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A square is inscribed in an isosceles right triangle so that square and triangle have one angle common show that the vertex of common angle bisects hypotenuse

Posted by Shri Niwas Jat 8 years, 10 months ago

CBSE > Class 09 > Mathematics

1 answers

Naveen Sharma 8 years, 10 months ago

Ans.

Given : An isosceles Right Triangle ABC. A square CMPN is Inscribed in it .

To Prove : CP bisects the hypotenuse AB. i.e. AP = PB
Proof : CMPN is square.
So,
CM = MP = PN = NC [ all sides are equal]

Also Triangle ABC is Isosceles.
So, AC = BC

=> AN + NC = CM + MB

=> AN = MB [as NC = CM]

Now, Consider Traingles ANP and PMB
AN = MB [Proved Above]

∠ANP = ∠ PMB [Both are 90]

PN = PM [Sides of square]

So, By SAS Rule
Triangle ANP = Triangle PMB

=> AP = PB [By CPCT]
Hence Proved

1Thank You

ANSWER

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