* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Download Powerpoint
Survey
Document related concepts
Multilateration wikipedia , lookup
Rational trigonometry wikipedia , lookup
Integer triangle wikipedia , lookup
Euler angles wikipedia , lookup
Euclidean geometry wikipedia , lookup
History of trigonometry wikipedia , lookup
Tessellation wikipedia , lookup
Trigonometric functions wikipedia , lookup
Pythagorean theorem wikipedia , lookup
Golden ratio wikipedia , lookup
List of works designed with the golden ratio wikipedia , lookup
Regular polytope wikipedia , lookup
Transcript
Fourth Six Weeks’ Test Review Find the Geometric mean between 4 and 25. =10 NM=9, MK=4, Find JM. =6 4 Find x 25 x =10 What equation can be formed? g 2 t 2 m2 m g t Find x x 6 8 =10 Find the leg of the right triangle: 15 17 x =8 Find x 20 x =12 16 Find x x 21.63 12 18 Find x 15 15 x 24 15 15 X= 9 12 12 24 Find x 45o 12 2 x =12 Find x x 8 2 8 8 x 10 2 10 10 o o o 45 -45 -90 5 5 5 2 o o o 45 - 45 -90 x 4 8 2 o o o 30 -60 -90 60 6 30 x 3 3 o o o 30 -60 -90 2 60 x 4 30 An equilateral triangle has a side of 12. What is its altitude? 6 3 5 3 x 10 10 10 What kind of triangle has sides 41, 40 and 9? Right What kind of triangle has sides of 8, 12 and 18? Obtuse Complete the given Ratio: B a C c b sin A a A c Complete the given Ratio: B a C c b cos A b A c Complete the given Ratio: B a C c b a sin A c A Complete the given Ratio: B a C c b a tan A b A Complete the given Ratio: B a C c b b cos A c A Complete the given Ratio: B a C c b b sin B c A Complete the given Ratio: B a C c b b tan B a A Complete the given Ratio: B a C c b a cos B c A Use your Calculator to find… sin 23 0.3907 Use your Calculator to find… 62 tan ___ 1.881 Set up a correct ratio to find x: 8 8 sin 29 x x 29 Set up a correct ratio to find x: x 34 18 x cos34 18 Set up a correct ratio to find x: 28 x 44 x tan 44 28 Set up a correct ratio to find x: 8 8 sin 29 x x 29 Solve for x: x sin 35 20 x 11.47 Solve for x: x cos 72 12 x 3.71 Solve for x: 20 sin 64 x x 22.25 Solve for x: 11 cos x 13 x 32.2 Solve for x: 14 tan 41 x x 16.11 Solve for x: 17 sin x 20 x 58.2 Solve for x: 14 tan x 9 x 57.3 Solve for x: 12 cos 72 x x 38.8 Fill in the blank…. cos ___ 40 sin 50 What term describes only the blue polygons? Convex What term describes only the blue polygons? Regular What is the relationship between an interior and exterior angle of a polygon ? Supplementary For polygons to “fit” around a vertex, the sum of their interior angles must be 360 A regular n-gon has n lines of symmetry and rotational of 360/n degrees Find the sum of the interior angles of a decagon: 1440 Find the measure of 1 interior angle of a regular 18-gon 160 Find the sum of the exterior angles of a 55-gon 360 Find the measure of one exterior angle of a regular 24-gon 15 The sum of the interior angles of what polygon is 4500? 27-gon The measure of 1 interior angle of what regular polygon is 170? 36-gon The measure of 1 exterior angle of what regular polygon is 8? 45-gon A regular octagon has 8 lines of symmetry and what degree of rotation? 45 The sum of its interior angles is 4 times the sum of its exterior angles. decagon What regular polygon is ? missing Another hexagon What regular ? polygon is missing Another Octagon What’s the symmetry of a regular decagon? 10 lines, 36 degr. rotational Find x (Given a regular octagon) X = 90 degrees x What 3 regular polygons will tessellate the plane? (name 1) Equilateral triangles Squares Regular Hexagons GIVEN : MLNK M 6.2" L 3" 52 K x FIND x N x 6.2 GIVEN : MLNK M 6.2" L x 3" 52 K FIND x N x 3 GIVEN : MLNK M 6.2" L x 3" 52 K FIND x N x 52 GIVEN : MLNK M 52 K FIND x 6.2" L 3" x N x 128 GIVEN : EFGH F G 8" x E FIND x 3" H x 8 Is the Quadrilateral a parallelogram? YES Is the Quadrilateral a parallelogram? YES Is the Quadrilateral a parallelogram? NO Is the Quadrilateral a parallelogram? 60 60 NO Is the Quadrilateral a parallelogram? 6" 35 35 6" YES Is the Quadrilateral a parallelogram? 72 72 72 YES Is the Quadrilateral a parallelogram? NO 90 Is the Quadrilateral a parallelogram? NO 6" 6" 6" Is the Quadrilateral a parallelogram? 72 72 108 YES Describe the symmetry of an average parallelogram... - No lines - o 180 rotational Complete the Theorem…. The diagonals of a BISECT parallelogram____ EACH OTHER ________. Opposite sides of a parallelogram are__________. congruent. (They are also parallel, but that is in the definition, not a theorem.) If the opposite angles of a quadrilateral are congruent, then__________ …then the quadrilateral is a parallelogram. Consecutive angles of a parallelogram are ____________. Supplementary. Always, Sometimes, or Never... The diagonals of a parallelogram _________ Always bisect each other. A quadrilateral is Sometimes a __________ parallelogram, The End