DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions

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The DAV Class 7 Maths Solution and DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions of Construction of Triangles offer comprehensive answers to textbook questions.

DAV Class 7 Maths Ch 10 WS 1 Solutions

Question 1.
Construct a ΔLMN in which LM = 5 cm, MN = 5.6 cm and NL = 4.2 cm.
Answer:
Steps of Construction:
DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 1

  1. Draw MN = 5.6 cm.
  2. Take M and N as centre and draw two arcs with radius 5 cm and 4.2 cm respectively.
  3. L is the point of intersection of the two arcs.
  4. Join ML and NL.
  5. ALMN is the required triangle.

Question 2.
Draw ΔDEF such that DE = DF = 4 cm and EF = 6 cm.
Answer:
Steps of Construction:
DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 2

  1. Draw EF = 6cm.
  2. Draw two arcs with centre E and F and radius 4 cm.
  3. Let the two arcs be cut at D.
  4. Join ED and FD.
  5. ΔDEF is the required triangle.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions

Question 3.
Draw an equilateral triangle one of whose sides is of length 5 cm.
Answer:
Steps of Construction:
DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 3

  1. Draw BC = 5 cm.
  2. Draw two arcs with centre B and C and with radius 5 cm.
  3. Let the two arcs be cut at A.
  4. Join AB and AC.
  5. ΔABC is the required equilateral triangle.

Question 4.
Draw A PQR in which QR = 4 cm, PQ = 3 cm, RP = 5 cm. Also draw perpendicular bisector of side PQ.
Answer:
Steps of Construction:
DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 4

  1. Draw PQ = 3 cm.
  2. Draw the arcs with centre P and Q and with radius 5 cm and 4 cm respectively.
  3. Let the two arcs be cut at R.
  4. Join PR and QR.
  5. ΔPQR is the required triangle.
  6. Draw a perpendicular bisector ST at PQ.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions

Question 5:
Is it possible to construct a triangle whose sides are 3 cm, 6.1 cm and 2.6 cm?
Answer:
To construct a triangle, the necessary condition is that the sum of any two sides of the triangle must be greater than the third side.
Here, 3 cm + 2.6 cm < 6.1 cm
⇒ 5.6 cm < 6.1 cm
Hence, triangle is not possible to construct.

Question 6.
Draw a ΔPQR in which PQ = 7 cm, QR = 3 cm, RP = 4 cm. Is the construction of triangle possible?
Answer:
Here, PQ = 7 cm, QR = 3cm and RP = 4 cm
QR + RP = PQ
3 + 4 = 7
7 = 7
∴ P, Q and R are collinear
Hence, the triangle is not possible to construct.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions

DAV Class 8 Maths Chapter 10 Worksheet 1 Notes

If A, B, C are three non-collinear points, the figure made by three line segments AB, BC and CA is called the triangle with vertex A, B, C.
The three line segments forming a triangle are called the sides of the triangle.

While constructing a triangle, the following facts are to be kept in mind.

  • The sum of the three angles of a triangle is 180°.
  • The sum of any two sides of a triangle is greater than the third side.
  • There are six components of a triangle, three angles and three sides.
  • Triangle is possible to construct if any three components are known independently.

A triangle can be constructed when

  •  All the three sides are given. (SSS triangle construction)
  • Two sides and an included angle are given. (SAS triangle construction)
  • Two angles and an included side are given. (ASA triangle construction)
  • Right angle with hypotenuse and one side are given. (RHS triangle construction)

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions

Example 1:
Construct a Δ PQR in which PQ = 3cm, PR = 4 cm and QR = 5 cm. What type of this triangle is?
Solution:
Steps of construction:

  1. Draw QR = 5 cm.
  2. Draw two arcs with radius 3 cm and 4 cm taking centres Q and R respectively to meet each other at P.
  3. Join PQ and PR.
  4. Δ PQR is the required triangle.
  5. Δ PQR is a right angled triangle.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 1

Example 2:
Construct a triangle whose any two sides are 3.5 cm and 4.5 cm and the included angle is 60°.
Solution:
Steps of Construction:

  1. Draw BC = 3.5 cm
  2. Draw ∠B = 600
  3. Cut BA = 4.5 cm B
  4. Join AC
  5. Δ ABC is the required triangle.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 2

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions

Example 3:
Construct Δ ABC in which ∠B = 60°, ∠C = 40° and BC = 4 cm.
Solution:
Steps of Construction:

  1. Draw BC = 4 cm.
  2. Draw ∠B = 60° and ∠C = 40° to meet each other at A.
  3. Δ ABC is the required triangle.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 3

Example 4:
Draw a right angle triangle whose hypotenuse is 5.5 cm and a side is 3.5 cm.
Answer:
Steps of Construction:

  1. Draw QR = 3.5 cm
  2. Draw ∠RQX = 90°
  3. Taking R as centre and radius 5.5 cm, draw an arc to meet QX at P
  4. Join PR
  5. Δ PQR is the required triangle.

DAV Class 7 Maths Chapter 10 Worksheet 1 Solutions 4