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Answers
Answer:
Therefore ∠1>∠3 and BC>DC as size opposite to greater angle are also greater in length. Hence it is proved that either side of triangle is always greater than difference of remaining two sides
Step-by-step explanation:
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Given: XYZ is a triangle.
To Prove: (XY + XZ) > YZ, (YZ + XZ) > XY and (XY + YZ) > XZ
Construction: Produce YX to P such that XP = XZ. Join P and Z.
Statement
1. ∠XZP = ∠XPZ.
2. ∠YZP > ∠XZP.
3. Therefore, ∠YZP > ∠XPZ.
4. ∠YZP > ∠YPZ.
5. In ∆YZP, YP > YZ.
6. (YX + XP) > YZ.
7. (YX + XZ) > YZ. (Proved)
Reason
1. XP = XZ.
2. ∠YZP = ∠YZX + ∠XZP.
3. From 1 and 2.
4. From 3.
5. Greater angle has greater side opposite to it.
6. YP = YX + XP
7. XP = XZ
Similarly, it can be shown that (YZ + XZ) >XY and (XY + YZ) > XZ.