Question

In a triangle ABC, AM is the median. Prove that

AB+BC+CA > 2AM

2. In a triangle ABC, O is an interior point. Prove that

2(OA+OB+OC) > AB+BC+CA

3. Find the unknown value:-

(a) In the triangle ABC, B= 90°, AB = 3cm, BC = 4cm,

AC = ?

(b) In the triangle ABC, A= 90°, AB = 6cm , AC = 8cm

, BC=?

(c) In the triangle ABC, C= 90°, BC= 12cm, AC = 5cm,

BC=?

(d) In the triangle PQR, Q = 90°, PQ= 12cm, PR =

13cm , QR=?

(e) In the triangle KLM,L = 90°, KM = 17cm,KL=

12cm , LM=?

(f)In the triangle NOW, NO= 40cm, OW= 9cm and NW=

41cm. find the degree measure of O.

4. The length of two sides of a triangle are 12cm and 15 cm .

Between what two measures should the length of the third

side fall?

5. In a quadrilateral ABCD, Prove that AB+BC+CD+AD >

AC +BD.

6. PQR is a triangle, right-angled at P. If PQ = 10 cm and PR

= 24 cm, find QR. pls tell quick​

Answer 1

Answer:

10cm

Step-by-step explanation:

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Answer 2

Answer:

As we know that the sum of lengths of any two sides in a triangle should be greater than the length of third side.

Therefore,

In △ABM

AB+BM>AM.....(i)

In △AMC

AC+MC>AM.....(2)

Adding eq

n

(1)&(2), we have

(AB+BM)+(AC+MC)>AM+AM

⇒AB+(BM+MC)+AC>2AM

⇒AB+BC+AC>2AB

Hence AB+BC+AC>2AB