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ABC and DEF ABCD altitudes angle formed Apply base bisector bisects called chord circle circum circumference circumscribed common consequent Construct contains CONVERSELY COROLLARY DEFINITION described diagonals diameter difference divided Draw drawn EFGH equally distant equiangular equilateral triangle equivalent EXERCISE exterior angles externally extremities figure Find four given given circle given line given point greater half hexagon homologous hypotenuse included increased inscribed intercepted length less Let ABC limit line joining mean measure medians meet middle points opposite sides parallel parallelogram passes perimeter perpendicular polygon prolonged Proof proportion PROPOSITION Prove quadrilateral radii radius ratio rectangle regular inscribed regular polygon Required respectively right angles secants sector segments Show sides similar square straight line Suggestion tangent THEOREM third trapezoid triangle ABC unequal unit vertex Whence
Σελίδα 202 - 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 diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 90 - In the same circle or in equal circles equal chords are equally distant from the center; and conversely, chords that are equally distant from the center are equal.
Σελίδα 53 - 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...
Σελίδα 195 - Similar triangles are to each other as the squares of their homologous sides.
Σελίδα 30 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Σελίδα 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.