Question

Is abc~def? If so, identify the similarity postulate or theorem that applies.

Answer 1

Answer:

Similarity cannot be determined ⇒ answer D

Step-by-step explanation:

* Lets revise the cases of similarity

1) AAA similarity : two triangles are similar if all three angles in the first

  triangle equal the corresponding angle in the second triangle

- Example : In ΔABC and ΔDEF, m∠A = m∠D, m∠B = m∠E and

 m∠C= m∠F then ΔABC ≈ ΔDEF by AAA

2) AA similarity : If two angles of one triangle are equal to the

   corresponding angles of the other triangle, then the two triangles

   are similar.

- Example : In ΔPQR and ΔDEF, m∠P = m∠D, m∠R = m∠F then

  ΔPQR ≈ ΔDEF by AA

3) SSS similarity : If the corresponding sides of two triangles are

   proportional, then the two triangles are similar.

- Example : In ΔXYZ and ΔLMN, if $\frac{XY}{LM}=\frac{YZ}{MN}=\frac{XZ}{LN}$

  then the two triangles are similar by SSS

4) SAS similarity : In two triangles, if two sets of corresponding sides

   are proportional and the included angles are equal then the two

   triangles are similar.

- Example : In triangle ABC and DEF, if m∠A = m∠D and $\frac{BA}{ED}=\frac{CA}{FD}$

  then the two triangles are similar by SAS

* Now lets solve the problem

- In the triangles ABC and DEF

∵ m∠B = m∠E = 105°

∵ AB/DE = 16/4 = 4

∵ AC/DF = 36/9 = 4

∴ AB/DE = AC/DF = 4

∴ The two pairs of sides are proportion

∵ ∠B and ∠E are not the including angles between the sides AB , AC

  and DE , DF

∵ We could not find the including angles from the information of the

  problem

∴ We cannot prove the similarity

* Similarity cannot be determined