prove that if two angles and one side of a triangle are equal to two angles and one side of another triangle. The triangles are congruent. Also check if the given pair of triangles are congruent?
Answers
Step-by-step explanation:
Consider two triangles, ΔABC and ΔPQR.
If two angles are equal, let those are A, B wrt P,Q.
So, A = P ; B = Q
Using 'sum of all angles = 180*', we can say the other angles will be:
180 - A - B and 180 - P - Q, since A = P, B = Q,
⇒ 180 - A - B = 180 - P - Q
Remaining angles are also equal, to each other. [ ∠C = ∠R ]
But, angles are equal, this can't prove them congruent.
Example:
Draw 2 triangles. One of length 3, 4, 5. Another of 6,8, 10. And measure the angles. Those will satisfy the equality of one angle in 1st triangle wrt 2nd triangle. But in both, lengths are not same. Hence, we can't say these triangles are congruent. To be congruent, length of at least one side must be given same.
Consider a triangle of lengths 3,4,5. And another of 4,5,3. In this condition, If the angles are same, triangles will be same shape and size. And then, they are congruent.