Are lines 𝑆𝑈 and 𝑉𝑇 congruent?
What do we know about congruent lines? Congruent lines have the same length. And that means we need to know if line segment 𝑆𝑈 has the same length as line segment 𝑉𝑇. Line segment 𝑆𝑈 has a length of eight 𝑎 plus four 𝑎. Line segment 𝑉𝑇 has a length of six 𝑎 plus six 𝑎.
The 𝑎 variable will stay the same. And we’ll add their coefficients together. We’ll add the numbers in front of the 𝑎 together. Here, eight plus four equals 12. And the 𝑎 stays the same. If we add the coefficients again for 𝑉𝑇, we get six plus six equals 12. And we bring down the 𝑎. We’re seeing that line segment 𝑆𝑈 measures 12𝑎. And line segment 𝑉𝑇 measures 12𝑎. They have the same length.
And that means yes, these lines are congruent.