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271. Essential Understanding of Geometry for English Language Learners

NCTM 2016 Annual Meeting & Exposition at San Francisco, CA

 

G3. Decomposing and Rearranging a Triangle into a Rectangle I.

Strategy: Halving the Height of the Triangle.

Slide 45. Decomposing and Rearranging an Acute Triangle into a Rectangle.

Slide 48. Rotation to create the left edge of the rectangle.

Decomposing and Rearranging an Obtuse Triangle into a Rectangle

Slide 54. The longest side is the base of the height.

Slide 55. 4. Undertake an identical process for an obtuse angle triangle. Choose the longest side as the base of the height.

Slide 60. 5. Now choose a different altitude and come up with an alternative approach to draw a rectangle that has the same area as your obtuse triangle.

 

G4. Decomposing and Rearranging a Triangle into a Rectangle II.

Strategy: Halving the Base of the Triangle.

Slide 89. 1. Draw an acute angle triangle. Now draw a rectangle that has the same area as your acute triangle. Tip: Halve the base of the triangle.

Slide 91. 3. Undertake an identical process for an obtuse angle triangle. Choose the longest side as the base of the altitude.

 

G5. Decomposing and Rearranging a Triangle into a Variety of Shapes.

Slide 124. Comparing a Triangle with a Heptagon.

Slide 131. Halving the Rectangle.

 

G6. Decomposing and Rearranging a Triangle into Rectangles.

Slide 160. Halving-the-height Approach.

Slide 161. Halving-the-base Approach.

Slide 163. 4. Can you relate the algebraic formulas to the figures? A = b·[(1/2)·h]

Slide 164. 4. Can you relate the algebraic formulas to the figures? A = [(1/2)·b]·h

 

G7. Comparing Triangles and Parallelograms.

Slide 187. Given a triangle T, how many different parallelograms can you find that are exactly twice the area of T ?

 

G8. Two Statements of the Pythagorean Theorem.

Slide 198. The square on the hypotenuse.

Slide 202. Dissection proof of the Pythagorean theorem.

Slide 209. Another Pythagorean theorem proof.