Question

Directions - For the following problem, write a paragraph proof to justify each step you make. All work must be neat,

Answer 1

$PS = \frac{4}{3} x$

Solution:

Given PRQ is a triangle.

ST is a line parallel to RQ.

$PT = x, \ PQ = 3x, \ SR=\frac{8}{3}x$

$TQ=PQ-PT$

$TQ=3x -x=2x$

Triangle proportionality theorem,

If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.

$\frac{PS}{SR} =\frac{PT}{TQ}$

$\frac{PS}{\frac{8}{3} x} =\frac{x}{2x}$

Do cross multiplication, we get

$PS \times 2x=x \times \frac{8}{3} x$

Divide by 2x on both sides, we get

$PS = \frac{4}{3} x$