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Triangle Slices

Unit 4 ● Lesson 3 ● Activity 1

Sketch an equilateral triangle and an altitude from any vertex in the equilateral triangle.

What do you notice? What do you wonder?

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Warm-up: Notice and Wonder

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Half an Equilateral Triangle

Unit 4

Lesson 3

Right Triangle Trigonometry

GEOMETRY

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Unit 4 ● Lesson 3

I can determine the side lengths of triangles with 30, 60, and 90 degree angles.

Learning

Targets

Geometry

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Decomposing Equilateral Triangles

Unit 4 ● Lesson 3 ● Activity 2

Here is an equilateral triangle with side length 2 units and an altitude drawn. Find the values of x and y.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Decomposing Equilateral Triangles

Unit 4 ● Lesson 3 ● Activity 2

  • The length y is about 1.7 times x.
  • The length y is exactly √3 times x.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Half an Equilateral Triangle

Unit 4 ● Lesson 3

In half an equilateral triangle (aka 30-60-90 triangle), the hypotenuse is twice the length of the shorter leg. The longer leg is the shorter leg times the square root of 3.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Lesson Synthesis

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Generalize Half Equilateral Triangles

Unit 4 ● Lesson 3 ● Activity 2

Calculate the lengths of the unlabeled sides.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

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Half of the Half

Unit 4 ● Lesson 3 ● Activity 4

Calculate the lengths of the 2 unlabeled sides.

Slides are CC BY NC Kendall Hunt Publishing. Curriculum excerpts are CC BY Illustrative Mathematics.

Lesson Synthesis

Cool-down