Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Duality (projective geometry) wikipedia , lookup
Noether's theorem wikipedia , lookup
Riemann–Roch theorem wikipedia , lookup
Trigonometric functions wikipedia , lookup
History of trigonometry wikipedia , lookup
Rational trigonometry wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Brouwer fixed-point theorem wikipedia , lookup
Line (geometry) wikipedia , lookup
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