Question

unit 2 study guide

1. state what theorem proves the triangles are similar and explain how you determined your answer.
2. determine if triangle rst and are not similar, and, if they are, state that figures are not necessarily similar.

the triangles __________ similar.
if they are similar, complete the sen
the triangles are similar because
word bank 1: (a) are, (b) are not
word bank 2: (a) sss: three sides proportionate, two sides proportionate, included - angle congruent, congruent, (e) aa: two angles congruent
similarity theorem = __________
word bank: (a) sas, (b) sss, (c) aa, (d) not similar

1. solve for x.

12x + 6 25

Explanation:

Step1: Check side - length ratios

For \(\triangle KLM\) with side - lengths \(KL = 24\), \(LM = 42\), \(KM = 40\) and \(\triangle RST\) with side - lengths \(RS = 56\), \(ST = 52\), \(RT = 31\). Calculate the ratios of corresponding sides: \(\frac{KL}{RT}=\frac{24}{31}\), \(\frac{LM}{ST}=\frac{42}{52}=\frac{21}{26}\), \(\frac{KM}{RS}=\frac{40}{56}=\frac{5}{7}\).
Since \(\frac{24}{31}
eq\frac{21}{26}
eq\frac{5}{7}\), the sides are not proportional.

Answer:

(d) Not Similar