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acute angle altitude angles are equal angles equal arms axiom base bisector bisects central angle CHAPTER chord circle circumference common congruent triangles Construct converse corresponding sides Define depend diagonal diameter distance divides Draw drawn ends equilateral triangle EXERCISES extended exterior external figure Find a point Find the area four geometry given line given point greater hexagon hypotenuse included angle Indirect inscribed intercepted interior angles intersect isosceles triangle length line joining lines drawn measure median meet Method is Art methods of proving middle points opposite sides parallel lines parallelogram perimeter perpendicular Place PROBLEM proof proportion proving lines quadrilateral radii radius ratio rectangle regular polygon right angle right triangle secant similar polygons similar triangles square statement straight line SUMMARY tangent theorem third side transversal trapezoid triangle ABC triangle equals twice unequal units vertex angle vertices
Page 24 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 77 - The areas of two triangles which have 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 8 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 18 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 8 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 33 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the centre.
Page 73 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides, minus twice the product of one of these sides and the projection of the other side upon it.
Page 114 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 21 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 59 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.