Question

Determine whether the two triangles:are congruent. If they are congruent, state by what theorem (55S, SAS; or ASA) they are congrient. Let d=9, d=5. C=10,if=5, e=9, and f=10 Yes, the two triangles are congruent by the 555 Theorem. Yes, the twe triangles are congruent by the SAS Theorem Yes, the two thangles are congrinent by the ASA Theorem No, the tho triangles are not congruent.

Answer 1

The two triangles are congruent by the SAS theorem based on the given information.

Step-by-step explanation:

The question is asking whether two triangles are congruent, and if so, by which theorem. To determine congruence, we need to compare the corresponding sides and angles of the triangles. Given the information d=9, d=5, C=10, if=5, e=9, and f=10, we can use the Side-Angle-Side (SAS) theorem to show that the two triangles are congruent.

First, we compare the sides DA₁ and BA₁. Both sides have length 9, so they are equal.

Next, we compare the angles ADC and BAC. Both angles have a measure of 55 degrees.

Finally, we compare the sides AC and BC. AC has a length of 10, while BC has a length of 10. Therefore, all corresponding sides and angles are equal, and the triangles are congruent by SAS theorem.