Question

In the right angled triangle PRQ, right angled at R. T is the midpoint of hypotenuse PQ.
R is joined to T and produced to a point S such that ST =RT. Point S is joined to Q.
Show that
(i) A PTR = AQTS (ii) ZSQR = 90°
(iii) A SQR ZAPRQ (iv) RT=PQ​

Answer 1

Answer:

pt=tq by radius of a circle by using 3 noncollinear points

rt=ts given

angleptr=angleqts vertically opposite angle

area of ptr=area of it's by congrency of triangles

Answer 2

Step-by-step explanation:

HEY IT'S THE QUESTION OF CLASS 9 NCERT

IT'S HARD TO WRITE WHOLE SOLUTION HERE SO I AM JUST GIVING YOU A HINT

GO AHEAD AND SOLVE IT

YOU JUST NEED TO PROVE ∆PTR =~ ∆ STQ

THEN YOU WILL GET PTR TO BE EQUAL TO QTS . THEY ARE VERTICALLY OPPOSITE ANGLES . NOW AS ANGLE PRT WILL BE EQUAL TO ANGLE QST YOU CAN SAY PR IS PARALLEL TO SQ

HENCE USING SUM OF CO INTERIOR ANGLES YOU WILL GET ANGLES SQR TOO BE 90

THIRD PART CAN BE PROVED USING SAS AS PR = SQ PROVED IN FIRST PART , TWO ANGLES ARE 90 AND THEY HAVE SAME BASE RQ

FOR FOURTH PART YOU GET PQ = SR BY CONGRUENCY

AS T IS MID POINT OF PQ

THEREFORE IT IS ALSO MID POINT OF SR AND YOU GET THE ANSWER

THANK YOU