Question

100 Points! Geometry question. Determine whether each pair of triangles is similar. If so, write a similarity statement. If not, what would be sufficient to prove the triangles similar? Explain your reasoning. Photo attached. Thank you!

Answer 1

We cannot determine if the triangles are similar.

Explanation:

The diagram shows two triangles, ΔABC and ΔDEF.

The tick marks on the sides of the triangles show that two corresponding sides are congruent:

• AB ≅ ED
• BC ≅ EF

In similar triangles:

• Corresponding angles are the same size.
• Corresponding sides are always in the same ratio.

As the diagram does not include any information about the interior angles or the length of the third side, we cannot determine if the triangles are similar.

To prove the triangles are similar by SAS similarity, we would need the measure of the included angles (angles B and E).

To prove the triangles are similar by SSS similarity, we would need the measure of the third side.

To prove the triangles are similar by AA similarity, we would need the measures of two corresponding angles.