Elements of Plane GeometryAmerican Book Company, 1901 - 247 Seiten |
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Seite 27
... bisectors of two supplementary adjacent angles are perpendicular to each other . 70. EXERCISE . Through the vertex of a right angle a line is drawn outside of the angle . What is the sum of the two acute angles formed ? [ ≤1 + 22 ...
... bisectors of two supplementary adjacent angles are perpendicular to each other . 70. EXERCISE . Through the vertex of a right angle a line is drawn outside of the angle . What is the sum of the two acute angles formed ? [ ≤1 + 22 ...
Seite 29
... bisectors of two opposite angles form a straight line . Let FE , HE , GE , and JE be the bi- sectors of AEC , CEB , BED , and DEA respectively . To Prove that FE and EG form a straight line , and HE and EJ form a straight line . F ...
... bisectors of two opposite angles form a straight line . Let FE , HE , GE , and JE be the bi- sectors of AEC , CEB , BED , and DEA respectively . To Prove that FE and EG form a straight line , and HE and EJ form a straight line . F ...
Seite 30
... bisector of an angle bisects its vertical angle . 80. EXERCISE . Two lines intersect , making the sum of one pair of vertical angles equal to five times the sum of the other pair of vertical angles . Find the values of the four angles ...
... bisector of an angle bisects its vertical angle . 80. EXERCISE . Two lines intersect , making the sum of one pair of vertical angles equal to five times the sum of the other pair of vertical angles . Find the values of the four angles ...
Seite 40
... angles of a triangle cannot equal two right angles . 120. EXERCISE . The bisectors of the equal angles 1 and 2 in the figure of § 118 , are parallel . PROPOSITION XIX . THEOREM 121. If two parallels are cut 40 PLANE GEOMETRY.
... angles of a triangle cannot equal two right angles . 120. EXERCISE . The bisectors of the equal angles 1 and 2 in the figure of § 118 , are parallel . PROPOSITION XIX . THEOREM 121. If two parallels are cut 40 PLANE GEOMETRY.
Seite 41
... bisectors of two alternate exterior angles , formed by a transversal cutting two parallel lines , are parallel . 125. EXERCISE . If a line joining two parallels is bisected , any other line through the point of bisection , and joining ...
... bisectors of two alternate exterior angles , formed by a transversal cutting two parallel lines , are parallel . 125. EXERCISE . If a line joining two parallels is bisected , any other line through the point of bisection , and joining ...
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AABC AB² ABC and DEF AC² adjacent angles altitudes angle formed angles equal apothem arc ABC arcs intercepted BC² 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 homologous homologous sides 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 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 ΔΑΒΟ ᎠᏴ
Beliebte Passagen
Seite 68 - 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.
Seite 163 - 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.
Seite 129 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D ; and read, A is to B as C to D.
Seite 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.
Seite 72 - The lines joining the middle points of the opposite sides of a quadrilateral bisect each other.
Seite 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.
Seite 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.
Seite 221 - Tangents to a circle at the middle points of the arcs subtended by the sides of a regular inscribed polygon...
Seite 11 - PERIPHERY of a circle is its entire bounding line ; or it is a curved line, all points of which are equally distant from a point within called the center.
Seite 61 - If the diagonals of a quadrilateral bisect each other, the figure is a parallelogram.