Elements of Geometry |
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Page 27
... included side of one equal to two angles and an included side of the other , they are congruent . The student will make the necessary constructions , and show that the triangles may be placed so as to coincide . - Exercise . Show that ...
... included side of one equal to two angles and an included side of the other , they are congruent . The student will make the necessary constructions , and show that the triangles may be placed so as to coincide . - Exercise . Show that ...
Page 28
... included angle of one equal to two sides and the included angle of the other , they are congruent . The student will supply the necessary constructions , and make application of one figure to the other . - Exercise . Show what ...
... included angle of one equal to two sides and the included angle of the other , they are congruent . The student will supply the necessary constructions , and make application of one figure to the other . - Exercise . Show what ...
Page 30
... included side are given . a B FIG . 28 . On the indefinite line BC lay off the segment BC equal to the given side , and at B and C construct the given angles , so that they shall be interior . There will be two constructions , but the ...
... included side are given . a B FIG . 28 . On the indefinite line BC lay off the segment BC equal to the given side , and at B and C construct the given angles , so that they shall be interior . There will be two constructions , but the ...
Page 31
... included angle are given . Construct the angle ; from the vertex lay off the given sides ; and join their extremities . с b A FIG . 30 . The student will show that there are two constructions , but the resulting triangles are congruent ...
... included angle are given . Construct the angle ; from the vertex lay off the given sides ; and join their extremities . с b A FIG . 30 . The student will show that there are two constructions , but the resulting triangles are congruent ...
Page 39
... included side of one equal to two angles and the included side of the other . Hence PFPB . Q. E. D. THEOREM . The distances of any point , not on the angle bisector , from the angle lines will not be equal . H FIG . 41 . Let Q represent ...
... included side of one equal to two angles and the included side of the other . Hence PFPB . Q. E. D. THEOREM . The distances of any point , not on the angle bisector , from the angle lines will not be equal . H FIG . 41 . Let Q represent ...
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Common terms and phrases
AB² altitude Analysis apothem approach auxiliary line axis base bisect called centre chord circumference circumscribed polygon coincide cone convex convex polygon corresponding lines curve cylinder decagon determine diagonals diameter dicular diedral distance ellipse equally distant figure Find the locus fixed point frustum Geometry given circle given line given point given segment greater Hence hypothenuse inscribed polygon interior angles isosceles joining lines be drawn middle point move NOTE number of sides oblique parabola parallel parallelogram parallelopiped pass perimeter perpen perpendicular bisector point of intersection position prism PROBLEM pyramids Q. E. D. Exercises quadrangle radii radius ratio re-entrant polygon rectangle regular polygon represent right angles right circular cone right triangle rotation secant Show side opposite similar sphere spherical triangle square subtended surface THEOREM three sides triangular prism triedral vertex vertices volume
Popular passages
Page 25 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 26 - If two triangles have two sides and the included angle of one equal to two sides and the included angle of the other, each to each, the other homologous parts are also equal, and the triangles are equal.