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About Constructions & Tessellations — Class 7 CBSE

Use ruler and compass for constructions; explore tessellation patterns. This topic is part of the CBSE Class 7 mathematics syllabus (chapter: Chapter 14). On this page you can practice 60 questions across three difficulty levels — 20 easy, 20 medium, and 20 hard — each with a visual step-by-step solution, plus a timed 35-question mastery test with a live leaderboard. Worked examples and sample questions from the topic are below.

What you'll learn in Constructions & Tessellations

  • Introduction to Geometric Constructions
  • Constructing Angles and Perpendiculars
  • Constructing Parallel Lines and Angle Bisectors
  • Introduction to Tessellations
  • Exploring Tessellations and Advanced Patterns

Interactive lesson · about 15 minutes · checkpoint question after every unit

Constructions & Tessellations — solved examples for Class 7 CBSE

Example 1easy

When constructing a line parallel to a given line 'l' through a point 'P' not on 'l', using the alternate interior angles method, which of the following properties is primarily used?
  1. A)Sum of adjacent angles is 180°
  2. B)Vertically opposite angles are equal
  3. C)Corresponding angles are equal
  4. D)Alternate interior angles are equal

Step-by-step solution

  1. The method of constructing a parallel line often involves drawing a transversal and then copying an angle at a different position.
  2. If the alternate interior angles formed by a transversal with two lines are equal, then the lines are parallel. This is the geometric principle applied in this construction method.

Answer: Alternate interior angles are equal

Example 2medium

Rohan wants to construct a line parallel to a given line 'l' passing through a point 'P' not on 'l'. He draws a line 'm' through P intersecting 'l' at Q. He then measures ∠PQl. What is the crucial next step he must perform to ensure the constructed line is parallel to 'l'?
  1. A)Draw an arc centered at Q intersecting 'l' and 'm'.
  2. B)Construct an angle equal to ∠PQl at P on line 'm' such that it forms corresponding angles with ∠PQl.
  3. C)Draw a perpendicular from P to line 'l'.
  4. D)Measure the distance between P and 'l'.

Step-by-step solution

  1. For two lines to be parallel, the corresponding angles formed by a transversal must be equal, or alternate interior angles must be equal.
  2. Rohan has drawn a transversal 'm' intersecting 'l' at Q and passing through P.
  3. To construct a line parallel to 'l' through P, he needs to construct an angle at P that is equal to ∠PQl (or an alternate interior angle) to form a pair of equal corresponding angles (or alternate interior angles).
  4. Constructing an angle equal to ∠PQl at P on line 'm' in the corresponding position will create a parallel line.

Answer: Construct an angle equal to ∠PQl at P on line 'm' such that it forms corresponding angles with ∠PQl.

Example 3hard

Ravi attempts to construct a line parallel to a given line 'l' passing through a point 'P' not on 'l'. His steps are:
1. Draw a line segment PQ, where Q is on line 'l'.
2. With Q as center, draw an arc intersecting 'l' at R and PQ at S.
3. With P as center and the *same radius*, draw an arc intersecting PQ at T.
4. Measure the chord length of arc RS with a compass.
5. With T as center and the measured chord length, draw an arc intersecting the previous arc (from step 3) at U.
6. Draw a line through P and U.
Ravi claims that line PU is parallel to 'l'. Which step, if any, contains a crucial flaw in guaranteeing parallelism?
  1. A)Step 2
  2. B)Step 3
  3. C)Step 5
  4. D)There is no flaw, the construction is correct.

Step-by-step solution

  1. The construction method described is a standard way to construct parallel lines by copying an angle (either corresponding or alternate interior).
  2. Step 2 defines the angle at Q (e.g., ∠RQS). Step 3 prepares for copying this angle at P. Step 4 measures the opening of the angle at Q.
  3. Step 5, 'With T as center and the measured chord length, draw an arc intersecting the previous arc (from step 3) at U', creates a point U. However, an arc often intersects another arc at two points.
  4. The description does not specify *which* of the two possible intersection points for U should be chosen, nor does it explicitly ensure that U is positioned to form a corresponding or alternate interior angle relative to the original angle at Q. Choosing the incorrect intersection point for U would result in a line PU that is not parallel to 'l'. This ambiguity is a crucial flaw in guaranteeing parallelism without further instruction.

Answer: Step 5

Practice questions on Constructions & Tessellations

  1. Q1.easy

    Ravi is constructing a triangle PQR where PQ = 5 cm, QR = 3 cm, and RP = 7 cm. He draws a line segment PQ of length 5 cm. What is a valid first arc he could draw to locate point R?
    1. A)An arc with center P and radius 3 cm.
    2. B)An arc with center Q and radius 3 cm.
    3. C)An arc with center P and radius 7 cm.
    4. D)An arc with center Q and radius 5 cm.
    Show answer

    Answer: An arc with center Q and radius 3 cm.

