WILL MARK BRAINLYIEST!!!! Ellie drew ΔLMN, in which m∠LMN = 90°. She then drew ΔPQR, which was a dilation of ΔLMN by a scale factor of one half from the center of dilation at point M. Which of these can be used to prove ΔLMN ~ ΔPQR by the AA similarity postulate?
Answers
Final answer:
The triangles ΔLMN and ΔPQR are similar as per the AA similarity postulate. This is because ΔLMN and ΔPQR have two pairs of congruent corresponding angles: ∠LMN and ∠PQR, and ∠LM and ∠PQ, contemporaneously proving the AA (Angle-Angle) similarity postulate.
Explanation:
The given problem involves two triangles ΔLMN and ΔPQR. Here, ΔLMN is the original triangle, and ΔPQR is a dilated version of ΔLMN by a scale factor of one-half centered at point M.
For the AA (Angle-Angle) similarity postulate, we need to confirm that two angles of one triangle are congruent to two angles of another triangle. If we can establish this, we can deduce that the two triangles are similar.
Firstly, it is given that m∠LMN is 90°. As a property of dilation, it preserves the measures of angles. This means that m∠PQR will also be 90°. Secondly, since the dilation happens at point M, ∠M of ΔLMN will be the same as ∠P of ΔPQR. Thus, we have two sets of corresponding angles (LMN and PQR, and LM and PQ) that are congruent, satisfying the AA similarity postulate. Therefore, we can conclude that ΔLMN is similar to ΔPQR by the AA similarity postulate.
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Final answer:
The triangles ΔLMN and ΔPQR can be proven similar by the AA similarity postulate.
Explanation:
The triangles ΔLMN and ΔPQR are similar to each other by the AA (Angle-Angle) similarity postulate.
AA similarity postulate states that if two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
In this case, since ΔPQR is a dilation of ΔLMN with a scale factor of one half, the angles of ΔPQR are congruent to the corresponding angles of ΔLMN.
Therefore, we can conclude that ΔLMN ~ ΔPQR by the AA similarity postulate.
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