Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 16
... bisects the angle BAC . Prove that AD also bisects BC . Suggestion . Show by § 30 that the AABD and ADC are equal in all respects . Then , by the principle of § 31 , BD = DC . 34. EXERCISE . ABC is a triangle having AB BC . BE is laid ...
... bisects the angle BAC . Prove that AD also bisects BC . Suggestion . Show by § 30 that the AABD and ADC are equal in all respects . Then , by the principle of § 31 , BD = DC . 34. EXERCISE . ABC is a triangle having AB BC . BE is laid ...
Seite 18
... bisects ZABC and is perpendicular to AC . Prove that BD bisects AC and that AB = BC . 38. EXERCISE . ABC is a △ having △ BAC A = BCA . AD bisects BAC and CE bisects LBCA . Prove AD CE . = A D E B B w B Suggestion . Prove & ADC and AEC ...
... bisects ZABC and is perpendicular to AC . Prove that BD bisects AC and that AB = BC . 38. EXERCISE . ABC is a △ having △ BAC A = BCA . AD bisects BAC and CE bisects LBCA . Prove AD CE . = A D E B B w B Suggestion . Prove & ADC and AEC ...
Seite 24
... required △ because it fulfills all the required conditions ; i.e. it is right angled at C , and the sides about C are equal respectively to m and n . Q.E.F PROPOSITION VI . PROBLEM 55. To bisect a given line 24 PLANE GEOMETRY.
... required △ because it fulfills all the required conditions ; i.e. it is right angled at C , and the sides about C are equal respectively to m and n . Q.E.F PROPOSITION VI . PROBLEM 55. To bisect a given line 24 PLANE GEOMETRY.
Seite 25
... bisect AB . For , the points C and D are each equally distant from the extremities of AB ( construction ) . .. CD bisects AB ( § 49 ) . 56. EXERCISE . Divide a given line into quarters . Q.E.F. 57. EXERCISE . If the radius used for ...
... bisect AB . For , the points C and D are each equally distant from the extremities of AB ( construction ) . .. CD bisects AB ( § 49 ) . 56. EXERCISE . Divide a given line into quarters . Q.E.F. 57. EXERCISE . If the radius used for ...
Seite 30
... bisects its vertical angle . 80. EXERCISE . Two lines intersect , making the sum of one pair of vertical angles equal to five times the sum of the other pair of vertical angles . Find the values of the four angles . PROPOSITION X ...
... bisects its vertical angle . 80. EXERCISE . Two lines intersect , making the sum of one pair of vertical angles equal to five times the sum of the other pair of vertical angles . Find the values of the four angles . PROPOSITION X ...
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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
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.