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The statements below can be used to prove that the triangles are similar.
On a coordinate plane, right triangles A B C and X Y Z are shown. Y Z is 3 units long and B C is 6 units long.
StartFraction A B Over X Y EndFraction = StartFraction 4 Over 2 EndFraction
?
StartFraction A C Over X Z EndFraction = StartFraction StartRoot 52 EndRoot Over StartRoot 13 EndRoot EndFraction
△ABC ~ △XYZ by the SSS similarity theorem.
Which mathematical statement is missing?
StartFraction Y Z Over B C = StartFraction 6 Over 3 EndFraction
∠B ≅ ∠Y
StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
∠B ≅ ∠Z
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StartFraction B C Over Y Z EndFraction = StartFraction 6 Over 3 EndFraction
You need the third corresponding side ratio to show all three ratios equal (AB/XY = AC/XZ = BC/YZ = 2), so SSS similarity applies.
You need the third corresponding side ratio to show all three ratios equal (AB/XY = AC/XZ = BC/YZ = 2), so SSS similarity applies.
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