Question

Determine how the triangles are similar, if possible.

A: SAS
B: AA
C:Not similar
D: SSS

Answer 1

The two triangles are similar by SAS postulate of similarity ⇒ A

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 the given figure

∵ There are 2 triangles

∵ The ratio between 2 corresponding sides in the Δs is
`(28)/(40)`

∵
`(28)/(40)` = 0.7

∵ The ratio between the other 2 corresponding sides in the Δs is
`(42)/(60)`

∵
`(42)/(60)` = 0.7

→ That means 2 sets of corresponding sides have an equal ratio

∴ The 2 sets of corresponding sides are proportional

→ By using the parallel sides

∵ There are two parallel sides

∴ The angles between the sides 28, 42, and the sides 40, 60 equal

because they are corresponding angles

∴ The included angles are equal in measures

→ By using case 4 above

∴ The two triangles are similar by SAS postulate of similarity