Question

State if the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement. Part 4​
a. similar, SSS similarity
b. similar, SAS similarity triangle LSR
c. not similar

Answer 1

Answer: a) similar, SSS similarity

Step-by-step explanation:

ΔLSR sides in order from least to greatest are: 24, 33, 36

ΔLNM sides in order from least to greatest are: 112, 154, 168

If the triangles are similar then their corresponding sides will be proportional

$\dfrac{LS}{LN}=\dfrac{SR}{NM}=\dfrac{LR}{LM}\\\\\\\\\\\dfrac{LS}{LN}=\dfrac{24}{112}\quad \rightarrow \dfrac{3}{14}\\\\\\\dfrac{SR}{NM}=\dfrac{33}{154}\quad \rightarrow \dfrac{3}{14}\\\\\\\dfrac{LR}{LM}=\dfrac{36}{168}\quad \rightarrow \dfrac{3}{14}$

Their corresponding sides are proportional so

ΔLSR ≅ ΔLNM by Side-Side-Side Similarity Theorem