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P Pankaj Sanodiya
As we know the sum of the angles of any triangle is always 180. So, Now. Since PQR is a right-angled triangle with right angle at P. So   Hence option (ii) is correct.

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P Pankaj Sanodiya
As we know,  In a Right-angled Triangle: By Pythagoras Theorem, (i) , , 6 cm. As we know the hypotenuse is the longest side of the triangle, So Hypotenuse = 6.5 cm Verifying the Pythagoras theorem,   Hence it is a right-angled triangle. The Right-angle lies on the opposite of the longest side (hypotenuse) So the right angle is at the place where 2.5 cm side and 6 cm side meet. (ii) 2 cm, 2...

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P Pankaj Sanodiya

Here. As we can see, The ladder with wall forms a right-angled triangle with 

the vertical height of the wall = perpendicular = 12 m

length of ladder = Hypotenuse = 15 m

Now, As we know

In a Right-angled Triangle: By Pythagoras Theorem,

(Hypotenus)^2=(Base)^2+(Perpendicular)^2

(15)^2=(Base)^2+(12)^2

(Base)^2=(15)^2-(12)^2

(Base)^2=225-144

(Base)^2=81

Base=9 m

Hence the distance of the foot of the ladder from the wall is 9 m.

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P Pankaj Sanodiya
As we know,  In a Right-angled Triangle: By Pythagoras Theorem, As ABC is a right-angled triangle with  Base = AC= 7 cm. Perpendicular = BC Hypotenuse = AB = 25 cm So, By Pythagoras theorem, Hence, Length od BC is 24 cm.

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P Pankaj Sanodiya
As we know,  In a Right-angled Triangle: By Pythagoras Theorem, As PQR is a right-angled triangle with  Base = PQ = 10 cm. Perpendicular = PR = 24 cm. Hypotenuse = QR So, By Pythagoras theorem, Hence, Length od QR is 26 cm.  

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P Pankaj Sanodiya
As we know in a Right-angled Triangle: By Pythagoras Theorem, So, using this theorem, i)  . ii) iii) iv) v) in this question as we can see from the figure, it is making the right angle with the half-length of x, so . vi)

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P Pankaj Sanodiya
Let the intersection point of the two diagonals be O. As we know that the sum of two sides of ANY triangle is always greater than the third side(Triangles Inequality Rule). So, In  : In  : In  : In  : Now, Adding all four equations we, get which can also be expressed as  Hence this is true.

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P Pankaj Sanodiya
As we know that the sum of two sides of ANY triangle is always greater than the third side(Triangles Inequality Rule). So, In  : In  : Adding (1) and (2) we get, Hence The given statement is True.  

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P Pankaj Sanodiya
Let ABC be a triangle with AB = 12cm and BC = 15cm Now As we know that the sum of two sides of ANY triangle is always greater than the third side(Triangles Inequality Rule). AB + BC > CA 12 + 15 > CA CA < 27......(1) Also, in a similar way AB + CA  > BC  CA > BC -  AB CA > 15 - 12  CA > 3............(2) Hence from (1) and (2), we can say that the length of third side of the triangle must be...

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P Pankaj Sanodiya
As we know that the sum of two sides of ANY triangle is always greater than the third side(Triangles Inequality Rule). So, In  : In  : Adding (1) and (2), we get As we can see M is the point in line BC So, we can say So our equation becomes . Hence it is a True statement.  

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P Pankaj Sanodiya
i) As POQ is a triangle, the sum of any two sides will always be greater than the third side. so  Yes,   . ii) As ROQ is a triangle, the sum of any two sides will always be greater than the third side. so  Yes,   iii) As ROQ is a triangle, the sum of any two sides will always be greater than the third side. so  Yes,

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P Pankaj Sanodiya
As we know, According to the Triangle inequality law, the sum of lengths of any two sides of a triangle would always greater than the length of the third side. So Verifying this inequality by taking all possible combinations, we have, (i) 2 cm, 3 cm, 5 cm 3 + 5 > 2 ----> True 2 + 5 >  3---->  True 2 + 3 > 5 ---->False Hence the triangle is not possible. (ii) 3 cm, 6 cm, 7 cm  3 + 6 > 7 ----->...

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P Pankaj Sanodiya
i) As we know, in an isosceles triangle, two sides and the angles they make with the third side are equal. So, Now,  As we know the sum of internal angles of a triangle is 180. so, Hence, . ii)  As we know, in an isosceles triangle, two sides and the angles they make with the third side are equal. AND the sum of internal angles of a triangle is 180. so, Also, . Hence . iii) As we...

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P Pankaj Sanodiya
As we know, in an isosceles triangle, two sides and the angles they make with the third side are equal. and the sum of angles of the triangle is equal to . So, i)  ii)  iii)  iv)  v) vi) vii) viii) As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle. So,  ix)As we know when two lines are intersecting, the opposite angles are equal. So

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P Pankaj Sanodiya
i) As we know, the exterior angle is equal to the sum of opposite internal angles in a triangle. Now, As we know the sum of internal angles of a triangle is 180. so, Hence, . ii)  As we know when two lines are intersecting, the opposite angles are equal. So Now, As we know the sum of internal angles of a triangle is 180. so, Hence, . iii) As we know, the exterior angle is equal to...

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P Pankaj Sanodiya
As we know that the sum of the internal angles of the triangle is equal to . So, i)  ii)  iii)  iv)  v)  vi) 

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P Pankaj Sanodiya
As we know that the exterior angle is equal to the sum of the opposite internal angles. So,  i)  ii)  iii)  iv)  v)  vi) 

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P Pankaj Sanodiya
As we know that the exterior angle is equal to the sum of the opposite internal angles. So,  i)  ii)  iii)  iv)  v)  vi)   

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P Pankaj Sanodiya
Yes, The measure of the exterior angle is given wrong. As we know that in a triangle, the exterior angle is equal to the sum of opposite interior angles. So, Exterior angle =                         =  Hence the exterior angle should be equal be  instead of .
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