Question
Complete the following proof.
Given: LM ⊥ MO, PN ⊥ MO
Prove: ΔLMO ~ ΔPNO
3) ∠PNO = ∠LMO = ?
4) ∠O ≈ ∠O = ?
5) ΔLMO ~ ΔPNO
Given: LM ⊥ MO, PN ⊥ MO
Prove: ΔLMO ~ ΔPNO
3) ∠PNO = ∠LMO = ?
4) ∠O ≈ ∠O = ?
5) ΔLMO ~ ΔPNO
Answers
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3) Since LM ⊥ MO and PN ⊥ MO, it follows that ∠MOP is a right angle. Therefore, ∠LMO and ∠PNO are complementary angles, meaning that they add up to 90 degrees. Thus, ∠PNO = ∠LMO = 90 - ∠MOP.
4) ∠O is a common angle between the two triangles. Therefore, ∠O ≈ ∠O by the reflexive property of congruence.
5) Using the angle-angle similarity theorem, we have shown that ΔLMO ~ ΔPNO since ∠LMO ≈ ∠PNO and ∠O ≈ ∠O.
4) ∠O is a common angle between the two triangles. Therefore, ∠O ≈ ∠O by the reflexive property of congruence.
5) Using the angle-angle similarity theorem, we have shown that ΔLMO ~ ΔPNO since ∠LMO ≈ ∠PNO and ∠O ≈ ∠O.