Mathematics
Which of the following is true for the given figure:
ΔAPC ≅ ΔBPD
CP = DP
AB and CD bisect each other
all of the above are true.
Answer
In ΔAPC and ΔBPD,
⇒ ∠ACP = ∠BDP (Both are 90°)
⇒ ∠APC = ∠BPD (Vertically opposite angles are equal)
⇒ AC = BD (Given)
∴ ΔAPC ≅ ΔBPD (By AAS congruency criterion)
By C.P.C.T.,
⇒ CP = DP and AP = BP
Thus, AB and CD bisect each other.
∴ All the options are correct.
Hence, option 4 is the correct option.
Related Questions
Which of the following will hold true for the given figure :
AD = DC
CD = CB
∠ACD ≠ ∠ACB
∠B ≠ ∠D
In the given figure, AM is the perpendicular bisector of BC. Then :
AB = AM
AC = BM
AB ≠ AC
AM bisects ∠BAC
In the following figure, ∠BAD = ∠EAC, BD = EC and ∠B = ∠E, then :
△ ABD ≇ △ AEC
△ ABC ≅ △ AED
△ ABC ≇ △ AED
△ ABD ≅ △ ADE
Which of the following is true for the given figure :
△ ABD ≅ △ ACD
angle BAD ≠ angle CAD
△ ABD ≇ △ ACD
∠EAB = ∠BAD
