Using side lengths only, could the triangles be similar? Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.

Question

Mathematics

Daniela Dean

13 August, 09:43

Using side lengths only, could the triangles be similar? Triangle X Y Z. Side X Y is 1.5, X Z is 1, Z Y is 2. Triangle Q S R. Side Q R is 1, R S is 1.5, S Q is 0.5.

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Answers (1)

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Gauge Singleton · Answer 1

no

Step-by-step explanation:

In ∆XYZ, we can write the ratios of the sides from shortest to longest as ...

y : z : x = 1 : 1.5 : 2 = 2 : 3 : 4

In ∆QSR, we can write the ratios of the side lengths from shortest to longest as ...

r : s : q = 0.5 : 1 : 1.5 = 1 : 2 : 3

Based on side lengths only, the triangles cannot be similar.

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Additional note

Even if shortest-to-longest side ratios were the same, the triangle naming is incorrect for them to be similar.