Question

which of the following ratios would indicate that triangles are similar by sas similarity?
a. 6/3 = 9/4.5
b. 5/3 = 10/7
c. 7/3 = 14/5
d. 4/3 = 8/4
which of the following is an example of a correct proportion for similar triangles?
a. ab/de = ac/df
b. ab = ac = de = df
c. ab + de = ac + df
d. ab × de = ac × df

Explanation:

Step1: Recall the SAS similarity ratio

For two triangles to be similar by SAS (Side - Angle - Side) similarity, the ratio of two corresponding sides should be equal. That is, if we have two triangles \(\triangle ABC\) and \(\triangle DEF\), \(\frac{AB}{DE}=\frac{AC}{DF}\) (assuming the included angles are equal).

Step2: Check each option

• Option a: \(\frac{6}{3}=\frac{9}{4.5}\)

Calculate \(\frac{6}{3} = 2\) and \(\frac{9}{4.5}=2\). So this ratio is correct for SAS similarity.

• Option b: \(5/3 = 10/7\), \(\frac{5}{3}\approx1.67\) and \(\frac{10}{7}\approx1.43\), not equal.
• Option c: \(7/3 = 14/5\), \(\frac{7}{3}\approx2.33\) and \(\frac{14}{5} = 2.8\), not equal.
• Option d: \(4/3=8/4\), \(\frac{4}{3}\approx1.33\) and \(\frac{8}{4} = 2\), not equal.

Answer:

a. \(6/3 = 9/4.5\)