Construction of Triangle using ASA Criteria


 
 
Concept Explanation
 

Construction of Triangle using ASA Criteria

Construction of Triangle using ASA Criteria: We can construct a triangle using ASA criteria only when the given side must necessarily be the one that is enclosed by the given angles . For Example if we are given the two angles as ∠CAB and ∠BCA the the side that is given should be BC. Let us say, in a triangle ABC, the measures of the angles are ∠CAB = 45 degrees and ∠ABC = 60 degrees. The length of side AB = 3cm.

To construct a triangle when two of its angles,say B and C, and the included side BC are given,we proceed as follows :

Step 1 : Draw a line segment BC.
Step 2 : Draw ∠CBX of measure equal to that of ∠B.
Step 3 : Draw ∠BCY with Y on the same side of BC as X, such that its measure is equal to that of ∠C. 
Step 4 : Let BX and CY intersect at A. Then, ΔABC is the required triangle.

Example : Construct a ΔABC in which BC = 6 cm, ∠B = small 35^0 and ∠C = small 100^0.

Step 1 : Draw a line segment BC = 6 cm.

Step 2 : Draw ∠CBX, such that ∠CBX = small 35^0

Step 3 : Draw ∠BCY with Y on the same side of BC as X such that ∠BCY = small 100^0

Step 4 : Let BX and CY intersect at A. ΔABC is the required triangle. 

Sample Questions
(More Questions for each concept available in Login)
Question : 1

If the angles of a triangle are in the ratio 1 : 2 : 7 then the triangle is _____________

Right Option : B
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Explanation
Question : 2

If two angles in a triangle are large 65^0 and large 85^0, then the third angle is ____________

Right Option : A
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Explanation
Question : 3

A triangle has _______________

Right Option : C
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Explanation
 
 
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