Elements of Plane GeometryAmerican book Company, 1901 - 247 σελίδες |
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Αποτελέσματα 1 - 5 από τα 87.
Σελίδα 16
... Show by § 30 that the AABD and ADC are equal in all respects . Then , by the principle of § 31 , BD = DC . AB 34. EXERCISE . ABC is a triangle having BC . BE is laid off equal to BD . - Prove AD CE . = Suggestion . Show that E B B Д D ...
... Show by § 30 that the AABD and ADC are equal in all respects . Then , by the principle of § 31 , BD = DC . AB 34. EXERCISE . ABC is a triangle having BC . BE is laid off equal to BD . - Prove AD CE . = Suggestion . Show that E B B Д D ...
Σελίδα 26
... in a line , and on the same side of the line , is two right angles . SUGGESTION . Show that the sum of all the angles at C equals E or ZFCA + ZFCB ZGCA + ZGCB , etc. A B 64. COROLLARY IV . The sum of all the angles 26 PLANE GEOMETRY.
... in a line , and on the same side of the line , is two right angles . SUGGESTION . Show that the sum of all the angles at C equals E or ZFCA + ZFCB ZGCA + ZGCB , etc. A B 64. COROLLARY IV . The sum of all the angles 26 PLANE GEOMETRY.
Σελίδα 28
... Show , by drawing triangles , that the converse of this propo- sition , i.e. " if the angles of one triangle are equal respectively to the angles of another , the sides of the first triangle are equal respectively to those of the second ...
... Show , by drawing triangles , that the converse of this propo- sition , i.e. " if the angles of one triangle are equal respectively to the angles of another , the sides of the first triangle are equal respectively to those of the second ...
Σελίδα 30
... Show that ABD and BDC are equal in all respects . Whence ZA = 2C . Q.E.D. 82. COROLLARY . An equilateral triangle is equiangular . B 83. EXERCISE . ABC is an isosceles triangle . D is the middle point of the base AC . E and F are the ...
... Show that ABD and BDC are equal in all respects . Whence ZA = 2C . Q.E.D. 82. COROLLARY . An equilateral triangle is equiangular . B 83. EXERCISE . ABC is an isosceles triangle . D is the middle point of the base AC . E and F are the ...
Σελίδα 32
... Show that PE is perpendicular to CD . Q.E.F. 90. EXERCISE . Draw a perpendicular to AB from the point C. B 91. EXERCISE . If the line AB ( see § 89 ) were situated at the bottom of this page , and there were no room below it for the ...
... Show that PE is perpendicular to CD . Q.E.F. 90. EXERCISE . Draw a perpendicular to AB from the point C. B 91. EXERCISE . If the line AB ( see § 89 ) were situated at the bottom of this page , and there were no room below it for the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc AC arcs intercepted BC² BD² bisector chord circles are tangent circum circumference Construct a triangle COROLLARY DEFINITION Describe a circle diagonals diameter divided EFGH equal circles equally distant equiangular polygon equilateral triangle EXERCISE exterior angles figure given angle given circle given line given point hexagon homologous hypotenuse inscribed angle isosceles triangle joining the middle Let ABC Let To Prove line joining mean proportional medians meet middle points mutually equiangular opposite sides parallelogram passes perimeter perpendicular point of intersection prolonged PROPOSITION Prove ABCD Prove Proof quadrilateral radius ratio rectangle regular inscribed regular polygon rhombus right angles right-angled triangle SCHOLIUM secants segments Show similar polygons similar triangles straight line tangent THEOREM trapezoid triangle ABC unequal vertex vertical angle Whence ᎠᏴ
Δημοφιλή αποσπάσματα
Σελίδα 202 - 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 180 - In any inscribed quadrilateral, the product of the diagonals is equal to the sum of the products of the opposite sides.
Σελίδα 90 - In the same circle or in equal circles equal chords are equally distant from the center; and conversely, chords that are equally distant from the center are equal.
Σελίδα 53 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Given A ABC and A'B'C...
Σελίδα 195 - Similar triangles are to each other as the squares of their homologous sides.
Σελίδα 30 - In an isosceles triangle the angles opposite the equal sides are equal.
Σελίδα 120 - If a quadrilateral is circumscribed about a circle, the sum of one pair of opposite sides is equal to the sum of the other pair.
Σελίδα 203 - In any obtuse triangle, the square of the side opposite the obtuse angle is equal to the sum of the squares of the other two sides, increased by twice the product of one of these sides and the projection of the other side upon it.
Σελίδα 15 - If two triangles have two sides and the included angle of one equal respectively to two sides and the included angle of the other, the triangles are equal.
Σελίδα 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.