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Hand in your homework please =) Focus Time • No talking • No eye-contact Cellphone reminder! Options Will you have your cellphone at the end of class? Don’t take your phone out at all during class YES Leave your phone at the front so you don’t get tempted (for JUST 75 mins!) YES Get caught using it in class, have it taken away and given to a VP NO Homework Pg. 381 #2, 3, 6, 7b, 10(a,e) Pg. 391 #1c, 2b, 3c, 6, 7a www.nss-gr9.wikispaces.com • Videos • Links • Powerpoint from class Having trouble? Come to room 120 any day at lunch for help! Hotel in Portugal House in California Company Building in Mexico Remember! Triangles Quadrilaterals >> >> All interior angles add to 180° All interior angles add to 360° All exterior angles add to 360° All exterior angles add to 360° Find m Find a a m 94° 120° 56° 130° 75° 100° Find t Find h Challenge! h 79° 83° t 119° 39° 33° 84° Find m m 120° 75° 130° The interior angles of a quadrilateral always add up to 360° m + 120 + 75 + 130 = 360 m + 325 = 360 m + 325 – 325 = 360 – 325 m = 35° Find a a 94° 56° 100° The exterior angles of a quadrilateral always add up to 360° a + 94 + 56 + 100 = 360 a + 250 = 360 a + 250 – 250 = 360 – 250 a = 110° Find t 79° t The interior angles of a quadrilateral always add up to 360° t + 79 + x + 119 = 360 83° x 119° Can’t find t without x t + 79 + 97 + 119 = 360 x + 83 = 180 x + 83 – 83 = 180 - 83 x = 97° t + 295 = 360 t + 295 - 295 = 360 - 295 t = 65° Find h Start with what you need to find and work backwards! h o 84° 39° 33° h + o = 180 Can’t find h without o Find h Start with what you need to find and work backwards! h o 84° 39° 33° h + o = 180 Can’t find h without o m The interior angles of a quadrilateral always add up to 360° o + 39 + 84 + m = 360 Can’t find o without m Find h Start with what you need to find and work backwards! h o 84° 39° 33° h + o = 180 Can’t find h without o m e m + e = 180 Can’t find m without e The interior angles of a quadrilateral always add up to 360° o + 39 + 84 + m = 360 Can’t find o without m Find h Start with what you need to find and work backwards! h o 84° h + o = 180 Can’t find h without o h + 114 = 180 h = 66° 39° 33° m e m + e = 180 Can’t find m without e m + 57 = 180 m = 123 The interior angles of a quadrilateral always add up to 360° The interior angles of a triangle always add up to 180° e + 33 + 90 = 180 e = 57° o + 39 + 84 + m = 360 Can’t find o without m o + 39 + 84 + 123 = 360 o = 114° Parallelogram Sketchpad Demo Parallelogram Rule >> a b >> b a Opposite angles are always equal in a parallelogram! C - rule > > a b When there are two parallel lines and a 3rd line that intersects both of them, the inside of the C-shape add up to 180° a + b = 180° 55° a 125° b b Challenge! >> a b >> >> a c d >> 70° c 55° a 125° b In a parallelogram, opposite angles are equal 55° 125° 125° 55° In a parallelogram, opposite angles are equal a = 125° b = 55° >> a b >> 70° c >> a 70° >> 70° c Since the two horizontal lines are parallel, we can use the ‘C’ rule a + 70 = 180 a + 70 – 70 = 180 - 70 a = 110° >> 110° 70° >> 70° c Since the two horizontal lines are parallel, we can use the ‘C’ rule a + 70 = 180 a + 70 – 70 = 180 - 70 a = 110° >> 110° 70° >> 110° 70° Since the two horizontal lines are parallel, we can use the ‘C’ rule a + 70 = 180 a + 70 – 70 = 180 - 70 a = 110° >> a b >> c d e The interior angles of a triangle add up to 180 e + e + 90 = 180 2e + 90 = 180 2e + 90 – 90 = 180 - 90 2e = 90 2 2 e = 45° e Start with any info you have (the triangle) Since the triangle has 2 sides of equal length, the 2 corners have the same angle (lets call them ‘e’) >> a d 45° b >> c 45° Start with any info you have (the triangle) Since the triangle has 2 sides of equal length, the 2 corners have the same angle (lets call them ‘e’) The interior angles of a triangle add up to 180 e + e + 90 = 180 2e + 90 = 180 2e + 90 – 90 = 180 - 90 2e = 90 2 2 e = 45° c + 45 = 180 c + 45 – 45 = 180 - 45 c = 135° >> a d 45° b >> 135° 45° Start with any info you have (the triangle) Since the triangle has 2 sides of equal length, the 2 corners have the same angle (lets call them ‘e’) The interior angles of a triangle add up to 180 e + e + 90 = 180 2e + 90 = 180 2e + 90 – 90 = 180 - 90 2e = 90 2 2 e = 45° c + 45 = 180 c + 45 – 45 = 180 - 45 c = 135° Floating Home in Germany Cubic Homes in Netherlands ROM in Toronto Checking out polygons on Sketchpad Sum of Interior Angles = 180(n-2) n represents how many sides the polygon has Pentagon n=5 Hexagon n=6 Heptagon n=7 SIA = 180(5-2) SIA= 180(3) SIA= 540° SIA = 180(6-2) SIA= 180(4) SIA= 720° SIA = 180(7-2) SIA= 180(5) SIA= 900° Use the new equation to find the sum of the interior angles of a triangle What angle does each corner of a regular octagon have? Find w How many sides does a polygon have if the sum of its interior angles is 1800°? Challenge! w Use the new equation to find the sum of the interior angles of a triangle Sum of interior angles = 180(n-2) A triangle has 3 sides so n = 3 Sum of interior angles = 180(3-2) Sum of interior angles = 180(1) Sum of interior angles = 180° We already knew this What angle does each corner of a regular octagon have? Sum of interior angles = 180(n-2) An octagon has 8 sides so n = 8 Sum of interior angles = 180(8-2) Sum of interior angles = 180(6) Sum of interior angles = 1080° Since a regular octagon means that all 8 corners have the same angle, we divide 1080° by 8 (the # of corners) to get 135° for each corner. How many sides does a polygon have if the sum of its interior angles is 1800°? Sum of interior angles = 180(n-2) We don’t know the number of sides (n) but we know the sum of interior angles 1800 = 180(n-2) 180 180 10 = n-2 10 + 2 = n – 2 + 2 12 = n A polygon with an interior angle sum of 1800° has 12 sides. Find w Since the triangle has 2 sides of equal length, it also has 2 corners of equal angle x w w w + w + x = 180 2w + x = 180 Can’t find w without x Find w Since the triangle has 2 sides of equal length, it also has 2 corners of equal angle x w w + w + x = 180 w 2w + x = 180 Can’t find w without x 2w + 108 = 180 w = 36° Since this is a regular pentagon (n = 5) Sum of interior angles = 180(5-2) Sum of interior angles = 180(3) Sum of interior angles = 540° Since all 5 corners are equal, you get x by dividing 540° by 5. This means x = 108°