Question

Please help me with question 16

Pls help

Answer 1

Hi mate here is the answer:--

Question:-

In Figure, D and E are points on side BC of a ΔABC such that BD = CE and AD = AE. Show that ΔABD ≅ ΔACE.

Answer:-

Given: In ΔABC,

BD = CE and AD = AE.

In ΔADE,AD = AE⇒ ∠ADE = ∠AED …(1)

(opposite angles to equal sides are equal)

Now, ∠ADE + ∠ADB = 180° (linear pair)

∠ADB = 180° - ∠ADE ..(2)

Also, ∠AED + ∠AEC = 180° (linear pair)

∠AEC = 180° - ∠AED

∠AEC = 180° - ∠ADE .. (3)

(∵∠ADE = ∠AED)

From (2) and (3)

∠ADB = ∠AEC ..(4)

Now, In ΔADB and ΔAEC,AD = AE (given)BD = EC (given)∠ADB = ∠AEC (from (4)Hence, ΔABD ≅ΔACE (by SAS)

Hope it helps you ❣️❣️❣️