Question

check whether triangle PST~trianglePQR.when ps=2.4cm,sq=7.2cm.,pt=1.8cm,tr=5.4cm

Answer 1

In similar triangles, the ratio of corresponding sides is equal. So, if ∆PST ~ ∆PQR, then,

PS/PQ should be equal to PT/PR


PQ = PS + SQ

=> PQ = 2.4 cm + 7.2cm

=> PQ = 9.6 cm

So, PS/PQ

= 2.4/9.6

= 1.2/4.8

= 1/4

And, PR = PT + TR

=> PR = 1.8 + 5.4

=> PR = 7.2 cm

So, PT/PR

= 1.8/7.2

= 1/4

Now, PS/PQ = 1/4

and PT/PR = 1/4

=> PS/PQ = PT/TR

Since the ratio of corresponding sides is equal, the traingles are similar.


Hope it helps dear friend ☺️✌️