## Elements of Geometry |

### From inside the book

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**perpendicular**to CD . 11. Every angle BAC ( fig . 4 ) , less than a right angle , is an acute angle ; and every angle , DEF , greater than a right angle is an obtuse angle . 12. Two lines are said to be parallel ( fig . 5 ) , when ... Page 4

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**perpendicular**, oblique , and parallel Lines . THEOREM . 27. ALL right angles are equal . Demonstration . Let the straight line CD be**perpendicular**to Fig . 16. AB ( fig . 16 ) , and GH to EF , the angles ACD , EGH , will be equal ... Page 5

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**perpendicular**to Fig . 18 . AB ; reciprocally , AB is also**perpendicular**to DE . For , since DE is**perpendicular**to AB , it follows that the angle ACD is equal to its adjacent angle DCB , and that they are both right angles . But ... Page 6

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**perpendicular**to each other , they will comprehend the same space as the successive angles , ACB , BCD , & c . These are often called vertical angles . THEOREM . 3 36. Two triangles are equal , when Ꮳ Elements of Geometry . Page 7

... in CA ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their intersection A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of

... in CA ; whence the point D , which must be at the same time in the lines BA and CA , can only be at their intersection A ; therefore the two triangles ABC , Fig . 23 . Fig . 24 . Fig . Of

**Perpendicular**and Oblique Lines . 7.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence