Hey!

Thanks for checking my question out!
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1. R , S, and T are the vertices of one triangle. E, F, and D are the vertices of another triangle. m∠R = 60, m∠S = 80, m∠F = 60, m∠D = 40, RS = 4, and EF = 4. Are the two triangles congruent? If yes, explain and tell which segment is congruent to line RT (1 point)

a) yes, by ASA; line FD

b) yes, by AAS; line ED

c) yes, by SAS, line ED

d) No, the triangles are not congruent

My Answer: A
Could someone please check my answer?

Thanks!
- Da Fash

3 answers

looks good

Thanks! :)

To determine if the two triangles are congruent, we need to check if their corresponding angles and sides are equal. If all the corresponding angles and sides are equal, the triangles are congruent.

In this case, we are given that m∠R = 60, m∠S = 80, m∠F = 60, m∠D = 40, RS = 4, and EF = 4.

To check for congruence, the following conditions need to be satisfied:

1. Angle-angle-side (AAS): If two angles and a side between them in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.
2. Angle-side-angle (ASA): If two angles and a side in between that are adjacent to one of the given angles in one triangle are congruent to the corresponding angles and side in another triangle, then the triangles are congruent.
3. Side-angle-side (SAS): If two sides and the angle between them in one triangle are congruent to the corresponding sides and angle in another triangle, then the triangles are congruent.

Let's check the options one by one:

a) Yes, by ASA; line FD: To use ASA, we need to have two angles and the included side congruent. In this case, we have m∠F = 60 and m∠D = 40, which are not congruent angles.

b) Yes, by AAS; line ED: To use AAS, we need to have two angles and the non-included side congruent. In this case, we have m∠F = 60, m∠D = 40, and EF = 4, which are not congruent.

c) Yes, by SAS; line ED: To use SAS, we need to have two sides and the included angle congruent. In this case, we have RS = 4, EF = 4, and m∠S = 80, which are not congruent.

d) No, the triangles are not congruent: From the analysis above, we can conclude that none of the given conditions for congruence are met. Therefore, the triangles are not congruent.

So, your answer (d) No, the triangles are not congruent, is correct.