Download Perpendicular Lines

PERPENDICULAR
LINES
2.5
Perpendicular Lines Definition
Two lines that intersect to form _____________
Theorems
• 2-4: If two lines are perpendicular, then
they form _____________________
• 2-5 If two lines form congruent adjacent
angles, then the lines are _____________
• Theorem 2-5 is the __________ of
Theorem 2-4
Theorems Contd
• Theorem 2-6: If the exterior sides of 2 adjacent
acute angles are perpendicular, then the angles
are _____________
• If 𝐴𝐵 ⊥ 𝐴𝐶 then _______________
Theorem 2-4 Proof
• If 2 lines are perpendicular, then they
form congruent adjacent angles.
Given: l ⊥ n
Prove: <1, <2, <3, <4 are congruent angles
STATEMENTS
1. l ⊥ n
2. <1, <2, <3, <4 are 90 degrees
3. <1. <2, <3, <4 are congruent
angles
PROOF
Find the value of x
• Given 𝐵𝐸 ⊥ 𝐴𝐶, 𝐵𝐷 ⊥ 𝐵𝐹
• 1. m <2 = 2x +10, m <3 =40
• 2. m <3 = 2x + 5, m <4= 3x
Find the value of x
• Given 𝐵𝐸 ⊥ 𝐴𝐶, 𝐵𝐷 ⊥ 𝐵𝐹
3. m <1 = 2x, m <2 = 2x + 10,
m <3= 3x -20, m <4 = 3x-10
3. m <1= 3x + 1, m <2= 4x + 5, m <3= 2x +13
TRUE or FALSE
• Given: 𝐴𝐵 ⊥ 𝐶𝐷
𝐴𝐵 ⊥ 𝐸𝐹
<CGB is a right angle
<CGA is a right angle
m< DGB = 90
<EGC and <EGA are complements
<DGF is complementary to <DGA
<EGA is complementary to <DGF