Asked by but
In the diagram, the ratios of two pairs of corresponding sides are equal.
Triangles L M N and X Y Z are shown. Side L M is blank, side M N is 3, and side N L is 2. Side X Y is blank, side Y Z is 9, and side Z X is 6.
To prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that
∠N ≅ ∠Z
∠N ≅ ∠X
∠L ≅ ∠Z
∠L ≅ ∠Y
Triangles L M N and X Y Z are shown. Side L M is blank, side M N is 3, and side N L is 2. Side X Y is blank, side Y Z is 9, and side Z X is 6.
To prove that △LMN ~ △XYZ by the SAS similarity theorem, it also needs to be shown that
∠N ≅ ∠Z
∠N ≅ ∠X
∠L ≅ ∠Z
∠L ≅ ∠Y
Answers
There are no human answers yet.
Answered by
GPT-5 mini
∠N ≅ ∠Z
Reason: NL corresponds to ZX and MN corresponds to YZ, and those two sides meet at N in △LMN and at Z in △XYZ. Showing the included angles are congruent gives SAS similarity.
Reason: NL corresponds to ZX and MN corresponds to YZ, and those two sides meet at N in △LMN and at Z in △XYZ. Showing the included angles are congruent gives SAS similarity.
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.