Are two triangles congruent if two sides and an angle of one triangle are respectively equal to two sides and an angle of the other?if not then under what conditions will they be congruent?
 

Asked by shailjashubham | 28th Oct, 2014, 04:37: PM

Expert Answer:

The Side-Side-Angle condition is the ambiguous case, and two different triangles can be formed from the given information.
Consider the following figure.
Consider the triangles PQR and PQT
Since PR and PT are the radii of the circle, PR = PT.
PQ = PQ (common)
But Q R not equal to Q T
Thus increment P Q R ≄ increment P Q T
Observe the following triangles:
Two different triangles can be formed from the given information.

Therefore triangle P Q R space a n d space triangle P Q T space a r e space n o t space c o n g r u e n t.
We need some additional information such as the measure of the corresponding angles and in some cases the lengths of the two pairs of corresponding sides.
 
There are a few possible cases.
 
Consider the following example.
 
Assume that the two triangles satisfy the condition SSA.

If the length of the side opposite the angle is greater than or equal to the length of the adjacent side, then the two triangles are congruent.
 



Answered by Vimala Ramamurthy | 29th Oct, 2014, 10:09: AM

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