Multiple Choice
R , S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. mangleR = 60, mangleS = 80, mangleF = 60, mangleD = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to modifying above R T with bar.
(1 point)
Responses
yes, by ASA; Modifying above upper F upper D with bar
yes, by ASA; Image with alt text: Modifying above upper F upper D with bar
yes, by AAS; Modifying above upper E upper D with bar
yes, by AAS; Image with alt text: Modifying above upper E upper D with bar
yes, by SAS; Modifying above upper E upper D with bar
yes, by SAS; Image with alt text: Modifying above upper E upper D with bar
No, the triangles are not congruent
The correct answer is:
No, the triangles are not congruent.
The correct answer is: No, the triangles are not congruent.
To determine whether the two triangles are congruent, we need to analyze their angles and sides.
First, let's focus on the angles. We know that m∠R = 60°, m∠S = 80°, m∠F = 60°, and m∠D = 40°.
To determine the congruence of the triangles using angle-angle-side (AAS) or angle-side-angle (ASA), we need to find a pair of congruent angles and a corresponding congruent side.
However, in this case, we don't have any congruent angles between the two triangles. Therefore, we can't use AAS or ASA to prove the triangles congruent.
Next, let's look at the sides. We know that RS = 4 and EF = 4.
If we can find a pair of congruent sides and a corresponding congruent angle, we can use side-angle-side (SAS) to prove the triangles congruent.
In this case, we have RS = EF = 4, which means we have a pair of congruent sides. However, we don't have a congruent angle corresponding to those sides. Therefore, we can't use SAS to prove the triangles congruent.
Based on the information given, we can conclude that the two triangles are not congruent.
Therefore, the correct response is:
No, the triangles are not congruent.