NCERT Class 10 Chapter 7 Triangles Official CBSE Board Sample Problems Short Answer

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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

Right angled

Right Angled

Right angled

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 )

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

Airport two aero planes

Airport Two Aero Planes

Airport two aero planes

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.

Parallelogram

Parallelogram

Parallelogram

Question

Parallelogram

Parallelogram

Parallelogram

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

Parallelogram

Parallelogram

Parallelogram

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

Traingle

Traingle

Traingle

Solution

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