# Download Geometry 2

Penrose tiling wikipedia , lookup

Duality (projective geometry) wikipedia , lookup

Golden ratio wikipedia , lookup

Tessellation wikipedia , lookup

Perspective (graphical) wikipedia , lookup

Technical drawing wikipedia , lookup

Reuleaux triangle wikipedia , lookup

History of geometry wikipedia , lookup

Multilateration wikipedia , lookup

Rational trigonometry wikipedia , lookup

Line (geometry) wikipedia , lookup

Trigonometric functions wikipedia , lookup

Euler angles wikipedia , lookup

History of trigonometry wikipedia , lookup

Area of a circle wikipedia , lookup

Pythagorean theorem wikipedia , lookup

Geometry 2 Euclidean Geometry in the Plane Given parallel lines r and s, what do we know to be true about the measures of the following sets of angles? 1 and 2 1 and 4 3 and 6 2 and 7 4 and 8 Assume m2 is not equal to m7. Then m2 > m7 m2 + m4 = 180 degrees m7 = m6 m4 + m6 < m4 + m2 = 180 degrees so the lines are not parallel. If m1 = m2, then lines r and s are parallel. Assume r and s are not parallel, then you can show that a set of interior angles are less than 180 degrees and m1 and m2 cannot be equal. Triangles Why do we study triangles so diligently? Classified by length of side: Scalene: Sides are unequal. Isosceles: Two sides are equal. Equilateral: Three sides are equal. Classified by length of angle: Right: One 90 degree angle. Obtuse: One angle greater than 90 degrees. Acute: All angles less than 90 degrees. The classifications are interrelated. Isosceles triangles have what characteristics of angles? Equilateral triangles have what characteristics of angles? m1 = m2 and m3 = m4 = m5. Given triangle, ABC is isosceles with AB BC and AD CE and F is the midpoint of AC , prove ADC CEF . is equilateral with m1 = m2 = m3, show that FBA ECB DAC . ABC Hexagon: What do you know about this figure? Six sides and six angles and made up of triangles. Polygon: Triangles are the building blocks. Triangles are rigid: Measurement of three sides determine the triangle. Why? What are examples of polygons with number of sides greater than 3 where the sides determine the polygon? Definition: Regular polygons have equal sides and equal angles. Perimeter: Distance around a figure. Area: Number of square units contained in a closed plane figure. Parallelogram: Area = Base x Height Triangle: area = bh/2 Trapazoid: area = h(a+b)/2 Circles What is ? The ratio of the circumfrance of a circle to its diameter? c d 2 r area r 2