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Question
AB is a line segment and P is its mid-point. D and E are points on the same side of
AB such that ∠BAD=∠ABE and ∠EPA=∠DPB (See the given figure).
Then, which of the following is true?
AB is a line segment and P is its mid-point. D and E are points on the same side of
AB such that ∠BAD=∠ABE and ∠EPA=∠DPB (See the given figure).
Then, which of the following is true?
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Solution
The correct option is A ΔDAP≅ΔEBP
It is given that,∠EPA=∠DPB∠EPA+∠EPD=∠DPB+∠EPD [adding ∠EPD on both sides]∠APD=∠BPE…(i)In ΔDAP and ΔEBP,AP=BP (P is a midpoint of AB)∠APD=∠BPE (From (i))∠BAD=∠ABE (Given)∴ΔDAP≅ΔEBP (By ASA congruence rule)
It is given that,∠EPA=∠DPB∠EPA+∠EPD=∠DPB+∠EPD [adding ∠EPD on both sides]∠APD=∠BPE…(i)In ΔDAP and ΔEBP,AP=BP (P is a midpoint of AB)∠APD=∠BPE (From (i))∠BAD=∠ABE (Given)∴ΔDAP≅ΔEBP (By ASA congruence rule)
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