Δ ACD, show thatPM ofΔ ABD isABthatSidtripr6, in Fig 637, if Δ ABE.

1.	Δ ACD, show thatPM ofΔ ABD isABthatSidtripr6, in Fig 637, if Δ ABE. In Fig 6.38, altitudes AD and CE of A ABCintersect each other at the point P. Showthat(i) ΔΑΕΡ-dCDPCit) ΔΑ1D-3CBE(iii) ΔΑΕΡ-3ADBFig. 637
Answer» Solution:Since Δ ABE ≅ Δ ACD Hence, BE = CD And ∠DBE = ∠ECD In Δ DBE and Δ ECD BE = CD (proved earlier) ∠DBE = ∠ECD (proved earlier) DE = DE (common) Hence, Δ DBE ≅ Δ ECD This means; DB = EC This also means; AD/DB=AE/EC Hence; DE \|\| BC Thus, Δ ADE ∼ Δ ABC proved.

Δ ACD, show thatPM ofΔ ABD isABthatSidtripr6, in Fig 637, if Δ ABE. In Fig 6.38, altitudes AD and CE of A ABCintersect each other at the point P. Showthat(i) ΔΑΕΡ-dCDPCit) ΔΑ1D-3CBE(iii) ΔΑΕΡ-3ADBFig. 637

Answer»

Solution:Since Δ ABE ≅ Δ ACD

Hence, BE = CD

And ∠DBE = ∠ECD

In Δ DBE and Δ ECD

BE = CD (proved earlier)

∠DBE = ∠ECD (proved earlier)

DE = DE (common)

Hence, Δ DBE ≅ Δ ECD

This means; DB = EC

This also means;

AD/DB=AE/EC

Hence; DE || BC

Thus, Δ ADE ∼ Δ ABC proved.