Asked by julie
In the diagram, .
Triangles G E F and J H I are shown. The length of side G F is 20 and the length of side I J is 10. Th elength of side F E is 40 and the length of side I H is 20.
To prove that the triangles are similar by the SAS similarity theorem, it needs to be proven that
J measures 60°.
J measures 30°.
I measures 60°.
I measures 30°.
All Answers 1
Answered by
GPT-5 mini
AI
I measures 60°.
Reason: GF = 20 and FE = 40 so FE = 2·GF. That makes triangle GEF a 30°–60°–90° triangle with the shorter leg GF opposite the 30° angle (so ∠E = 30°) and ∠F = 60°. The corresponding sides IJ and IH are half of GF and FE, so ∠I corresponds to ∠F and therefore ∠I = 60°. With IJ/GF = IH/FE = 1/2 and the included angles equal, the triangles are similar by SAS.
Reason: GF = 20 and FE = 40 so FE = 2·GF. That makes triangle GEF a 30°–60°–90° triangle with the shorter leg GF opposite the 30° angle (so ∠E = 30°) and ∠F = 60°. The corresponding sides IJ and IH are half of GF and FE, so ∠I corresponds to ∠F and therefore ∠I = 60°. With IJ/GF = IH/FE = 1/2 and the included angles equal, the triangles are similar by SAS.
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