Check if the corresponding sides of these triangles are proportional.
Are the triangles similar? Yes. Similarity statement: △ XUZ~△ WUY Explanation: See solution.
Practice makes perfect
Since we are given all sides lengths of △ XUZ and △ WUY, we will check if the corresponding sides of these triangles are proportional to determine if they are similar.
Let's evaluate the ratios between the corresponding sides. We will start with the longest sides.
XZ/WY=14/10= 7/5= 1.4
Now, we will evaluate the ratio between the medium-length sides. Remember that, according to the Segment Addition Postulate, the length of ZU is the sum of lengths of ZY and YU.
ZU/YU=2+ 5/5= 7/5= 1.4
Finally, let's evaluate the ratio between the shortest sides. Again, notice that the length of XU is the sum of lengths of XW and WU.
XU/WU=3.2+ 8/8= 11.2/8= 1.4
As we can see, the ratio between corresponding sides is the same for each pair. This means that the sides in these two triangles are proportional. Therefore, by the Side-Side-Side Similarity Theorem, △ XUZ and △ WUY are similar triangles.
