Multiple Choice
Looking at triangleDEF, which statement below is true?
Triangle D E F is shown. Angle E measures 61 degrees. Angle D measures 58 degrees.
(1 point)
Responses
Modifying above upper E upper D with bar is congruent to Modifying above upper E upper F with bar
Image with alt text: Modifying above upper E upper D with bar is congruent to Modifying above upper E upper F with bar
angle upper D is congruent to angle upper F
Image with alt text: angle upper D is congruent to angle upper F
Modifying above upper F upper D with bar is congruent to Modifying above upper E upper D with bar
Image with alt text: Modifying above upper F upper D with bar is congruent to Modifying above upper E upper D with bar
Modifying above upper E upper F with bar is congruent to Modifying above upper F upper D with bar
Modifying above upper E upper F with bar is congruent to Modifying above upper F upper D with bar
The correct statement is "Modifying above upper E upper D with bar is congruent to Modifying above upper E upper F with bar."
To determine which statement is true, you need to understand the properties and relationships of angles in a triangle.
In a triangle, the sum of the interior angles is always 180 degrees. Therefore, if angle E measures 61 degrees and angle D measures 58 degrees, you can find the measure of angle F by subtracting the sum of angles E and D from 180:
180 - (61 + 58) = 180 - 119 = 61 degrees
Now let's evaluate each statement with the information we have:
1. Modifying above upper E upper D with bar is congruent to Modifying above upper E upper F with bar:
This statement suggests that angle ED is congruent to angle EF. However, we don't have any information about angle ED or angle EF, so we cannot determine whether they are congruent. This statement is not true based on the given information.
2. angle upper D is congruent to angle upper F:
This statement suggests that angle D is congruent to angle F. Since we found earlier that angle F measures 61 degrees and angle D measures 58 degrees, it means that angle D is not congruent to angle F. This statement is not true based on the given information.
3. Modifying above upper F upper D with bar is congruent to Modifying above upper E upper D with bar:
This statement is suggesting that angle FD is congruent to angle ED. Again, we don't have any information about angle FD or angle ED, so we cannot determine whether they are congruent. This statement is not true based on the given information.
4. Modifying above upper E upper F with bar is congruent to Modifying above upper F upper D with bar:
This statement suggests that angle EF is congruent to angle FD. Given that we found earlier that angle F measures 61 degrees and angle D measures 58 degrees, this statement is true. Angle EF, which is 61 degrees, is indeed congruent to angle FD. Therefore, this statement is true based on the given information.
Therefore, the correct answer is:
Modifying above upper E upper F with bar is congruent to Modifying above upper F upper D with bar.