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M2-050-A02-V02
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G-SRT.5
Warmup
M2-050-A02-V02
Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Prove triangles similar using a valid criterion
Problem
\(\text{All}~\text{three}~\text{pairs}\) of corresponding sides in \(\text{two}~\text{triangles}\) have the same ratio. Name the similarity criterion this evidence satisfies and distinguish proportional sides from equal side lengths.
Answer choices
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A
This matches SAS similarity because comparing side lengths means you use a side-angle-side test, even if no angle information is stated.
B
This matches SSS congruence because having all three corresponding side ratios equal means the triangles have the same side lengths and must be identical.
C
This matches AA similarity because if the side ratios are equal, the corresponding angles must be equal, so angle-angle proves the triangles are similar.
D
SSS similarity applies because all three corresponding side pairs share one ratio. The sides are proportional, not necessarily equal; they are equal only when the common ratio is 1.
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Curriculum context
Standard G-SRT.5
Category Geometry
Domain Similarity, Right Triangles, and Trigonometry
Objective Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Problem type Prove triangles similar using a valid criterion
