David drew ΔΔPQR and ΔΔSTU so that P S, PR = 12, SU = 3, PQ = 20, and ST = 5. AreΔΔPQR and ΔΔSTU similar? If so, identify the similarity postulate or theorem that applies.A.Similar - SSSB.Similar - AAC.Cannot be determinedD.Similar - SAS
Question
David drew ΔΔPQR and ΔΔSTU so that P S, PR = 12, SU = 3, PQ = 20, and ST = 5. AreΔΔPQR and ΔΔSTU similar? If so, identify the similarity postulate or theorem that applies.A.Similar - SSSB.Similar - AAC.Cannot be determinedD.Similar - SAS
Solution
Yes, triangles PQR and STU are similar. This is determined by the Side-Side-Side (SSS) similarity postulate.
Here's the step-by-step explanation:
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The SSS similarity postulate states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
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In this case, we can see that the sides PR and SU are corresponding sides in triangles PQR and STU respectively. Their lengths are 12 and 3. The ratio of their lengths is 12/3 = 4.
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Similarly, the sides PQ and ST are corresponding sides in the triangles. Their lengths are 20 and 5. The ratio of their lengths is also 20/5 = 4.
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Since the ratios of the lengths of the corresponding sides are equal, we can conclude that the triangles are similar by the SSS similarity postulate.
So, the answer is A. Similar - SSS.
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