Question

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

Answer 1

Δs DEF and DRQ not similar ⇒ 2nd answer

Explanation:

Let us 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
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
3. SSS similarity : If the corresponding sides of the two triangles are proportional, then the two triangles are similar
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.

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