Question

Select the reason why these triangles are

similar. If they are not, select "Not similar".
A. AA
B. SAS
C. SSS
D. Not similar

Answer 1

The reason why these triangles are similar is;

A. AA

Explanation:

A two column proof can be presented using the drawing of the question diagram created with Microsoft Visio as follows;

Statement
`{}` Reason

`\overline {AB}` ║
`\overline {DE}`
`{}` Given

∠ACB ≅ ∠DCE
`{}` Vertically opposite angles

∠BAC ≅ ∠DEC
`{}` Alternate interior angles theorem

∠ABC ≅ ∠CED
`{}` Alternate interior angles theorem

ΔABC ~ ΔCDE
`{}` By Angle-Angle (AA) similarity postulate

Therefore, the correct option is AA.