Plane and Solid GeometryCentury Company, 1906 - 418 σελίδες |
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Σελίδα 19
... bisects one of two verti- cal angles bisects the other also . [ Let HK bisect ZAOD ; then HK bisects / COB . PROOF . 23 = 22 , and 4 = 21 by § 112. But 21 = 22 by hyp . : .23 = 24 by Ax . 11. ] 20 The bisectors of vertical angles form ...
... bisects one of two verti- cal angles bisects the other also . [ Let HK bisect ZAOD ; then HK bisects / COB . PROOF . 23 = 22 , and 4 = 21 by § 112. But 21 = 22 by hyp . : .23 = 24 by Ax . 11. ] 20 The bisectors of vertical angles form ...
Σελίδα 40
... Prove Ex . 54 by drawing the triangles on opposite sides of the base . B H N 56 HK and MN bisect each other at P. Prove Δ ΗΡΜ = Δ ΚΡΝ . [ § 162. ] P M K PROPOSITION XIX . THEOREM 173 In an isosceles triangle , 40 PLANE GEOMETRY - BOOK I.
... Prove Ex . 54 by drawing the triangles on opposite sides of the base . B H N 56 HK and MN bisect each other at P. Prove Δ ΗΡΜ = Δ ΚΡΝ . [ § 162. ] P M K PROPOSITION XIX . THEOREM 173 In an isosceles triangle , 40 PLANE GEOMETRY - BOOK I.
Σελίδα 41
... bisects the vertical angle and is perpendicular to the base . 175 COROLLARY 2. An equilateral triangle is equiangular . EXERCISES 57 The exterior angles at the base of an isosceles triangle are equal . 58 The triangle formed by joining ...
... bisects the vertical angle and is perpendicular to the base . 175 COROLLARY 2. An equilateral triangle is equiangular . EXERCISES 57 The exterior angles at the base of an isosceles triangle are equal . 58 The triangle formed by joining ...
Σελίδα 43
... bisects the base at right angles . [ § 162. ] 67 If the bisector of an angle of a triangle is perpendicular to the opposite side , the triangle is isosceles . [ § 169. ] 68 If two isosceles triangles have their vertical angles equal ...
... bisects the base at right angles . [ § 162. ] 67 If the bisector of an angle of a triangle is perpendicular to the opposite side , the triangle is isosceles . [ § 169. ] 68 If two isosceles triangles have their vertical angles equal ...
Σελίδα 44
... of the one of the other . " § 168 Q. E. D. EXERCISE 77. The altitude of an isosceles triangle bisects the base , the vertical angle , and the triangle . [ § 178. ] PROPOSITION XXII . THEOREM 179 If two sides of a 44 PLANE GEOMETRY - BOOK I.
... of the one of the other . " § 168 Q. E. D. EXERCISE 77. The altitude of an isosceles triangle bisects the base , the vertical angle , and the triangle . [ § 178. ] PROPOSITION XXII . THEOREM 179 If two sides of a 44 PLANE GEOMETRY - BOOK I.
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Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angles are equal arc BC assigned quantity base bisectors bisects chord circumference circumscribed circle CONCLUSION cone construct COROLLARY cylinder diagonals diameter diedral angles divided equiangular equiangular polygon equidistant equilateral triangle exterior angle Find the area Find the locus Find the ratio frustum given circle given line given point homologous sides hypotenuse HYPOTHESIS inches inscribed intersecting isosceles trapezoid isosceles triangle lateral area legs line of centers mean proportional median mid-points number of sides parallelogram parallelopiped perimeter perpendicular polyedral angle polyedron prism PROOF Draw Prove pyramid Q. E. D. EXERCISES Q. E. D. PROPOSITION quadrilateral radii radius rectangle regular polygon rhombus right angles right triangle SCHOLIUM secant segments similar triangles slant height SOLUTION sphere spherical polygon spherical triangle straight line surface tangent THEOREM trapezoid triangle ABC triedral vertex volume
Δημοφιλή αποσπάσματα
Σελίδα 168 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 41 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 38 - ... greater than the included angle of the second, then the third side of the first is greater than the third side of the second.
Σελίδα 35 - Any side of a triangle is less than the sum of the other two sides...
Σελίδα 242 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 174 - In any triangle, the product of two sides is equal to the product of the segments of the third side formed by the bisector of the opposite angle plus the square of the bisector.
Σελίδα 172 - If from a point without a circle a tangent and a secant are drawn, the tangent is the mean proportional between the whole secant and its external segment.
Σελίδα 171 - If two chords intersect within a circle, the product of the segments of one is equal to the product of the segments of the other.
Σελίδα 192 - The areas of two rectangles having equal altitudes are to each other as their bases.
Σελίδα 65 - The perpendicular bisectors of the sides of a triangle meet in a point. 12. The bisectors of the angles of a triangle meet in a point. 13. The tangents to a circle from an external point are equal. 14...