of two sides and the angle between them are known.
Reason (R): This is known as the Side-Angle-Side (SAS) criterion for triangle construction.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q171 Mark
Assertion (A): A quadrilateral can be constructed with four sides of different lengths.
Reason (R): A quadrilateral can be formed with any four line segments as long as they satisfy the triangle inequality.
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Correct answer: Option 2 —
Both A and R are true, but R is not the correct explanation of A.
Q181 Mark
Assertion (A): To construct a perpendicular bisector, you need a compass and a straightedge.
Reason (R): A perpendicular bisector divides a line segment into two equal parts at a right angle.
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Correct answer: Option 1 —
Both A and R are true, and R is the correct explanation of A.
Q191 Mark
Assertion (A): A circle can be drawn with any three points on its circumference.
Reason (R): Three points must be non-collinear to define a unique circle.
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Correct answer: Option 3 —
A is true, but R is false.
Q201 Mark
Assertion (A): It is possible to construct a triangle with sides measuring 2 cm, 3 cm, and 6 cm.
Reason (R): The sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
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Correct answer: Option 4 —
A is false, but R is true.
Statement-Based Questions5 questions
Q211 Mark
Statement 1: A triangle can be constructed if the lengths of all three sides are known.
Statement 2: A quadrilateral can be constructed if only two sides are known.
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Correct answer: Option 1 —
Both statements are true.
Q221 Mark
Statement 1: To construct a perpendicular bisector of a line segment, you need a compass and a straightedge.
Statement 2: The angle bisector of an angle divides it into two equal angles.
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Correct answer: Option 1 —
Both statements are true.
Q231 Mark
Statement 1: A circle can be drawn with a radius of any length using a compass.
Statement 2: You cannot construct a triangle with sides measuring 2 cm, 3 cm, and 6 cm.
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Correct answer: Option 1 —
Both statements are true.
Q241 Mark
Statement 1: It is possible to construct a triangle with angles measuring 30°, 60°, and 90°.
Statement 2: A rectangle can be constructed using only one side length.
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Correct answer: Option 2 —
Only Statement 1 is true.
Q251 Mark
Statement 1: The sum of the angles in any triangle is always 180°.
Statement 2: A square can be constructed with only one angle known.
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Correct answer: Option 4 —
Both statements are false.
