Pythagoras Theorem and its Applications
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Q1
In the given figure, the value x is
Marks:1Answer:
10
Explanation:
In the given figure of rightangled triangle, we have
YZ^{2} = YX^{2} + XZ^{2} [By Pythagoras theorem]^{ }
x^{2} = 6^{2} + 8^{2}
x = 36 + 64 = 100
x = 10 
Q2
In right angled triangle PQR, which of the following is true?
Marks:1Answer:
m^{2 }= l^{2} + n^{2}
Explanation:
According to the Pythagoras theorem, we have
(Hypotenuse)^{2} = (Altitude)^{2} + (Base)^{2}Therefore, the property, which holds true for given right angled triangle, will be
m^{2 }= l^{2} + n^{2} 
Q3
In a right angled triangle, the hypotenuse is
Marks:1Answer:
the longest side.
Explanation:
Since, opposite side of greater angle is greater in a triangle. Since hypotenuse is opposite side of right angle in triangle so it is the longest side.

Q4
ABC is a right angled triangle in which A = 90°^{ }and
AB = AC. Find B and C.Marks:1Answer:
45°, 45°
Explanation:
In ABC, A = 90° and AB = AC Then B = C
According to angle sum property,
A + B + C = 180°90°^{ }+ B + C = 180°
90°^{ }+ 2 B = 180°
2 B = 180°^{ } 90°^{ }
= 90°^{ }
B = C = 45° 
Q5
In a right angled isosceles triangle shown below, what is the value of angle ACO.
Marks:1Answer:
135^{o}
Explanation:
Since, it is an Isosceles right angle triangle, so the values of angles other than 90^{o }are 45^{o }each. And angle ACO and angle ACB are forming a linear pair, which means their sum will be 180^{o} and hence the value of angle ACO is 135^{o}.