Can you find a pair of similar triangles in the given diagram?
31.5 cm
Practice makes perfect
Let's begin with drawing one laser beam. Label the vertices of this laser beam with consecutive letters. We can see that △ ABC and △ ADE have one congruent corresponding angle, as ∠ BAC≅ ∠ DAE by the Reflexive Property.
Also, we are given that angles ∠ ABC and ∠ ADE are right angles are they create supplementary angles with right angles. This means that these triangles are similar by Angle-Angle Similarity Theorem.
△ ABC~ △ ADERecall that in similar triangles corresponding sides are proportional. Using this fact, we can write a proportion to find the length of DE.
AB/AD=BC/DE
Let's substitute the lengths of sides we know and solve for DE. Notice that, by the Segment Addition Postulate, we will add AB and BD to evaluate AD.
Since we know that certain medical treatments involve laser beams forming similar triangles, the distance between the laser sources will be twice the length of DE.
Therefore, we will multiply the length of DE, 15.75 cm, by 2.
15.75*2=31.5
The distance between the laser sources is 31.5 cm.
