Mathematics
In the given figure : AB // FD, AC // GE and BD = CE; prove that :
(i) BG = DF
(ii) CF = EG.
Triangles
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Answer
Given,
⇒ BD = CE
Adding DE on both sides, we get :
⇒ BD + DE = CE + DE
⇒ BE = DC.
In △ BGE and △ DFC,
⇒ BE = DC (Proved above)
⇒ ∠GBE = ∠FDC (Corresponding angles are equal)
⇒ ∠GEB = ∠FCD (Corresponding angles are equal)
∴ ∆ BGE ≅ ∆ DFC (By A.S.A. axiom)
We know that,
Corresponding parts of congruent triangles are equal.
∴ BG = DF and CF = EG.
Hence, proved that BG = DF and CF = EG.
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Related Questions
Which of the following pairs of triangles are congruent ? In each case, state the condition of congruency :
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(b) In △ ABC and △ DEF, ∠B = ∠E = 90°; AC = DF and BC = EF.
(c) In △ ABC and △ QRP, AB = QR, ∠B = ∠R and ∠C = ∠P.
(d) In △ ABC and △ PQR, AB = PQ, AC = PR and BC = QR.
(e) In △ ABC and △ PQR, BC = QR, ∠A = 90°, ∠C = ∠R = 40° and ∠Q = 50°.
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