Question

4. In the given figure, P is the point on the side BC of A ABC.
Complete each of the following statements using
symbol = < or so as to make it true :
(8) AP
AB + BP
(1) AP
AC + PC
B
(1) AP
(AB + AC + BC)​

Answer 1

Answer:

i) In △APB, AP < AB + BP because the sum of any two sides of a triangle is greater than the third side.

(ii) In △APC, AP < AC + PC because the sum of any two sides of a triangle is greater than the third side.

(iii) AP < ½ (AB + AC + BC) In △ABP and △ACP, we can write as AP < AB + BP…

(i) (Because the sum of any two sides of a triangle is greater than the third side) AP < AC + PC …

(ii) (Because the sum of any two sides of a triangle is greater than the third side)

On adding (i) and (ii),

we have:

AP + AP < AB + BP + AC + PC 2AP < AB + AC + BC (BC = BP + PC) AP < (AB – AC + BC).