Question

consider the two triangles.
to prove that $\triangle lmn \sim \triangle xyz$ by the sss similarity theorem using the information provided in the diagram, it would be enough additional information to know that
$circ$ lm is 3 units and xz is 5 units.
$circ$ lm is 4 units and xz is 6 units.
$circ$ lm is 5 units and xz is 3 units.
$circ$ lm is 6 units and xz is 4 units.

Explanation:

Step1: Identify known side pairs

Known sides: $NL=2$, $XZ=2$; $NM=3$, $YZ=9$; $XY=12$

Step2: Find similarity ratio

Calculate ratio of $NM$ to $YZ$: $\frac{NM}{YZ}=\frac{3}{9}=\frac{1}{3}$

Step3: Match ratio for other sides

For SSS similarity, $\frac{LM}{XY}=\frac{1}{3}$. Substitute $XY=12$:
$LM = 12 \times \frac{1}{3}=4$
Also, $\frac{NL}{XZ}$ must equal $\frac{1}{3}$. Substitute $NL=2$:
$XZ = 2 \div \frac{1}{3}=6$

Answer:

LM is 4 units and XZ is 6 units.