## Plane Geometry |

### From inside the book

Results 1-5 of 14

Page 3

...

...

**ABCD**( Fig . 3 ) move to the right to the position EFGH , the points A , B , C , and D gener- ating the lines AE , BF , CG , and DH , respectively . The lines AB , BC , CD , and DA will generate the surfaces AF , BG , CH , and DE ... Page 53

...

...

**ABCD**and A'B'C'D ' , let AB be equal to A'B ' , AD to A'D ' , and angle A to A ' . To prove that the are equal . Proof . Place the**ABCD**on the □ A'B'C'D ' . so that AD will fall on and coincide with its equal , A'D ' . Then AB will ... Page 61

...

...

**ABCD**be a quadrilateral , having AB equal to AD , and CB equal to CD , and having the diagonals AC and BD . To prove that the diagonal AC is an axis of symmetry , and that it is to the diagonal BD . Proof . In the △ ABC and ADC , AB ... Page 74

...

...

**ABCD**, BE is cut off equal to BC , and EF is drawn perpendicu- lar to BD meeting DC at F , then DE is equal to EF and also to FC . = 45 ° ; and DE = EF . LEDF = 45 ° , and ZDFE : Rt . △ BEF = rt . △ BCF ( § 151 ) ; and EF = FC . D E B ... Page 94

...

...

**ABCD**inscribed in a circle , and E , F , H , K the middle points of the arcs subtended by the sides of the square . If we draw the lines AE , EB , BF , etc. , we shall have an inscribed polygon of double the number of sides of the ...### Other editions - View all

### Common terms and phrases

ABē ABCD ACē adjacent angles altitude apothem base bisector bisects centre chord circumscribed circle coincide construct a square decagon diagonals diameter divided draw equiangular equidistant equilateral triangle exterior angle feet Find the area Find the locus given angle given circle given length given line given point given square given straight line given triangle greater Hence homologous sides hypotenuse inches inscribed circle intersecting isosceles trapezoid isosceles triangle limit line drawn mean proportional median middle point number of sides obtuse parallel parallelogram perimeter perpendicular PROBLEM Proof prove Q. E. D. PROPOSITION Q. E. F. Ex quadrilateral quantities radii rectangle regular polygon rhombus right angle right triangle secant segments similar polygons square equivalent straight angle tangent THEOREM third side trapezoid triangle ABC triangle is equal vertex vertices

### Popular passages

Page 94 - Any two sides of a triangle are together greater than the third side.

Page 42 - If two triangles have two sides of the one equal, respectively, to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second.

Page 191 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. To prove that Proof. A Let the triangles ABC and ADE have the common angle A. A ABC -AB X AC Now and A ADE AD X AE Draw BE.

Page 156 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.

Page 75 - 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 centre.

Page 71 - The sum of the perpendiculars dropped from any point within an equilateral triangle to the three sides is constant, and equal to the altitude.

Page 38 - Two triangles are equal if the three sides of the one are equal respectively to the three sides of the other. In the triangles ABC and A'B'C', let AB = A'B', AC = A'C', BC=B'C'. To prove A ABC= A A'B'C'. Proof. Place A A'B'C' in the position AB'C, having its greatest side A'C' in coincidence with its equal AC, and its vertex at B', opposite B ; and draw BB'.

Page 55 - 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 50 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.

Page 33 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles, and therefore greater than either of them.