GEOMETRY IN THE WORLD AROUND US

Trapezoid, Rectangle, & Square

• The window in red is a trapezoid because it has 1 pair of parallel sides.
• The yellow shape is a square because all 4 sides are the same (& all parallel).
• Some of the small window outlines surrounding the octagon are rectangles because they have 4 straight sides and 4 right angles, but one pair of parallel sides are longer than the other, so it's not a square.

Cylinder & Cone

• V=πr²h (Cylinder Volume).
• V=1⁄3πr²h (Cone Volume).
• A cone's volume is 1/3 of the volume of a cylinder of the same height & width.

Parallel Lines Cut By A Third Line

• If a set of 2 parallel lines is crossed or cut by another line (a transversal), each of the parallel lines cut by the transversal have 4 angles surrounding the intersection. At each of the parallel lines, there are two pairs of vertical angles. Each angle in the pair is congruent to the other angle in the pair.

Acute, Obtuse, & Right Triangle

• Right triangle: has one 90° angle and two 45° angles.
• Acute: has three angles less than 90°.
• Obtuse: one angle that is greater than 90°.

CIRCLE

• Circumference = πd Or Circumference = 2πr

Regular Polygon (Hexagon).

• Area formula for a regular hexagon: A=3√3/2•a²

Pythagorean Spiral

• The Pythagorean spiral is really cool, which is why we chose it.
• Geometric relationship: spiral made of right triangles sharing borders.

PARALLELOGRAM, RECTANGLES, TRIANGLES.

• The shape of the building is a parallelogram because it's a 4-sided shape with opposite parallel sides.
• The 3-sided shapes in the windows are triangles because they have 3 straight sides & 3 angles.
• Some of the windows are rectangles because they have 4 straight sides and 4 right angles, but one pair of parallel sides are longer than the other, so it's not a square.