In `(PS)/(SQ)=(PT)/(TR)` and `angle PST= angle PRQ`. Prove that PQR is an isosceles triangle.

If in given Fig. , PQ = PT and angleTPS = angleQPR , Prove that triangle PRS is isosceles.

If in given Fig. , PQ = PT and angleTPS = angleQPR , Prove that triangle PRS is isosceles.

In a right angles triangle, prove that r+2R=s.

In Fig. 6.15, angle PQR = angle PRQ , then prove that angle PQS = angle PRT .

Try to draw rough sketches of a right angled isosceles triangle.

Try to draw rough sketches of an obtuse angled isosceles triangle.

ABCD is a quadrilateral in which AD = BC and angle DAB =angle CBA (see Fig. 7.17). Prove that (i) triangle ABD cong triangle BAC (ii) BD = AC (iii) angle ABD = angle BAC .

In Fig 7.51, PR > PQ and PS bisects angle QPR . Prove that angle PSR > angle PSQ .

Draw a rough sketch of the following Acute angled isosceles triangle

If two medians of a triangle are equal, prove that the triangle is isosceles.