Common Core Math: High School Geometry: Similarity & Trigonometry

High school students work with triangles in the contexts of similarity and trigonometry. Students learn to determine when two triangles are similar and to justify their answer using theorems about similar triangles. For right triangles, students compute the trigonometric ratios sine, cosine and tangent and use their values to explore relationships between the angles and sides of triangles. Students extend their knowledge of trigonometric ratios to include the laws of sines and cosines, allowing them to solve for missing measurements in all types of triangles.

Common Core Standards

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CCSS.Math.Content.HSG-SRT.A.2
high school right triangles common core standard c6

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right triangles common core standards

Trigonometry

Compute and work with trigonometric ratios.

Define and compute trigonometric ratios for right triangles (CCSS.Math.Content.HSG-SRT.C.6):

sin(30 deg)
cosine of 45 degrees
tan(17 degrees)
SOHCAHTOA

Explore relationships between complementary angles (CCSS.Math.Content.HSG-SRT.C.7):

sin(20) vs cos(70)
(sin(x) + cos(pi/2 - x))/(cos(x))
csc(35) - sec(55)

Solve for unknown measurements in right triangles (CCSS.Math.Content.HSG-SRT.C.8):

Pythagorean theorem a = 10, b = 24
is 4-8-11 a right triangle?
solve right triangle with hypotenuse 9 and leg 5
area of triangle with hypotenuse 5 and side 3

Compute the area of any triangle (CCSS.Math.Content.HSG-SRT.D.9):

area of triangle SAS 7 32deg 5
area of triangle with lengths 4, 7, 8
heron's formula

Apply the laws of sines and cosines (CCSS.Math.Content.HSG-SRT.D.11):

law of sines a = 6cm, b = 8cm, A = 40 deg
law of cosines calculator
angles of a 8-11-6 triangle
triangle with lengths 7 and 5 and angle 72 degrees

Similarity

Define and recognize geometrically similar figures.

Visualize dilations (CCSS.Math.Content.HSG-SRT.A.1):

triangle {(0,0), (15,0), (0,20)} vs triangle {(0,0), (3,0), (0,4)}
rectangle {(2,1),(4,1),(4,2),(2,2)} vs rectangle {(6,3),(12,3),(12,6),(6,6)}
dilation mathematical definition

Compare figures to determine if they are similar (CCSS.Math.Content.HSG-SRT.A.2):

SSS 3-4-5 triangle vs SSS 6-8-10 triangle
triangles with angles 105 deg and 48 deg
triangle {{-15, 15}, {40, 30}, {20, -5}} vs triangle {{-3, 3}, {8, 6}, {4, -1}}

Describe related angles (CCSS.Math.Content.HSG-SRT.B.5):

vertical angles
complementary angles
supplementary angles

相关示例

  • Common Core Math: Circles
  • Common Core Math: Congruence
  • Common Core Math: Expressing Geometric Properties with Equations
  • Common Core Math: Measurement & Dimension
  • Common Core Math: Modeling with Geometry
  • Common Core Math: Trigonometric Functions
  • Geometry