Question

Notice that two sides and a nonincluded angle of δabc are congruent to the corresponding parts of δabd , but the triangles are not congruent. must δefg be congruent to δabd if e f=10, f g=6 , and ∠ e≅∠ a ? explain. part e despite the sizes of the two triangles, what do you notice about the ratios of each corresponding pair of sides in δabc and δade?

Answer 1

No, ΔEFG cannot be congruent to ΔABD. In order for two triangles to be congruent, at least three elements must be identical. The ratios of corresponding sides in ΔABC and ΔADE are equal.

Step-by-step explanation:

No, ΔEFG cannot be congruent to ΔABD. Even though two sides and a non-included angle of ΔABC are congruent to the corresponding parts of ΔABD, it is not enough to prove congruence. In order for two triangles to be congruent, at least three elements (sides and/or angles) must be identical.When comparing the ratios of each corresponding pair of sides in ΔABC and ΔADE, we can notice a pattern. The ratios of the sides in the two triangles are equal. For example, if we take the ratio of AB to AC and the ratio of ADE to AE, they will be the same. This is known as the side-splitter theorem.So, in summary, ΔEFG is not congruent to ΔABD and the side ratios in ΔABC and ΔADE are equal.