Triangle DEF is shown below: 110° Use the drop-down menus and choose an answer from each menu: – Choose 90 degrees, an angle triangle similar to DEF will have an angle that measures 90 degrees; – Choose 45 degrees, an angle that measures 45 degrees; – Choose 60 degrees.
The Correct Answer and Explanation is:
Based on the diagram of triangle DEF, the correct answer from the drop-down menus is:
A triangle similar to DEF will have an angle that measures 110 degrees, an angle that measures 45 degrees, and an angle that measures 25 degrees.
Here’s the reasoning:
All triangles have one fundamental property in common. The sum of their interior angles is always 180 degrees. Triangle DEF shows one angle explicitly labeled as 110 degrees. If another angle is 45 degrees, we can calculate the third angle by subtracting the sum of the known angles from 180.
Third angle=180−(110+45)=180−155=25 degrees\text{Third angle} = 180 – (110 + 45) = 180 – 155 = 25 \text{ degrees}
Triangles that are similar do not need to have the same side lengths, but they do have corresponding angles that are equal in measure. This means any triangle similar to DEF must also contain angles measuring 110 degrees, 45 degrees, and 25 degrees. The orientation, size, or side proportions might vary, but the interior angles will remain unchanged.
This property is a direct result of the similarity postulates in geometry. Triangles are considered similar when their corresponding angles are equal and the sides are in proportion. Because triangle DEF has fixed angle measures, any triangle drawn with identical angles will be similar by Angle-Angle-Angle (AAA) similarity.
Choosing 90 degrees or 60 degrees for a triangle similar to DEF would be incorrect. Those values would change the angle relationships and alter the triangle’s identity entirely. Therefore, the valid choices from the drop-down are 110, 45, and 25 degrees, preserving the unique angle signature of triangle DEF and upholding geometric similarity.
