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 [tex]\frac{XY}{LM}=\frac{YZ}{MN}=\frac{XZ}{LN}[/tex]
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 [tex]\frac{BA}{ED}=\frac{CA}{FD}[/tex]
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
