Question

A triangle ABC is necessarily congruent to another triangle PQR if (A) ∠A=∠P, ∠B=∠Q, ∠C=∠R (B) ∠A=∠P, ∠B=∠Q, AB =QR (c) AB =PQ, BC =QR, ∠C=∠Q (D) ∠B=∠Q, ∠C=∠R, BC =QR

Answer 1

Solution:

Option D is correct.

∠B=∠Q, ∠C=∠R, BC =QR

∆ABC congruent to ∆PQR

(By ASA Congruence rule)




It is necessary to write a correspondence of vertices correctly for writing the congruence of triangles in symbolic form.

Criteria for congruence of triangles:


There are 4 criteria for congruence of triangles.

SAS( side angle side):
Two Triangles are congruent if two sides and the included angle of a triangle are equal to the two sides and included angle of the the other triangle.


ASA(angle side angle):
Two Triangles are congruent if two angles and the included side of One triangle are equal to two angles & the included side of the  other triangle.


SSS(side side side):
Three sides of One triangle are equal to the three sides of another triangle then the two Triangles are congruent.


RHS(right angle hypotenuse side):
In two right angled triangles, the hypotenuse and one side of One triangle are equal to the hypotenuse and one side of the Other triangle, then the two Triangles are congruent.


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Hope this will help you...

Answer 2

We know that elements of one set is equal to another set if only and if they are congruent. We can say that congruent parts of congruent triangles are equal ( C.P.C.T).

A triangle ABC is necessarily congruent to another triangle PQR if
∠A = ∠ P
∠B = ∠Q
∠C = ∠R
AB =PQ
BC =QR
CA = RP.

We also know that Only angles can't determine the congruency, hence we need three sides to be equal,or two angles and included side or two sides and included angle.

Hence, Option is D