## 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 , since ... 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. Page 9

... ( 43 ) the angle B is equal to the angle C. 46. Corollary . An equilateral triangle is also equiangular ; that is , it has its angles equal . GEOH 2 Fig . 29 . - 47. Scholium . From the Of

... ( 43 ) the angle B is equal to the angle C. 46. Corollary . An equilateral triangle is also equiangular ; that is , it has its angles equal . GEOH 2 Fig . 29 . - 47. Scholium . From the Of

**Perpendicular**and Oblique Lines . 9.### Other editions - View all

### Common terms and phrases

ABC fig adjacent angles altitude angle ACB angle BAC 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 angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence