Question

In the given figure , AE bisects angle CAD and angle B= angle C. Prove that AE ||BC.
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Answer 1

Step-by-step explanation:

angle B+angle C=angleCAD. (sum of opposite angles are equal to exterior angle)

angle DAE=angle CAE. (AE bisect the angle CAD)

angle B +angle C=2 DAE. (DAE=CAE)

angle B+B=2 DAE. (angle B=angle c,given)

2B=2DAE

angle B=angle DAE

corresponding angles are equal so AE||BC

Answer 2

Step-by-step explanation:

ᴀɴɢʟᴇ ʙ+ᴀɴɢʟᴇ ᴄ-ᴀɴɢʟᴇ ᴄᴀᴅ. (ꜱᴜᴍ ᴏꜰ ᴏᴩᴩᴏꜱɪᴛᴇ ᴀɴɢʟᴇꜱ ᴀʀᴇ ᴇqᴜᴀʟ ᴛᴏ ᴇxᴛᴇʀɪᴏʀ ᴀɴɢʟᴇ)

ᴀɴɢʟᴇ ᴅᴀᴇ-ᴀɴɢʟᴇ ᴄᴀᴇ.

(ᴀᴇ ʙɪꜱᴇᴄᴛ ᴛʜᴇ

ᴀɴɢʟᴇ ᴄᴀᴅ)

ᴀɴɢʟᴇ ʙ +ᴀɴɢʟᴇ ᴄ=2 ᴅᴀᴇ. (ᴅᴀᴇ=ᴄᴀᴇ)

ᴀɴɢʟᴇ ʙ+ʙ=2 ᴅᴀᴇ. (ᴀɴɢʟᴇ ʙ-ᴀɴɢʟᴇ

ᴄ,ɢɪᴠᴇɴ)

2ʙ = 2ᴅᴀᴇ

ᴀɴɢʟᴇ ʙ-ᴀɴɢʟᴇ ᴅᴀᴇ

ᴄᴏʀʀᴇꜱᴩᴏɴᴅɪɴɢ ᴀɴɢʟᴇꜱ ᴀʀᴇ ᴇqᴜᴀʟ ꜱᴏ ᴀᴇ || ʙᴄ

ᴍᴀʀᴋ ᴍᴇ ᴀꜱ ʙʀᴀɪɴʟɪꜱᴛ