Question

unit 2 study guide

1. state what theorem proves the triangles are similar and explain how you determined your answer.

similarity theorem =
word bank: (a) sas, (b) sss, (c) aa, (d) not similar

Explanation:

Step1: Check side - length ratios

For $\triangle KML$ with side - lengths $KM = 40$, $ML=42$, $KL = 24$ and $\triangle RST$ with side - lengths $RS = 56$, $ST = 52$, $RT=31$. Calculate the ratios of corresponding sides. $\frac{KM}{RS}=\frac{40}{56}=\frac{5}{7}$, $\frac{ML}{ST}=\frac{42}{52}=\frac{21}{26}$, $\frac{KL}{RT}=\frac{24}{31}$. Since $\frac{5}{7}
eq\frac{21}{26}
eq\frac{24}{31}$, the sides are not in proportion.

Step2: Determine similarity

Since the side - length ratios are not equal, and no angle information is given to use AA or SAS, the triangles are not similar.

Answer:

(d) Not Similar