Plane Geometry: A Complete Course in the Elements of the Science |
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Page 52
... ALTITUDE of the triangle is the perpendicular distance from the vertex to the base , or the base produced ; as CD in the triangle ABC . 67. An EXTERIOR ANGLE of a triangle is the angle included between any side and an adjacent side ...
... ALTITUDE of the triangle is the perpendicular distance from the vertex to the base , or the base produced ; as CD in the triangle ABC . 67. An EXTERIOR ANGLE of a triangle is the angle included between any side and an adjacent side ...
Page 64
... ALTITUDE of a trapezoid or a parallelogram is the perpendicular distance between its bases . 78. The DIAGONAL of a quadrilateral is a straight line joining the vertices of two opposite angles . PROPOSITION XXVIII . - THEOREM . Two ...
... ALTITUDE of a trapezoid or a parallelogram is the perpendicular distance between its bases . 78. The DIAGONAL of a quadrilateral is a straight line joining the vertices of two opposite angles . PROPOSITION XXVIII . - THEOREM . Two ...
Page 66
... altitude . COR . 3. - Two parallels included between two other parallels are equal . PROPOSITION XXX . - THEOREM . If the opposite sides of a quadrilateral are respec- tively equal , or if the opposite angles are respectively equal ...
... altitude . COR . 3. - Two parallels included between two other parallels are equal . PROPOSITION XXX . - THEOREM . If the opposite sides of a quadrilateral are respec- tively equal , or if the opposite angles are respectively equal ...
Page 144
... altitude of an isosceles triangle , to construct the triangle . 8. Given the base of a triangle , the altitude , and one angle at the base , to construct the triangle . 9. Given the base of an isosceles triangle and the radius of the ...
... altitude of an isosceles triangle , to construct the triangle . 8. Given the base of a triangle , the altitude , and one angle at the base , to construct the triangle . 9. Given the base of an isosceles triangle and the radius of the ...
Page 146
... altitudes . D To Prove . Then we are to prove that B ABCD is equivalent to ABEF . Proof . Place the figures so that their lower bases shall coincide ; then , since they have the same altitude , their upper bases will be in the same line ...
... altitudes . D To Prove . Then we are to prove that B ABCD is equivalent to ABEF . Proof . Place the figures so that their lower bases shall coincide ; then , since they have the same altitude , their upper bases will be in the same line ...
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Plane Geometry: A Complete Course in the Elements of the Science Edward Brooks, Jr. No preview available - 2016 |
Common terms and phrases
AB² ABC and DEF ABCD AC² acute angle adjacent angles altitude angle equal angles ACD angles are equal apothem base BC² bisector centre chord circumference circumscribed circle construct a square decagon denote diagonals diameter distance divided draw equal angles equally distant equiangular equiangular polygon equilateral triangle exterior angle figure geometry given angle given circle given line given point greater Hence homologous hypotenuse inches inscribed circle inscribed regular intersect isosceles triangle Let ABC line joining mean proportional measured by one-half middle points number of sides obtuse parallel parallelogram perimeter perpendicular Proof PROPOSITION prove quadrilateral quantities radii radius ratio rectangle regular hexagon regular polygon respectively equal rhombus right angles right triangle SCHOLIUM secant segments similar square equivalent suppose tangent theorem trapezoid triangle ABC triangles are equal vertex vertical angle Whence
Popular passages
Page 112 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 244 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Page 60 - If two triangles have two sides of the 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.
Page 57 - In an isosceles triangle the angles opposite the equal sides are equal.
Page 28 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal. 4. If equals be added to unequals, the wholes are unequal. 5. If equals be taken from unequals, the remainders are unequal. 6. Things which are double of the same are equal to one another.
Page 48 - If two parallel lines are cut by a transversal, the sum of the two interior angles on the same side of the transversal is two right angles.
Page 53 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 183 - If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Page 156 - From this proposition it is evident, that the square described on the difference of two lines is equivalent to the sum of the squares described on the lines respectively, minus twice the rectangle contained by the lines.
Page 179 - If two polygons are composed of the same number of triangles, similar each to each and similarly placed, the polygons are similar.