ABCD is a square. A is joined to point P on BC and D is joined to a point Q on AB. If AP=DQ, prove that AP⊥DQ
Answers
Answered by
6
Answer:
Given: A square ABCD with AP = DQ
To prove: AP⊥DQ
Proof:
In Δs ADQ and APB,
∠A=∠B (Angles of a square is always 90°)
AD = AB (sides of a square)
DQ = AP (Given)
⇒ ΔADQ ≅ Δ APB
⇒ ∠ADQ = ∠BAP
Now in ΔADQ,
∠DAQ= 90°
⇒ ∠DAP + ∠PAB = 90°
⇒ ∠DAP + ∠ADQ = 90°....(ii)
i.e., ∠DAO +∠ADO =90° (from i)
∴ In Δ AOD,
∠DAO + ∠ADO+∠DOA = 180°
⇒ ∠DOA = 180°-90°
= 90°
DQ⊥AP (is proved).
Answered by
9
Given: A square ABCD with AP = DQ
To prove: AP | DQ
Prove:
In/\ ADQ and APB
/_ A = /_B Angles of a square is always 90•
AD = AB sides of square
DQ= AP (Given)
DQ = AP (proved)
Please mark me as a Brainlist and follow me plz......
Similar questions
English,
5 months ago
Computer Science,
5 months ago
Science,
9 months ago
Math,
9 months ago
Science,
1 year ago