Let's use colors to indicate corresponding vertices in the given congruence.
△ R S T≅△ J K L
Drawing the Figure
Let's use the colors also on the diagram.
Finding x
To find x, let's focus on the segments where the length is given in terms of x.
Notice, that these are corresponding sides in the congruent triangles, so they are congruent.
R T≅J L
Congruent segments have the same measure. This allows us to set up and solve an equation for x.
To find y, let's focus on the segment where the length is expressed in terms of y.
We also need to consider the information given about the corresponding segment in the other triangle.
Corresponding sides in the congruent triangles are congruent.
R S≅J K
Congruent segments have the same measure. This allows us to set up and solve an equation for y.
In the solution above we found, that x=19, so the side lengths of triangle â–ł RST are as follows.
RS&=7
ST&=5
TR&=9+19=28
If you try to construct a triangle like this, you will not succeed.
Points T and R are too far away to be able to reach through S with the short segments RS and ST.
Even though the algebra was correct in our solution, a triangle like this is impossible to construct.
