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altitude Analysis angle base bisect bisector centre chord circle circumference circumscribed common cone Const Construction describe diagonals diameter difference Discussion distance divide Draw Draw AC drawn edge ellipse equal equidistant equilateral equivalent face feet figure Find Find the locus formed given length given plane given point height Hence hexagon inches inscribed intersection isosceles joining Let ABCD manner measured median meet middle point opposite parallel pass perimeter perpendicular plane MN polygon produced Proof proportional prove pyramid Q. E. D. Ex quadrilateral radii radius ratio rectangle regular respectively segment sides similar solution sphere spherical square square feet straight line surface Take tangent tetrahedron touch trapezoid triangle vertex vertices volume Нур
Side 6 - 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. Given A ABC and A'B'C...
Side 121 - The square constructed upon the difference of two straight lines is equivalent to the sum of the squares constructed upon these two lines, diminished by twice the rectangle of these lines. Let AB and AC be the two straight lines, and BC their difference.
Side 121 - The square constructed upon the sum of two straight lines is equivalent to the sum of the squares constructed upon these two linec, increased by twice the rectangle of these lines.
Side 17 - The sum of the perpendiculars dropped from any point in the base of an isosceles triangle to the legs, is equal to the altitude upon one of the arms.
Side 17 - The sum of the perpendiculars from any point within an equilateral triangle to the three sides is equal to the altitude of the triangle (Fig.
Side 145 - The sides of a triangle are 10 feet, 17 feet, and 21 feet. Find the areas of the parts into which the triangle is divided by the bisector of the angle formed by the first two sides.
Side 53 - Prove that the locus of the vertex of a triangle, having a given base and a given angle at the vertex, is the arc which forms with the base a segment capable of containing the given angle (§ 318).
Side 187 - I cannot see why it is so very important to know that the lines drawn from the extremities of the base of an isosceles triangle to the middle points of the opposite sides are equal! The knowledge doesn't make life any sweeter or happier, does it?
Side 120 - 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'.