Jerry drew ΔΔJKL and ΔΔMNP so that ∠𝐾≅∠𝑁, ∠𝐿≅∠𝑃∠K≅∠N, ∠L≅∠P, JK = 6, and MN = 18. Are ΔΔJKL and ΔΔMNP similar? If so, identify the similarity postulate or theorem that applies.A.Similar - AAB.Cannot be determinedC.Similar - SSSD.Similar - SAS
Question
Jerry drew ΔΔJKL and ΔΔMNP so that ∠𝐾≅∠𝑁, ∠𝐿≅∠𝑃∠K≅∠N, ∠L≅∠P, JK = 6, and MN = 18. Are ΔΔJKL and ΔΔMNP similar? If so, identify the similarity postulate or theorem that applies.A.Similar - AAB.Cannot be determinedC.Similar - SSSD.Similar - SAS
Solution
Yes, ΔJKL and ΔMNP are similar. The similarity postulate that applies is the Angle-Angle (AA) postulate. This is because two pairs of corresponding angles are congruent (∠𝐾≅∠𝑁 and ∠𝐿≅∠𝑃), which is enough to say that the triangles are similar by the AA postulate. The lengths of the sides are not necessary for this postulate. So, the correct answer is A. Similar - AA.
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