Question 2 of 10David 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.Cannot be determinedB.Similar - SSSC.Similar - AAD.Similar - SAS
Question
Question 2 of 10David 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.Cannot be determinedB.Similar - SSSC.Similar - AAD.Similar - SAS
Solution
The triangles ΔPQR and ΔSTU are similar. We can determine this by using the Side-Side-Side (SSS) Similarity Postulate.
The SSS Similarity Postulate states that if the lengths of the corresponding sides of two triangles are proportional, then the triangles are similar.
In this case, we can see that the sides PR and SU are proportional because 12/3 = 4. Similarly, the sides PQ and ST are proportional because 20/5 = 4.
Since the corresponding sides of the triangles are proportional, we can conclude that the triangles are similar by the SSS Similarity Postulate.
So, the answer is B. Similar - SSS.
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