Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 13
... drawn joining two points . [ It follows from this axiom that two straight lines can intersect in only one point . ] 14. The shortest distance from one point to another is meas- ured on the straight line joining them . 15. Through a ...
... drawn joining two points . [ It follows from this axiom that two straight lines can intersect in only one point . ] 14. The shortest distance from one point to another is meas- ured on the straight line joining them . 15. Through a ...
Seite 21
Alan Sanders. PROPOSITION IV . THEOREM 47. If a perpendicular is drawn to a line at its middle point , I. Any point on the ... Draw PA and PB . = PB , for PA and PB measure the [ It is required to prove PA distance from P to A and B ...
Alan Sanders. PROPOSITION IV . THEOREM 47. If a perpendicular is drawn to a line at its middle point , I. Any point on the ... Draw PA and PB . = PB , for PA and PB measure the [ It is required to prove PA distance from P to A and B ...
Seite 22
... Draw PA and PB . [ It is required to prove PA and PB unequal . ] Proof . One of these lines , as PA , will intersect the perpen- dicular CD in some point , as E. Draw EB . PB < PE + EB . Axiom 14 . EBEA . By Case I. Substitute EA for EB ...
... Draw PA and PB . [ It is required to prove PA and PB unequal . ] Proof . One of these lines , as PA , will intersect the perpen- dicular CD in some point , as E. Draw EB . PB < PE + EB . Axiom 14 . EBEA . By Case I. Substitute EA for EB ...
Seite 30
... Draw BD bisecting AC . ( § 55. ) B and D are each equally distant from and C ' ; .. ≤1 and ≤2 are R.A.'s . ( ? ) A ... drawn making 21 = 22 . Prove 23 = 24 . Α B 3 A PROPOSITION XI . THEOREM 85. If two triangles have three 30 PLANE ...
... Draw BD bisecting AC . ( § 55. ) B and D are each equally distant from and C ' ; .. ≤1 and ≤2 are R.A.'s . ( ? ) A ... drawn making 21 = 22 . Prove 23 = 24 . Α B 3 A PROPOSITION XI . THEOREM 85. If two triangles have three 30 PLANE ...
Seite 31
... Draw EG . Prove = 212 and ≤ 3 = ≤ 4 . Adding , 21 + Z3 = 22 + 4 , or DEF = DGF . Prove A DEF and DGF equal in all respects . .. A DEF and ABC are equal in all respects . 86. EXERCISE . Construct a triangle having given its three sides ...
... Draw EG . Prove = 212 and ≤ 3 = ≤ 4 . Adding , 21 + Z3 = 22 + 4 , or DEF = DGF . Prove A DEF and DGF equal in all respects . .. A DEF and ABC are equal in all respects . 86. EXERCISE . Construct a triangle having given its three sides ...
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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
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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.