Exercise 81 Page 659

Consider the given triangle.

We are asked to find the values of x and y. We will do it one at a time.

Finding x

Note that the segments with lengths 2x+3 and 6-x are congruent. Therefore, their measures are equal. 2x+3=6-x Let's solve the equation using the Properties of Equality.

Finding y

Since we are given three parallel lines that intersect two transversals, we can use the Corollary to the Triangle Proportionality Theorem.

Let's write an equation in terms of y using the above theorem. 4/3y+1=2y Now we will solve the equation.