Plane Geometry: With Problems and ApplicationsAllyn and Bacon, 1910 - 280 páginas |
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Página 16
... intersection c ' ( § 5 ) . Hence , the triangles coincide and are , therefore , congruent ( § 27 ) . 36 . EXERCISES . 1. In the figure of § 35 is it necessary to move ABC out of the plane in which the triangles lie ? Is it necessary in ...
... intersection c ' ( § 5 ) . Hence , the triangles coincide and are , therefore , congruent ( § 27 ) . 36 . EXERCISES . 1. In the figure of § 35 is it necessary to move ABC out of the plane in which the triangles lie ? Is it necessary in ...
Página 71
... intersection is a center of symmetry of the figure . Outline of Proof : It is to be shown that for every point P in the figure , a point P " also in the figure can be found such that Po = P " O and POP " is a 12 straight line . Draw PP ...
... intersection is a center of symmetry of the figure . Outline of Proof : It is to be shown that for every point P in the figure , a point P " also in the figure can be found such that Po = P " O and POP " is a 12 straight line . Draw PP ...
Página 77
... intersection points draw the horizontal lines , thus fixing the division points on AC and BD . Prove that the resulting triangles are equilateral and congruent to each other . SUGGESTION . Use in order the converse of § 159 , Ex . 14 ...
... intersection points draw the horizontal lines , thus fixing the division points on AC and BD . Prove that the resulting triangles are equilateral and congruent to each other . SUGGESTION . Use in order the converse of § 159 , Ex . 14 ...
Página 96
... intersection of the diagonals of trapezoids formed by the sides of an isosceles triangle and lines parallel to its base . 8. Two vertices of a triangle slide along two parallel lines . What is the locus of the third vertex if the ...
... intersection of the diagonals of trapezoids formed by the sides of an isosceles triangle and lines parallel to its base . 8. Two vertices of a triangle slide along two parallel lines . What is the locus of the third vertex if the ...
Página 103
... intersection part of this locus ? Discuss fully . 6. Show that not more than one circle can be drawn through three given points , and hence that two circles which coincide in three points coincide throughout . 227. PROBLEM . To ...
... intersection part of this locus ? Discuss fully . 6. Show that not more than one circle can be drawn through three given points , and hence that two circles which coincide in three points coincide throughout . 227. PROBLEM . To ...
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Términos y frases comunes
ABCD acute angle adjacent angles altitude angle formed angles are equal apothem axes of symmetry axioms base bisects called central angle chord circle tangent circumscribed coincide congruent corresponding sides Definition diagonal diameter distance divided dodecagon Draw drawn equal angles equal circles equiangular equilateral triangle EXERCISES exterior angle figure Find the area Find the locus Find the radius fixed point geometric Give the proof given point given segment given triangle Hence hypotenuse hypothesis inches inscribed intersection isosceles trapezoid isosceles triangle l₁ length line-segment measure meet middle points number of sides Outline of Proof parallel lines parallelogram perigon perimeter plane proof in full quadrilateral radii ratio rectangle regular hexagon regular octagon regular polygon rhombus right angles right triangle secant semicircle Show shown square straight angle straight line subtend SUGGESTION THEOREM trapezoid triangle ABC vertex vertices width
Pasajes populares
Página 223 - If two triangles have two sides of the one equal to two sides of the other...
Página 41 - An exterior angle of a triangle is equal to the sum of the two opposite interior angles.
Página 121 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.
Página 60 - The straight line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of it 46 INTERCEPTS BY PARALLEL LINES.
Página 182 - The areas of two regular polygons of the same number of sides are to each other as the squares of their radii, or as the squares of their apothems.
Página 161 - The formula states that the square of the hypotenuse of a right triangle is equal to the sum of the squares of the base and altitude.
Página 227 - Find the locus of a point such that the difference of the squares of its distances from two fixed points is a constant.
Página 210 - The area of a rectangle is equal to the product of its base and altitude.
Página 31 - Kuclid divided unproved propositions into two classes: axioms, or "common notions," which are true of all things, such as, " If things are equal to the same thing they are equal to each other"; and postulates, which apply only to geometry, such as,