Question

1. In AABC and ADEF, AB = DE and BC = EF (Fig. 9.19).
A
B
С
E
F
Fig. 9.19
What additional information is required to make the two triangles congruent by SAS
congruence condition?​

Answer 1

Step-by-step explanation:

(i) Consider the quadrilateral ABED

We have , AB=DE and AB∥DE

One pair of opposite sides are equal and parallel. Therefore

ABED is a parallelogram.

(ii) In quadrilateral BEFC , we have

BC=EF and BC∥EF. One pair of opposite sides are equal and parallel.therefore ,BEFC is a parallelogram.

(iii) AD=BE and AD∥BE ∣ As ABED is a ||gm ... (1)

and CF=BE and CF∥BE ∣ As BEFC is a ||gm ... (2)

From (1) and (2), it can be inferred

AD=CF and AD∥CF

(iv) AD=CF and AD∥CF

One pair of opposite sides are equal and parallel

⇒ ACFD is a parallelogram.

(v) Since ACFD is parallelogram.

AC=DF ∣ As Opposite sides of a|| gm ACFD

(vi) In triangles ABC and DEF, we have

AB=DE ∣ (opposite sides of ABED

BC=EF ∣ (Opposite sides of BEFC

and CA=FD ∣ Opposite. sides of ACFD

Using SSS criterion of congruence,

△ABC≅△DEF