Question

AngleA= angle D= 90° ∆ABE congruent ∆DCE by the congruence conditions

Answer 1

ɪɴ ∆ᴀʙᴇ ᴀɴᴅ∆ ᴅᴄᴇ
ᴀɴɢʟᴇ ᴀ =ᴀɴɢʟᴇ ᴅ (ɢɪᴠᴇɴ)
ᴀꜱ=ᴅᴇ (ɢɪᴠᴇɴ)
ᴀɴɢʟᴇ ᴀᴇʙ = ᴀɴɢʟᴇ ᴄᴇᴅ ( ᴠᴇʀᴛɪᴄᴀʟʟy ᴏᴩᴩᴏꜱɪᴛᴇ ᴀɴɢʟᴇꜱ)
ʜᴇɴᴄᴇ ʙy ᴀꜱᴀ ᴛʀɪᴀɴɢʟᴇ ᴄʀɪᴛᴇʀɪᴏɴ ∆ᴀʙᴇ ᴀɴᴅ∆ ᴅᴄᴇ ᴀʀᴇ ᴄᴏɴɢʀᴜᴇɴᴛ

Answer 2

Given,

∠ A = ∠ D = 90°

AE = DE

To find,

We have to find the congruency condition of ∆ABE and ∆DCE.

Solution,

AngleA= angle D= 90° ∆ABE congruent ∆DCE by the congruence condition ASA.

In ∆ABE and ∆DCE

      ∠ A = ∠ D (Each 90°)

       AE = DE (Given)

 ∠ AEB = ∠DEC (Vertically opposite angles)

By the ASA congruency rule,

      ∆ABE ≅ ∆DCE

Hence, AngleA= angle D= 90° ∆ABE congruent ∆DCE by the congruence condition ASA.