## An Elementary Geometry |

### From inside the book

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Page 7

... angles without the parallels are called external ; those within , internal ; thus , AGE , EG B , CHF , FHD are ex- ternal angles ; AGH , BGH , GHC , GHD are

... angles without the parallels are called external ; those within , internal ; thus , AGE , EG B , CHF , FHD are ex- ternal angles ; AGH , BGH , GHC , GHD are

**internal angles**. Two in- ternal angles on the same side of the G A B H Ꭰ F C ... Page 8

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**internal angles**are equal . 2d . If the alternate**internal angles**are equal . 3d . If the**internal angles**on the same side are supplements of each other . = Let EF cut the two lines A B and CD so as to make E G B G H D , or AGH GHD , or ... Page 10

... angles are all acute ; as DEF . Acute and obtuse - angled triangles are called oblique - angled triangles . 32. The ...

... angles are all acute ; as DEF . Acute and obtuse - angled triangles are called oblique - angled triangles . 32. The ...

**internal angles**( 17 ) ; BCD but therefore B , being alternate**internal angles**( 17 ) ; hence DCE + BCD + BCA = A + B ... Page 11

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**angles**of the other , the remaining**angles**are equal . 36. Cor . 3. In a triangle there can be but one right**angle**...**interior**and opposite.n THEOREM VIII . 40. If two triangles have two sides and the included**angle**of the one ... Page 19

... angles G C F and FDH ( 17 ) ; and the side CF is equal to FD ; therefore the triangles GFC and DFH are equal ( 41 ) , and GF FH GH - = A D H But as A B G H is a parallelogram , G H = BA ( 62 ) ; therefore ...

... angles G C F and FDH ( 17 ) ; and the side CF is equal to FD ; therefore the triangles GFC and DFH are equal ( 41 ) , and GF FH GH - = A D H But as A B G H is a parallelogram , G H = BA ( 62 ) ; therefore ...

**interior angles**of BOOK I. 19.### Other editions - View all

### Common terms and phrases

A B C A B D ABCD adjacent adjacent angles altitude angle ABC apothem base and altitude centre chord circ circumference cone construct the triangle convex surface Corollary cylinder diagonals diameter distance divided dodecagon equal altitudes equally distant equilateral feet frustum given angle given circle given line given point given side half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half mutually equiangular number of sides opposite sides parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC triangles are equal vertex