If in ∆ ABC and ∆ PQR, ொோ = ோ = ொ then:a) ∆PQR ~∆CAB b) ∆PQR ~∆ABC c) ∆CBA ~∆PQR d) ∆BCA ~∆PQR
Question
If in ∆ ABC and ∆ PQR, ொோ = ோ = ொ then:a) ∆PQR ~∆CAB b) ∆PQR ~∆ABC c) ∆CBA ~∆PQR d) ∆BCA ~∆PQR
Solution
Given that ∆ABC and ∆PQR have corresponding angles of ொோ and ோ, we can determine the similarity between the two triangles.
To prove the similarity, we need to show that the corresponding angles are equal and the corresponding sides are proportional.
a) To prove ∆PQR ~ ∆CAB, we need to show that the corresponding angles are equal. Since ∆ABC and ∆PQR have corresponding angles of ொோ and ோ, we can conclude that ∆PQR ~ ∆CAB.
b) To prove ∆PQR ~ ∆ABC, we need to show that the corresponding angles are equal. Since ∆ABC and ∆PQR have corresponding angles of ொோ and ோ, we can conclude that ∆PQR ~ ∆ABC.
c) To prove ∆CBA ~ ∆PQR, we need to show that the corresponding angles are equal. However, the given information does not provide the corresponding angles between ∆CBA and ∆PQR. Therefore, we cannot conclude that ∆CBA ~ ∆PQR.
d) To prove ∆BCA ~ ∆PQR, we need to show that the corresponding angles are equal. However, the given information does not provide the corresponding angles between ∆BCA and ∆PQR. Therefore, we cannot conclude that ∆BCA ~ ∆PQR.
Based on the given information, the correct answer is: a) ∆PQR ~ ∆CAB
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