Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 17
... point of intersection ; and since two straight lines have only one point of intersection ( Axiom 13 ) , the vertex B must fall at E. .. the ABC and DEF coincide throughout , and are equal in all respects . Q.E.D. SANDERS ' GEOM . -2 36 ...
... point of intersection ; and since two straight lines have only one point of intersection ( Axiom 13 ) , the vertex B must fall at E. .. the ABC and DEF coincide throughout , and are equal in all respects . Q.E.D. SANDERS ' GEOM . -2 36 ...
Seite 62
... point of intersection of the diagonals of a parallelogram and limited by the sides is bisected at the point . 213. EXERCISE . figure is a rectangle . If the diagonals of a parallelogram are equal , the 214. EXERCISE . Given a diagonal ...
... point of intersection of the diagonals of a parallelogram and limited by the sides is bisected at the point . 213. EXERCISE . figure is a rectangle . If the diagonals of a parallelogram are equal , the 214. EXERCISE . Given a diagonal ...
Seite 70
... point of AC . Q.E.D. 245. EXERCISE . The point of intersection of the medial lines divides each median into two segments that are to each other as two is to one . 246. EXERCISE . Given the middle points of the sides of a triangle , to ...
... point of AC . Q.E.D. 245. EXERCISE . The point of intersection of the medial lines divides each median into two segments that are to each other as two is to one . 246. EXERCISE . Given the middle points of the sides of a triangle , to ...
Seite 91
... point of intersection with the center of the circle . How do AB and CD compare in length ? 286. EXERCISE . Ο B If two equal chords intersect in a circle , the seg- ments of one chord are equal respectively to those of the other . 287 ...
... point of intersection with the center of the circle . How do AB and CD compare in length ? 286. EXERCISE . Ο B If two equal chords intersect in a circle , the seg- ments of one chord are equal respectively to those of the other . 287 ...
Seite 93
... points that are equally distant from A and B. ( ? ) The line GF contains all the points that are equally distant from B and C. ( ? ) Therefore their point of intersection is the only point that is equally distant from A , B , and C ...
... points that are equally distant from A and B. ( ? ) The line GF contains all the points that are equally distant from B and C. ( ? ) Therefore their point of intersection is the only point that is equally distant from A , B , and C ...
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Häufige Begriffe und Wortgruppen
AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc ABC arcs intercepted BC² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point homologous homologous sides hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ΔΑΒΟ ᎠᏴ
Beliebte Passagen
Seite 68 - 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.
Seite 163 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Seite 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Seite 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.
Seite 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Seite 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.
Seite 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.
Seite 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Seite 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Seite 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.