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NCERT Class 10 Chapter 7 Triangles Official CBSE Board Sample Problems Short Answer
Question
is right angled at C. If p is the length of the perpendicular from C to AB and a, b, c are the lengths of the sides opposite respectively then prove that
Solution
Given: In and .
Also, and
To prove:
Proof: In
Apply Pythagoras theorem
(i)
Now, area of - (ii)
Also area of - (iii)
Equation (iii) and (ii) we have
Put value of in equation (i)
(dividing both sides by a2 b2)
Question
From airport two aero planes start at the same time. If the speed of first aero plane due North is 500 km⟋h and that of other due East is 650 km⟋h, then find the distance between two aero planes after 2 hours.
Solution
Speed of aero plane along north = 500 km⟋h
Speed of aero plane along east = 650 km⟋b
Distance travelled by aero plane in 2 hours in
North direction.
Distance travelled by aeroplane in 2 hours in East direction.
Distance between both d roplanes after 2 hours = AB.
(By Pythagoras theorem in )
km
Question
R and S are points on the sides DE and EF respectively of a LDEF such that and . Find whether or not.
Solution
Construction: Join RS
To find: or not
Proof: WE have RE = 5 cm
and RD = 2.5 cm
Now
Similarly, we have,
and
Now,
Here
RS is not parallel to DF.
Question
In the figure, ABCD is a parallelogram and E divides BC in the ratio 1: 3. DB and AE intersect at F. Show that DF = 4FB and AF = 4FE
Solution
Given ABCD is a parallelogram and
To show DF = 4FB and AF = 4FE
Proof In and
(Alternate angles)
(V. O. A.)
(by AA)
AS
Put in (I) , we get
AND
Question
If the areas of two similar triangles are equal, prove that they are congruent.
Solution
Given, area and
We know that:
Similarly BC = QR and AC = PR
Thus, (SSS congruency criterion)
Question
In fig, if D is mid-point of BC, find the value of