Question

In triangle ABC, if D is any point on side BC, show that AB+BC+CA>2AD?
PLz plz

Answer 1

QUESTION:—

• AM is a median of a triangle ABC. Is AB+BC+CA>2AM?

ANSWER:—

In triangle ABC, AM is a median.

In triangle ABM, AB+BM>AM… (1) [the sum of two sides of a triangle are greater than the third side].

In triangle ACM, AC+CM>AM… (2) [the sum of two sides of a triangle are greater than the third side].

Add (1) and (2) to get

AB+BM+AC+CM>AM+AM, or

AB+(BM+CM)+AC>2AM, or

AB+BC+CA>2AM. Proved

Answer 2

Answer:

your answer is also given in the above attachment ( hand written)

Step-by-step explanation:

question:- In triangle ABC, if D is any point on side BC, show that AB+BC+CA>2AD?

solution:-

We know that:-

We know that:-In a triangle sum of two sides is always greater

We know that:-In a triangle sum of two sides is always greaterthan the third side.

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABD

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)In triangle ADC

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)In triangle ADCDC+CA > AD…………….(2)

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)In triangle ADCDC+CA > AD…………….(2)On adding (1) & (2)

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)In triangle ADCDC+CA > AD…………….(2)On adding (1) & (2)AB+BD+DC+CA > 2AD

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)In triangle ADCDC+CA > AD…………….(2)On adding (1) & (2)AB+BD+DC+CA > 2ADOn putting BD+DC=BC

We know that:-In a triangle sum of two sides is always greaterthan the third side.In truangleABDAB+BD > AD…………….(1)In triangle ADCDC+CA > AD…………….(2)On adding (1) & (2)AB+BD+DC+CA > 2ADOn putting BD+DC=BCAB+BC+CA > 2AD .

Proved.

hope it helps you!!