4. Which of the following can be the sides of a right
triangle?
(i) 2.5 cm,6.5 cm, 6 cm.
(ii) 2 cm, . 2 cm, 5 cm.
(i 1.5 cm, 2cm, 2.5 cm.
In the case of right-angled triangles, identify the
right angles.
Answers
Step-by-step explanation:
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For a triangle to be a right angled triangle, it should prove the Pythagoras theorem true,i.e.,
In triangle ABC...
Let us take angle B=90°
AC²=AB²+BC²
Now one by one we will apply Pythagoras theorem, and verify each of the number..
Highest value of a number will be taken as the hypotenuse..
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i)Here, In triangle ABC
AC=Hypotenuse=6.5cm
AB=Perpendicular=6cm
BC=Base=2.5cm
AC²=AB²+BC²
6.5²=6²+2.5²
42.25=36+6.25
42.25=42.25
Hence it is right angled triangle..
Its is right angled at B....
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ii) Here, In triangle ABC
AC=Hypotenuse=5
AB=Perpendicular=2
BC=Base=2
AC²=AB²+BC²
5²=2²+2²
25≠8
It is not a right angled triangle..
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iii) Here, In triangle ABC
AC=Hypotenuse=2.5cm
AB=Perpendicular=2cm
BC=Base=1.5cm
AC²=AB²+BC²
2.5²=2²+1.5²
6.25=4+2.25
6.25=6.25
It is right angled at B....