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acute angle algebra altitude angle equal angles are equal arc A B axiom base bisects central angle chord circumference circumscribed circle congruent construct a line construct a triangle construct the triangle cosine decagon denoted diagonals diameter distance divided divisor Draw a circle drawn equally distant equilateral triangle EXERCISES expressed exterior angle Find the area Find the side formula geometrical given angle given circle given line graph Hence homologous sides hypotenuse inches inscribed angle intersecting isosceles triangle line-segment mean proportional number of degrees number of sides parallel parallelogram pentagon perimeter perpendicular bisector Problem Proof PROPOSITION VII Prove quadratic equation quadrilateral radii radius ratio rectangle regular inscribed regular polygon remainder rhombus right angle right triangle root secant segment similar triangles sine square straight angle straight line tangent Theorem triangle A B C Fig unequal vertex
Page 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Page 150 - THEOREM If from a point without a circle a tangent and a secant be drawn, the tangent is a mean proportional between the whole secant and its external segment.
Page 77 - 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 141 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 223 - Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.
Page 214 - I label the two new points e and /." FIG. 2 With the help of this figure he then proceeds to the usual proof of the theorem that the area of a parallelogram is equal to the product of the base by the altitude, establishing the equality of certain lines and angles and the congruence of the pair of triangles.
Page 215 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Page 10 - If two sides and the included angle of one triangle are equal respectively to two sides and the included angle of another triangle, then the triangles are congruent.