P is the midpoint of hypothenuse AB in a right angled triangle ABC prove AB= 2CP find using midpoint theorems
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✪ᴇxᴘʟᴀɪɴᴀᴛɪᴏɴ✪
☆ɢɪᴠᴇɴ☆
- Right triangle ABC, right angled at C with P as the mid point of hypotenous AB.
☆ᴛᴏ ᴘʀᴏᴠᴇ☆
☆ᴄᴏɴsᴛʀᴜᴄᴛɪᴏɴ☆
- Draw PD and PE parallel to BC and AC respectively.
☆ᴘʀᴏᴏғ☆
Mid Point Theorem
If a line is drawn from mid point of one side of a triangle, parallel to another side and intersects the third side then it will bisect the third side of the triangle.
By mid point theorem
Also, but ,
is a rectangle
Again PE⊥BC, so ΔPCE is right triangle. Applying Pythagoras Theorem,
Applying Pythagoras Theorem in ΔABC,
[Using (1)]
[Using (2)]
[Using (3)]
Hence Proved
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