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GEOMETRY/TRIGONOMETRY 2 Name _______________________ Perpendicular lines () Definition: If two lines are perpendicular, then they form _______________. If two lines form ____________________, then the lines are perpendicular. M 2 1 3 4 J Theorem 2-4 K N If two lines are perpendicular, then they form _________________, ________________ angles. Theorem 2-5 (converse of 2-4) If two lines form _________________, ________________ angles, then the lines are perpendicular. Theorem 2-6 B If the exterior sides of two adjacent acute angles are perpendicular, then the angles are ______________________. D If AB AC, then BAD and DAC are _______________________. A C Name the definition or state the theorem that justifies the statement about the diagram. _______________________ 1) If AB BC, then ABC is a right angle. _______________________ 2) If BD AC, then 3 4. _______________________ 3) If DC DA, then 7 and 8 are comp. B 12 _______________________ 4) 4 5. A _______________________ 5) If 4 6, then AC BD. _______________________ 6) If 7 and 8 are comp., then m7 + m8 = 90. _______________________ 7) If ADC is a right angle, then mADC = 90. 3 4 5 6 7 8 D C E D F Given: BE AC, BD BF. Find the value of x. 2 3 1 A 4 B C 8) m2 = 2x + 10, m3 = 40. 8) x = _______ 9) m3 = 2x + 5, m4 = 3x. 9) x = _______ 10) m1 = 2x, m2 = 2x + 10, m3 = 3x - 20, m4 = 3x - 10. 10) x = _______ 11) m1 = 3x + 1, m2 = 4x + 5, m3 = 2x + 13 11) x = _______ Complete the following proofs by supplying the missing statements and reasons. A 12) Given: BA AC; 2 1 1 is complementary to 3 Prove: m2 = m3 3 C Statements D B Reasons 1) BA AC 1) _________________________ 2) 1 and 2 are complementary 2) _________________________ 3) _________________________ 3) Given 4) m1 + m2 = 90; m1 + m3 = 90 4) _________________________ 5) _________________________ 5) _________________________ 6) _________________________ 6) Reflexive Property 7) _________________________ 7) _________________________