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AABC and A'B'C ABCD adjacent angles algebraic altitude angle equal angle formed angles are equal apothem base angle bisector bisects central angle circumference circumscribed construct a triangle decagon diagonals diagram for Prop diameter draw drawn equiangular equiangular polygon equilateral triangle equivalent exterior angle find a point Find the area given circle given line given point given triangle HINT homologous sides hypotenuse inscribed intersecting isosceles triangle joining the midpoints line joining mean proportional median opposite sides parallel lines parallelogram perimeter perpendicular perpendicular-bisector point equidistant produced proof is left PROPOSITION prove Proof proving the equality quadrilateral radii rectangle regular hexagon regular polygon rhombus right angle right triangle SCHOLIUM School secant segments side equal similar polygons similar triangles straight angles straight line tangent THEOREM transversal trapezoid triangle ABC triangle are equal unequal vertex vertical angle
Page 144 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Page 163 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Page 43 - If two triangles have two sides of one equal respectively to two sides of the other, but the included angle of the first triangle greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Page 87 - To measure a quantity is to find how many times it contains another quantity of the same kind, called a unit of measurement.
Page 29 - The median to the base of an isosceles triangle is perpendicular to the base.
Page 139 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.
Page 176 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 162 - The areas of two rectangles are to each other as the products of their bases and altitudes. Hyp. Rectangles R and R' have the bases b and b' and the altitudes a and a