## Elements of Geometry |

### From inside the book

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**isosceles**( fig . 8 ) , when two only of its sides are equal , and scalene ( fig . 9 ) , when no two of its sides are equal . 16. A right - angled triangle is that which has one right angle . The side opposite to the right angle is ... Page 9

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**isosceles**triangle , the angles opposite to the equal sides are equal . Demonstration . Let the side AB = AC ( fig . 28 ) , then will Fig . 28 . the angle C be equal to B. Draw the straight line AD from the vertex A to the point D , the ... Page 10

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**isosceles**triangle to the middle of the base , is perpendicular to that base , and divides the vertical angle into two equal parts . In a triangle that is not**isosceles**, any one of its sides may be taken indifferently for a base ; and ... Page 35

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**isosceles**, and the angle BACABC ; the triangle CAD is also**isosceles**, and the angle CAD = ADC ; hence BAC + CAD , or BAD≈ ABD + ADB . But , if the two angles B and D of the triangle ABD are together equal to the third BAD , the three ... Page 53

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**isosceles**, we have AC = AB + BC = 2AB ; therefore the square described upon the diagonal AC is double of the square described upon the side AB . This property may be rendered sensible by drawing , through the points A and C , parallels ...### 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