## Modern Methods in Elementary Geometry |

### From inside the book

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Page 21

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**middle point**of AB let CD be drawn perpendicular to AB . Then every point on CD is equally distant from A and from B. For if P be any point on CD , and PA , PB be joined , these lines must be equal , being equally remote from the ... Page 24

... the one side of AD , there is a like point , line , or angle on the other . THEOREM XXI . The perpendiculars DG , EH , FK drawn through D , E , F , A E F K H B D the

... the one side of AD , there is a like point , line , or angle on the other . THEOREM XXI . The perpendiculars DG , EH , FK drawn through D , E , F , A E F K H B D the

**middle points**of the sides of a triangle ABC 24 ELEMENTARY GEOMETRY . Page 25

E. M. Reynolds. the

E. M. Reynolds. the

**middle points**of the sides of a triangle ABC , meet in one point , Let DG and EH intersect in O. Then since O is a point on DG , it is equally distant from B and C. [ I. 19 . And since O is a point on EH , it is ... Page 26

... point within it , shew that AB + BC + CA are greater than DA + DB + DC , and less than twice DA + DB + DC . 4. The two sides of a triangle are together greater than twice the straight line drawn from the vertex to the

... point within it , shew that AB + BC + CA are greater than DA + DB + DC , and less than twice DA + DB + DC . 4. The two sides of a triangle are together greater than twice the straight line drawn from the vertex to the

**middle point**of ... Page 27

... points thus determined . The figure so formed is a square . 19. If two triangles have two sides of the one equal to two sides of the other , each to each , but the angle included ...

... points thus determined . The figure so formed is a square . 19. If two triangles have two sides of the one equal to two sides of the other , each to each , but the angle included ...

**middle point**of one side of THE STRAIGHT LINE . 27.### Other editions - View all

### Common terms and phrases

Algebra alternate angle altitude ARITHMETIC base BC² BEGINNERS bisect BROOKE FOSS WESTCOTT Cambridge centre chord Christ's College circle touching circumference Clifton College cloth coincide congruent CONIC SECTIONS construct contains convex angle Crown 8vo describe a circle diagonals diameter dicular distance divide Edward Thring ELEMENTARY TREATISE equal angles equally distant equiangular equilateral triangle Examination Papers Exercises exterior angle Fcap Fellow of St GEOMETRY given circle given line given point given square given straight line greater Greek Text Head Master Hence inscribe intersect John's College Join JOSEPH WOLSTENHOLME Jugurtha late Fellow Latin Let ABCD line drawn locus Mathematical Lecturer measure meet middle point MIXED MATHEMATICS numerous parallel to BC parallelogram perpen perpendicular polygon problems quadrilateral figure radius rectangle right angles Second Edition Shew similar triangles student tangent THEOREM VII Third Edition trapezium triangle ABC vertex

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