Question

△abc and △ecd are shown below. which statement is true? △abc is similar to △ecd. △abc is not similar to △ecd. there is not enough information to determine whether the triangles are similar.

Explanation:

Step1: Analyze the properties of \(\triangle ABC\)

Since \(AB = AC\) and \(BC\) is the base, \(\triangle ABC\) is an equilateral triangle (all sides equal). So, \(\angle ABC=\angle ACB = 60^{\circ}\), and \(\angle BAC=60^{\circ}\)

Step2: Analyze the properties of \(\triangle ECD\)

Since \(EC = CD\) and \(\angle ECD = 90^{\circ}\), \(\triangle ECD\) is an isosceles right - triangle. So, \(\angle CED=\angle CDE = 45^{\circ}\)

Step3: Compare the angles of the two triangles

For two triangles to be similar, their corresponding angles must be equal.
In \(\triangle ABC\), angles are \(60^{\circ},60^{\circ},60^{\circ}\)
In \(\triangle ECD\), angles are \(90^{\circ},45^{\circ},45^{\circ}\)
Since the angles are not equal, the triangles are not similar.

Answer:

\(\triangle ABC\) is not similar to \(\triangle ECD\)