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ABCD altitude angle formed angles are equal bisector bisects central angle chord circumference circumscribed cone congruent Corollary cylinder diagonal diameter dihedral angles distance divided drawn equal altitudes equal bases equal circles equiangular equilateral triangle Exercise face angles figure Find the area Find the volume frustum geometry given circle given line given point greater hypotenuse inches inscribed regular intercepted interior angles intersection isosceles triangle lateral area lateral edges line joining line segment lune mean proportional measure meet midpoints number of sides parallel planes parallelogram parallelopiped perimeter perpendicular plane geometry plane MN polyhedral angle prism problem Proof Prove pyramid quadrilateral radii ratio rectangle rectangular parallelopipeds regular hexagon regular polygon respectively right angle right-angled triangle secant Show side opposite similar slant height spherical triangle square straight angle Suggestion surface symmetrical tangent THEOREM VII trapezoid trihedral unequal vertex
Sivu 158 - Pythagoras' theorem states that the square of the length of the hypotenuse of a right-angled triangle is equal to the sum of the squares of the lengths of the other two sides.
Sivu 63 - The line which joins the mid-points of two sides of a triangle is parallel to the third side and equal to one half of it.
Sivu 134 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I. The two triangles thus formed are similar to each other and to the whole triangle. II. The perpendicular is a mean proportional between the segments of the hypotenuse.
Sivu 42 - If two triangles have two sides of one respectively equal to two sides of the other, and the included angles unequal, the triangle which has the greater included angle has the greater third side. If two triangles have two sides of...
Sivu 118 - In any proportion, the product of the means is equal to the product of the extremes.
Sivu 221 - If the product of two numbers -is equal to the product of two other numbers, either pair may be made the means, and the other pair the extremes, of a proportion.
Sivu 120 - 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.
Sivu 223 - Prove that in any triangle the square on the side opposite an acute angle is equivalent to the sum of the squares on the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Sivu 270 - If a pyramid is cut by a plane parallel to the base : 1. The edges and altitude are divided proportionally. 2. The section is a polygon similar to the base. Let V-ABCDE be cut by a plane parallel to its base, intersecting the lateral edges in a, b, c, d, e, and the altitude in o.