Question

Please help if you can. Will give brainliest.

Use the image and information given to answer the following questions. Use numbers only. Do not add any words or symbols to your numerical answers.

Are the 2 triangles similar?

If they are similar, what postulate or theorem proves they are similar?

SSS
AA
SAS
They are not similar

Answer 1

Answer: SAS

Step-by-step explanation:

Here, the given triangles AEB and ADC,

B is the mid point of the line segment AC,

⇒ AC = 2 AB,

Also, m∠A = 30°, AD = 8, ED = 4, DC = 6,

$\frac{AE}{AD}=\frac{AD-ED}{8}=\frac{8-4}{8}=\frac{4}{8}=\frac{1}{2}$

$\frac{AB}{AC}=\frac{AB}{2AC}=\frac{1}{2}$

⇒  $\frac{AE}{AD}=\frac{AB}{AC}$

Also,

$\angle EAB\cong \angle DAC$

Here, ∠EAB of triangle AEB is congruent to the corresponding ∠DAC of another triangle ADC and the sides that include this angle are proportional,

Thus, by SAS postulate of similarity,

$\triangle AEB\sim \triangle ADC$

⇒ Third option is correct.