What Makes These Similar?

Geometry Level 1

In the above diagram, x = 21 , x=21, y = 14 , y=14, α = 35 ∘ , \alpha={35}^\circ, and β = 75 ∘ . \beta={75}^\circ. Which condition would mean that the two triangles are similar?

Note: The above diagram is not drawn to scale.

∣ A B ‾ ∣ = 18 , ∣ D E ‾ ∣ = 12 \lvert\overline{AB}\rvert=18, \lvert\overline{DE}\rvert=12 ∣ A C ‾ ∣ = 19 , ∣ D E ‾ ∣ = 12 \lvert\overline{AC}\rvert=19, \lvert\overline{DE}\rvert=12 ∣ A B ‾ ∣ = 19 , ∣ D F ‾ ∣ = 18 \lvert\overline{AB}\rvert=19, \lvert\overline{DF}\rvert=18 ∠ A = ∠ D = 7 0 ∘ \angle A=\angle D=70^\circ ∠ C = 7 0 ∘ , ∠ F = 3 0 ∘ \angle C=70^\circ, \angle F=30^\circ

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Gene Keun Chung by Gene Keun Chung , 50, South Korea

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1 solution

Eli Ross Staff
Oct 11, 2015

If ∠ A = ∠ D = 70 ∘ , \angle A=\angle D={70}^\circ, then ∠ C = 75 ∘ \angle C={75}^\circ and ∠ F = 35 ∘ , \angle F={35}^\circ, which implies that △ A B C \triangle ABC and △ D E F \triangle DEF satisfy the AA similarity criterion .

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