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.
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.
Solution 1
Yes, triangles PQR and STU are similar.
The reason is because the sides of the triangles are proportional. This is determined by comparing the ratios of the corresponding sides:
PR/SU = 12/3 = 4 PQ/ST = 20/5 = 4
Since these ratios are equal, the triangles are similar according to the Side-Side-Side (SSS) Similarity Theorem. This theorem states that if the ratios of the lengths of corresponding sides of two triangles are equal, then the triangles are similar.
Solution 2
Yes, triangles PQR and STU are similar.
The reason is because the sides of the triangles are proportional. If we divide the corresponding sides, we get:
PR/SU = 12/3 = 4 PQ/ST = 20/5 = 4
Since the ratios are equal, the triangles are similar according to the Side-Side-Side (SSS) Similarity Theorem. This theorem states that if the ratios of the lengths of corresponding sides of two triangles are equal, then the triangles are similar.
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