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pair is called Corresponding angles and they are equat to each other. They occupy the Same slot in the box of lines that M14132 intersect. 117% measure. This is how paraller 2 box. 48 132' 2 48 This looks interesting Summary G²+6²=c² ;f 90° If the hypotemuse 13 Smaker, is acute If bigger, Hts obtuse. Pythagorean Theorem b 7 a base b= height Subtopic 1. Approximating a Square root To approximate a squees root, Just Find 2 Squared rembers in which the square roat is in between. Exi 2³.NT, 3², Then Subtrad the highest numbers by the smallest in order to setup a fraction and got a decimud. You then add this degreed to the swell number. 27-25=22 36-25=11 The pythagorean theorem states that Q² + b² =C² if Here is an example: Q² +b² =c C=hypotenuse a²+ b² > c² Q³ + b³<C² Lets Solve now!, Solve 5² √27 6² Subtopic 3 Types of triangles 2 = 0.18 11 275.18 √27 This is a right or 90° triangle. = 25, 27, 36 5+0.185.19 This is an ecule or less than 90° triangle. This is an oblume of wore than 90° triangle Right triangle 9² +7² x 81 +49 = x² 130 11.4 = X Ex: Obtuse triangle a<b+c b<a+c The c<a+b Acute triangle y it's a right triangle Subtopic 2. Triangle or no the master But is how To know if 3 measures make a triangle, 2 side lengthe need to be greater than the third side. 4 7<14117 ✓ It's my right! 7, 14,17 a. b. с 1427617 ✓ not? 172 7+14 a triangle, is grader its a triangle way to prove/disprove is by adding 3² + 4 ² = 5² 9 + 16 = 25 25 = 25 3³ +4³ > 4² 16 25 > 16 > 16 3² +4² <6 9+16 ≤ 36 25 ≤ 36 Summary Know the formulas for distance and paint Distance and midpoint Distance and midpoint are important topics in geometry, they each have a formade you have to remember, I will introduce you to these topics, distance is the delance between two Coordinates on a graph, Coordinate in between two other Coordinates mean while, the midpoint is a Let go over the formules: Distance Formula d= √(x₂−X₁)² +Cy₂-y₁ J² Example: I want to know how for (4,2) is From (8,4). (4,2), (8,4) (8-4)² + (4-2)² ( 4 )² + ( 2 )² 16+ 4 20 4.47 the Conducts and Speak you see how easy that is! Subtopio 1. Find Missing end points Midpoint Formula (x₁+xa, yinya) 2 m= Example: • I wonder what the middle point of (8,4) and (12,-2) is. (8,4), (12,-2) 8+12 (20 Sup easy! greal work Ex: 1 (101) To find a pussing end point you need One endpoint and a midpoint. Calculate the difference between one and print and the midpoints. then apply that some difference from the undpoint onto the endpoint 7 446-23 (4,2) S₁4 22 (8)/(1) 4) 44 (12.6) سرلک Summary of Topic Cross multiply a=c 음. d ad = be Remember Thisl Take Notes of this! ax²+bx+c=0 Once you have your Facterised quadratic, aqual cash breakal 10.0 and Soles. Example (a+b)(a-b) a+b=o arba b OU An answer Negative! bad bad! a-b=o anbad +b ib auto Congruent Equal Similar 2 V (2 Similar Triangles AABC-ADEF 2+10= 12 AABCDEF 2+2=4 15 BA=12 EF=4 3/15 = 13 2+ may das use AABC ADEF Find X. 41=X+2 니 Simplify 2+x==3 15 (4) (12) = (x+10) (x+2) 48x²+2x+10x + 20 48 X³ +12x+20 -49 1414 = -14-14 x= 0= x² +12x-28 0²-2x+14x-29 O= x(x-2) 14 (x-2) O=(x+14) (x-2) X41410 L X-200 X-2=0 +2 42 15=10+3x 10 -10 3.3 1-X 1 I To Solve Similar triangles you have to Satup You X=2 T 2 proportions and Crass-multiply arrows in the order of the letters to label, Example Most importantly, make sure to remember the similar sign. Proportion 8 Simple This is the simple Kind of problem Quadratic +2/2 = = ✓ Slightly harder problem that invoer quadration but don't worry Salve H Ĉ Notes Main Notes! Adjecent Side is next to the angle given and the hypotom.co Remember! Trigonometry 1. -Sine -Cosine -Tangent The ratio of the leg adjacent to the angle to the hypotenuse. Sin= The ratio of the leg Opposite the angle to the hypotemuse. Cos= You may be wondering what Ingonometry is. Aul it is, is the study of triangles I trig there are things known as trigonometric ration, lets deep dive into there. There are 3 ralios The ratio of the leg Opposite •Tan A = the angle to the leg adjacent to the Angle. •Tan B =% Opp adj Tan=20 Sin A = 3/13 Cos A= ¹2/11 Soh Tan A = 5/12 Cah Ex: • Sin A = % •Sin B = "/c Tog •Cos A = "/c •Cos B = "/c •Remember. Try remembering the Soh Cah Toa Practice is key, lets do Some problems boood are a triangle. as adjacent Or Oppente h = hypotenume = 12/13 Sin C = b Cos C = 3/13 Tan C = 1215 13 B Trigonometry 2. ●●● Salve for missing side Q³ +16 ³ = 34 -15% -16% 4² = 100 do √900 030 Trigonometry is a fundamental in math, lots Continue practicing! Remember: Soh Sin w = 12/15 Cos W = 9/13 30 Tan w = 12/a 16 34 SOH hypotenuse Sine Cah Tog of Sin X= 9/19 Opposite Cos X = 15 Tan X= Sin L = Cos L = Tan L = 30/34 16/34 30/16 You might be wondering when to use Sine. Cosine, or tangent if not Spearically asked for one. Lets teach you. CAH hypotenuse adjacent Cosine 0 Selve for the hypotenuse. 9° +12³ = ² 81 +144 = ² 225 = ¹ oth IS: h 15 Sin M = Cos M = Tan M= TOA adjacent opposite Tangent