Construction of Triangle using SAS Criteria


 
 
Concept Explanation
 

Construction of Triangle using SAS Criteria

Construction of Triangle using SAS Criteria: In SAS Triangle construction we need to know the length of two sides and an angle. But the angle should lie between the two sides or we can say should be included between the two sides.

Let us suppose we have to construct a triangle ABC and we know the length of the two sides AB and BC, moreover we know the angle B. If we draw arough sketch we see that angle B is the included angle between the side AB and BC. Hence it satifies the condition for the construction of triangle using SAS Criteria.The steps of construction are as follows:

Step 1 : Draw a line segment AB of length given to us.
Step 2 : Using protractor, draw ∠ABK = small 70^0
Step 3 : On the line segment BK, using a compass and keeping the pointer at B and radius equal to the length of BC draw an arc and mark the point as C
Step 4 : Join A and C. ΔABC is the required triangle.

 

Illustration: Construct a ΔABC, in which ∠B = small 70^0, AB = 4.8 cm and BC = 5.2 cm.

Before doing construction, draw a rough sketch, so that you will get an idea which side is taken as a base.Here after drawing a rough sketch, we are sure that the base is AB = 4.8 cm.

Step 1 : Draw AB = 4.8 cm.

Step 2 : Using protractor, draw ∠ABK = small 70^0

Step 3 : On the line segment BK, cut off BC = 5.2 cm.

Step 4 : Join A and C. ΔABC is the required triangle.

Sample Questions
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Question : 1

Arrange the following sequence of DeltaABC in which AB = 3cm, BC = 5cm, and large <B=70^0

  • (A) Cut an are on BX at a distance of 5 cm at C.
  • (B) Join AC to get the required triangle.
  • (C) Draw angleXBA = 70^0
  • (D) Draw a line segment AB of length 3 cm.
Right Option : B
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Question : 2

If in a Delta ABC, large angle A=60^0 and AB = AC then triangle ABC is _______________

Right Option : D
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Explanation
Question : 3

Arrange the following of isosceles triangle PQR in which each of the equal sides is of length 3 cm and the angle between them is 45^0 .

  • (A) Join QR to get the required triangle.
  • (B) Cut an are on PX at a distance of 3 cm at R.
  • (C) Draw a line segment PQ of length 3 cm.
  • (D) Draw large <QPX=45^0
Right Option : A
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Explanation
 
 
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