Question

are these shapes similar?
k
51 m 51 m
i 29 m j
u 28 m s
51 m 39 m
t
yes no
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Explanation:

Step1: Recall similarity conditions

For triangles to be similar, their corresponding sides must be in proportion (SSS similarity) or corresponding angles equal (AA similarity). First, identify corresponding sides.

Step2: Analyze triangle \( \triangle KIJ \) and \( \triangle UST \) (assuming correspondence)

• \( \triangle KIJ \): Sides \( KI = 51 \), \( KJ = 51 \), \( IJ = 29 \)
• \( \triangle UST \): Sides \( US = 28 \), \( ST = 39 \), \( UT = 51 \)

Check ratios: \( \frac{KI}{UT}=\frac{51}{51}=1 \), \( \frac{KJ}{ST}=\frac{51}{39}=\frac{17}{13}\approx1.307 \), \( \frac{IJ}{US}=\frac{29}{28}\approx1.036 \). Ratios are not equal. Also, check angles: The marked angles don't show consistent correspondence (e.g., \( \triangle KIJ \) has two equal sides (isosceles), \( \triangle UST \) has sides 28, 39, 51 (scalene? No, 28,39,51: check if isosceles? No). So angles won't correspond. Thus, sides not proportional, angles not matching.

Answer:

no