find whether the given pair of triangles are congruent or not if the Triangles are congruent write them in symbolic form
Answers
Answers:
Figure A
In ΔABC and ΔPQR
∠C = ∠R
CB = PR
CA ≠ RQ
So, ΔABC and ΔPQR are not congruent.
Figure B
In ΔABC and ΔPQR
∠A = ∠P [90°]
AB = PQ
BC = QR
So, ΔABC and ΔPQR are congruent. -------- ΔABC ≅ ΔPQR [RHS congruency]
Figure C
In ΔABC and ΔPQR
∠A = ∠P
∠C = ∠Q
AB = PR
So, ΔABC and ΔPQR are congruent. -------- ΔABC ≅ ΔPQR [AAS congruency]
Figure D
In ΔABC and ΔPQR
AB = PQ
BC = QR
AC = PR
So, ΔABC and ΔPQR are congruent. -------- ΔABC ≅ ΔPQR [SSS congruency]
From these, we can infer that:
Figures B, C and D are congruent while A is not.
Knowledge Bytes:
→ Congruency Rules
Congruency rules are the specific set of rules that help us to determine whether two given triangles are congruent or not. Given below are those rules:
✳ SSS congruency
SSS congruency refers to Side-Side-Side congruency. This means that the three sides of one triangle is equal to the three sides of the other triangle.
✳ AAS congruency
AAS congruency refers to Angle-Angle-Side congruency. This means that the two angles and the non-included side of one triangle is congruent to the two angles and the non-included side of the other triangle.
✳ ASA congruency
ASA congruency refers to Angle-Side-Angle congruency. It means that the two angles and the included side of one triangle is congruent to the two angles and the included side of the other triangle.
✳ SAS congruency
SAS congruency refers to Side-Angle-Side congruency. It means that the two sides and an included angle of one triangle is congruent to the two sides and an included angle of the other triangle.
✳ RHS congruency
RHS congruency refers to Right Angle- Hypotenuse-Side congruency. It means that the the hypotenuse and a side of a right angled triangle is congruent to the hypotenuse and side of the other triangle.