Q1 of 76 Page 10

In two triangles one side an acute angle of one are equal to the corresponding side and angle of the other. Prove that the triangles are congruent.


Given that in two right angle triangles one side and acute angle of one are equal to the corresponding side and angle of the other.


We have to prove that the triangles are congruent.


Let us consider two right angle triangles. Such that,


∠B = ∠E = 90o (i)


AB = DE (ii)


∠C = ∠F (iii)


Now, observe the two triangles ABC and DEF


∠C = ∠F (iv)


∠B = ∠E [From (i)]


AB = DE [From (ii)]


So, by AAS theorem, we have




Hence, proved


More from this chapter

All 76 →
2

Two lines AB and CD intersect at O such that BC is equal and parallel to AD. Prove that the lines AB and CD bisect at O.

 3

BD and CE are bisectors of ∠B and ∠C of an isosceles Δ ABC with AB = BC. Prove that BD = CE.

 2

If the bisector of the exterior vertical angle of a triangle be parallel to the base. Show that the triangle is isosceles.

 3

In an isosceles triangle, if the vertex angle is twice the sum of the base angles, calculate the angles of the triangle.