State if the triangles in each pair are similar. If so, State how you know they are similar and complete the similarity statement

Δs DEF and DRQ not similar ⇒ 2nd answer

Step-by-step explanation:

Let us revise the cases of similarity

AAA similarity : two triangles are similar if all three angles in the first  triangle equal the corresponding angle in the second triangleAA similarity : If two angles of one triangle are equal to the  corresponding angles of the other triangle, then the two triangles  are similarSSS similarity : If the corresponding sides of the two triangles are  proportional, then the two triangles are similarSAS similarity : In two triangles, if two sets of corresponding sides  are proportional and the included angles are equal then the two  triangles are similar.  

In triangles DEF and DRQ

∵ m∠EDF = m∠REQ ⇒ vertical opposite angles

∵ m∠E ≠ m∠R

∵ m∠F ≠ m∠Q

Only one angle in the 1st triangle is equal to one angle in the other triangle, no other angles are equal, similarity needs at least two angles in one triangle equal to two angles in the other triangle

∴ The two triangle are NOT similar by any case of similarity

∴ Δs DEF and DRQ not similar