ΔABC and ΔABD are on a common base AB and AC = BD and BC = AD as shown in the given
figure.
Which of the following options is true?
Show answer & explanation
Correct answer: C
Explanation
The correct answer is Option 3 i.e. ΔABC ≅ ΔBAD.
In ΔABC:
Sides: AB (common base), AC, and BC
In ΔABD:
Sides: AB (common base), AD, and BD
Now,
AC = BD
BC = AD
In ΔABC and ΔABD:
AB = AB (common)
AC = BD (given)
BC = AD ⇒ means CB = DA (same segment, just reversed)
So in terms of matching:
AB = AB
AC = BD ⇒ we rewrite as AC = BD
BC = AD ⇒ we rewrite as BC = AD
So these are 3 pairs of equal sides in order,
ΔABC ≅ ΔBAD by SSS (Side-Side-Side) Congruence Rule