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M2-050-A02-V03
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G-SRT.5
Warmup
M2-050-A02-V03
Use triangle congruence and similarity criteria to solve problems and prove geometric relationships.
Prove triangles similar using a valid criterion
Problem
\(\text{Two}~\text{pairs}~\text{of}~\text{corresponding}~\text{sides}\) in \(\text{two}~\text{triangles}\) have the same ratio, and the angles included between those sides are congruent. Name the similarity criterion this evidence satisfies and justify the match.
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A
This matches SAS congruence because the side information and the included congruent angle show the triangles must have the same size and shape.
B
This matches SSS similarity because any time side ratios are equal, the triangles are similar without needing to use the angle information.
C
This matches SAS similarity because two corresponding side ratios are equal and the included angle between those sides is congruent.
D
This matches AA similarity because once one pair of angles is congruent, the side ratios are enough to show the triangles are similar by angles.
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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
