Diagram: △HGJ has HJ = 10, GJ = 12, and ∠G = 60°. △PQR has PQ = 8, QR = 9.6, and ∠R = 60°.
Are Δ's Similar? Similarity Ratio = ___ Δ HGJ ~ Δ ___ by: ___

Question

Diagram: △HGJ has HJ = 10, GJ = 12, and ∠G = 60°. △PQR has PQ = 8, QR = 9.6, and ∠R = 60°. Are Δ's Similar? Similarity Ratio = ___ Δ HGJ ~ Δ ___ by: ___

SnapAndSolve AI · Accepted Answer

Similarity cannot be established from the given information. Although 10/8 = 12/9.6 = 5/4 and ∠G = ∠R = 60°, the equal angles are not between the two given sides. This is SSA, which is not a valid similarity criterion. Select No if the choices are Yes/No; no similarity ratio or similarity theorem is justified.Note: The diagram also contains inconsistent measurements: in △HGJ, the sine rule would give sin H = 12 sin(60°)/10 ≈ 1.039, which is impossible.

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Diagram: △HGJ has HJ = 10, GJ = 12, and ∠G = 60°. △PQR has PQ = 8, QR = 9.6, and ∠R = 60°. Are Δ's Similar?

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