Question 1.
Question 1.
Correct Answer
Step-by-Step Solution
Given that ΔABC ~ ΔPQR using SAS similarity criteria, we know that the corresponding sides of similar triangles are in proportion. Therefore, we have the following relationships:
1. AC/AB = PR/PQ (corresponding sides AC and PR, AB and PQ)
2. BC/AC = QR/PR (corresponding sides BC and QR, AC and PR)
3. AC/BC = PR/QR (corresponding sides AC and PR, BC and QR)
Since we need to find which of the options is true based on the similarity, we can analyze option (A):
- AC/AB = PR/PQ is indeed true as it corresponds to the sides of the triangles.
Now, let's check the other options:
(B) BC/AC = PR/QR is not directly true based on the given similarity.
(C) AC/BC = PR/PQ is not directly true either.
(D) AC/BC = PR/QR is not true based on the given similarity.
Thus, the only correct option is (A).
Explanation
The answer is correct because it directly follows from the properties of similar triangles. When two triangles are similar, the ratios of their corresponding sides are equal. Since ΔABC is similar to ΔPQR, the ratio of AC to AB must equal the ratio of PR to PQ, making option (A) the correct choice.
Important Formula
If ΔABC ~ ΔPQR, then AC/AB = PR/PQ, BC/AC = QR/PR, AC/BC = PR/QR.
Final Answer
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