Q20 of 97 Page 205

In the given figure, PQ>PR and QS and RS are the bisectors of ∠Q and ∠R respectively. Show that SQ>SR

It is given in the question that,

PQ > PR

And, QS and RS are the bisectors of ∠ Q and ∠ R

We have, angle opposite to the longer side is greater

∴ PQ > PR

∠ R > ∠ Q

∠ SRQ > ∠ RQS

SQ > SR

Hence, proved

Each question consists of two statements, namely, Assertion (A) and Reason (R). Please select the correct answer.

Assertion (A)

Reason (R)

If AD is a median of ∆ABC, then AB+AC>2AD.

In a triangle the sum of two sides is greater than the third side.

Math the following columns:

Column I	Column II
(a)In ∆ABC, if AB=AC and ∠A=70°, then ∠C=………..	(p) less
(b) The vertical angle of an isosceles triangle is 120°. Each base angle is………	(q) greater
(c) The sum of three medians of a triangle is ………… than the perimeter.	(r) 30°
(d) In a triangle, the sum of any two sides is always …….. than the third side.	(s) 55°

The correct answer is:

(a)-……, (b)-……, (c)-……., (d)-……

In the given figure, ABC is a triangle right-angled at B such that ∠BCA=2∠BAC.

Show that AC=2BC.

S is any point in the interior of ∆PQR.

Show that (SQ+SR)<(PQ+PR).