Elements of Geometry: Plane and Solid |
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Page 13
... angles ACB , A'CB ' , which have been proved equal . 13. For then it ... angle may be acute , right , or obtuse . 16. Since the interior angles are ... vertical angles being equal ( 74 ) , the sides opposite those equal angles ...
... angles ACB , A'CB ' , which have been proved equal . 13. For then it ... angle may be acute , right , or obtuse . 16. Since the interior angles are ... vertical angles being equal ( 74 ) , the sides opposite those equal angles ...
Page 16
... angle . 67. Let A be the vertical angle , B and C the equal base angles . Then ZA + B + ZC = ZA +2 ZB = 2 ZA = 2 right angles ; ZA is equal to a right angle . 68. With the same symbol as above for the angles , we have ZA + ZB + 2 C ...
... angle . 67. Let A be the vertical angle , B and C the equal base angles . Then ZA + B + ZC = ZA +2 ZB = 2 ZA = 2 right angles ; ZA is equal to a right angle . 68. With the same symbol as above for the angles , we have ZA + ZB + 2 C ...
Page 17
... vertical angle is or is not a right angle . 82. For 6- 2 6 - = 2 83. An interior angle 3 = n n employing formula of Art . 127 . 2 straight angles , an exterior angle 2 n 2 1 - = straight angles ; hence , by the conditions , = ; n = 3 ...
... vertical angle is or is not a right angle . 82. For 6- 2 6 - = 2 83. An interior angle 3 = n n employing formula of Art . 127 . 2 straight angles , an exterior angle 2 n 2 1 - = straight angles ; hence , by the conditions , = ; n = 3 ...
Page 18
... angle . 101. 180 ° . 50 ° 130 ° , and one half of 130 ° is 65 ° . = = 102. The base angles together 45 ° × 2 = 90 ° ; hence the vertical angle 180 ° -90 ° = 90 ° . 103. Let A denote the vertical angle ; then ( 1 ) ZA + ZB + 2 C = ZA + 2 ...
... angle . 101. 180 ° . 50 ° 130 ° , and one half of 130 ° is 65 ° . = = 102. The base angles together 45 ° × 2 = 90 ° ; hence the vertical angle 180 ° -90 ° = 90 ° . 103. Let A denote the vertical angle ; then ( 1 ) ZA + ZB + 2 C = ZA + 2 ...
Page 19
... angle or two right angles , the sum of their halves is a right angle . 114 ... vertical AOC , BOD be OE , OF resp . ZAOE = △ BOF ; .. LAOE + ZAOF = ZBOF + ... angle is perpendicular to the bisector of the angle . Let DE cut off ...
... angle or two right angles , the sum of their halves is a right angle . 114 ... vertical AOC , BOD be OE , OF resp . ZAOE = △ BOF ; .. LAOE + ZAOF = ZBOF + ... angle is perpendicular to the bisector of the angle . Let DE cut off ...
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Common terms and phrases
AB² ABCD AC² AE² altitude angles formed arc BC axes of symmetry base BC² bisect bisector CD² chord circumf circumference coincide construct cutting denote describe an arc diagram for Ex diameter dihedral angles draw drawn edge EF² equal angles equilateral triangle exercises exterior angles given angle given circle given line given point Hence hypotenuse inscribed intercept intersection isosceles triangle Join AC Let AB Let ABC meet mid point par'm parallel to BC parallelogram parallelopiped pass a plane perpendicular plane passed point as required polygon prism produced Prop quadrilateral radii radius equal rectangle required locus respectively right angle right triangle segment sides straight angle straight line surface tangent theorem vertex vertical angle