    Hint: To locate the third vertex R, you need to use the given lengths of RP and QR from their respective endpoints P and Q.

  2. Q2.easy

    Which of the following sets of side lengths CAN form a triangle?
    1. A)2 cm, 2 cm, 5 cm
    2. B)4 cm, 5 cm, 8 cm
    3. C)3 cm, 4 cm, 7 cm
    4. D)1 cm, 2 cm, 3 cm
    Show answer

    Answer: 4 cm, 5 cm, 8 cm

    Hint: Remember the triangle inequality theorem: the sum of the lengths of any two sides of a triangle must be strictly greater than the length of the third side.

  3. Q3.easy

    When constructing a triangle ABC where AB = 6 cm, BC = 5 cm, and ∠B = 60°, what is the first step after drawing the base AB?
    1. A)Draw an arc with center A and radius 5 cm.
    2. B)Draw an arc with center B and radius 6 cm.
    3. C)Draw a ray BX making an angle of 60° with AB at B.
    4. D)Draw a ray AY making an angle of 60° with AB at A.
    Show answer

    Answer: Draw a ray BX making an angle of 60° with AB at B.

    Hint: You are given two sides and the included angle (SAS criterion). After drawing one side, the next step involves using the included angle.

  4. Q4.medium

    A carpenter is asked to create a triangular wooden frame. He is given three pieces of wood measuring 8 cm, 3 cm, and 4 cm. Can he construct a unique triangular frame using these pieces?
    1. A)Yes, because all three side lengths are given.
    2. B)No, because the sum of the two shorter sides is not greater than the longest side.
    3. C)Yes, because no angle information is required for SSS criterion.
    4. D)No, because the sides are not of equal length.
    Show answer

    Answer: No, because the sum of the two shorter sides is not greater than the longest side.

    Hint: Remember the triangle inequality theorem: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

  5. Q5.medium

    Which of the following conditions is NOT sufficient to construct a unique triangle?
    1. A)Three sides (SSS criterion)
    2. B)Two sides and the included angle (SAS criterion)
    3. C)Two angles and the included side (ASA criterion)
    4. D)Two sides and a non-included angle (SSA criterion)
    Show answer

    Answer: Two sides and a non-included angle (SSA criterion)

    Hint: Consider which criteria guarantee a single, specific triangle shape and size. Some combinations can lead to multiple possible triangles.

  6. Q6.medium

    A triangular park is to be designed such that one side is 7 cm long, and the angles at its ends are 60° and 80°. To construct this triangle using the ASA criterion, what would be the measure of the third angle?
    1. A)40°
    2. B)60°
    3. C)70°
    4. D)80°
    Show answer

    Answer: 40°

    Hint: Remember the angle sum property of a triangle. The sum of all interior angles in any triangle is always 180°.

  7. Q7.hard

    A student is given three lengths: (x + 3) cm, (2x - 1) cm, and (x + 7) cm. For which range of values of 'x' is it *impossible* to construct a triangle using these lengths?
    1. A)x ≤ 5 or x < -3
    2. B)x < 1 or x > 5
    3. C)x ≤ 1 or x ≥ 5
    4. D)x < 1 or x ≥ 5
    Show answer

    Answer: x ≤ 1 or x ≥ 5

    Hint: Remember the triangle inequality theorem and that side lengths must always be positive. Consider all three side combinations and the conditions for positivity.

  8. Q8.hard

    A craftsman wants to cut out a triangular piece of wood. He measures two sides as 8 cm and 10 cm and one angle as 60°. If he uses the SAS criterion for construction, which additional piece of information is *critical* to ensure he constructs *exactly one specific* triangle, given the current measurements?
    1. A)The third side length.
    2. B)The perimeter of the triangle.
    3. C)Whether the 60° angle is included between the 8 cm and 10 cm sides.
    4. D)The area of the triangle.
    Show answer

    Answer: Whether the 60° angle is included between the 8 cm and 10 cm sides.

    Hint: Recall what the 'included angle' means in the SAS congruence criterion and why its position is important for uniqueness.

  9. Q9.hard

    A surveyor measures two angles of a plot of land, ∠P = 70° and ∠R = 50°, and one side PR as 120 m. This triangle can be constructed using ASA. However, if the side measured was PQ = 120 m instead of PR, what *additional essential step* would be required before applying the ASA criterion for construction?
    1. A)Calculate the area of the triangle PQR.
    2. B)Find the length of side QR.
    3. C)Calculate the measure of angle Q.
    4. D)Determine if the triangle is a right-angled triangle.
    Show answer

    Answer: Calculate the measure of angle Q.

    Hint: For the ASA criterion, the side must be *included* between the two given angles. If PQ is the given side, which angles are needed?

These are 9 of the 60 questions available for Constructions & Tessellations. Start practicing above to unlock visual solutions, AI coaching, and the topic leaderboard — completely free.