Question

Find the value of x and explain how you found it. Make sure to cite the problem and share what you see before you explain your solution. In your explanation, include how you know that these triangles are similar. You may use a postulate such as AA, SSS, SAS, Triangle Proportionality Theorem, or a creative alternative. Justify why you were able to use the postulate/theorem and give the equation you used to find x.

Answer 1

THE VALUE OF X = 3 .

Explanation:

From the Δ RQP and Δ TSP ;

⇒ ∠ TPS = ∠ RPQ ( since both are common angle )

⇒ RQ ≈ TS ( parallel lines )

⇒ ∠ PRQ = ∠ PST ( Corresponding angle )

∴ Δ RQP ≅ Δ TSP ( BY ASA RULE )

Now ,

`(RP)/(TP) = (QP)/(PS)`

`(9 + X)/(9) = (6 + 2)/(6)`

⇒ X = 3