Drill Book in Plane GeometryPalmer Company, 1922 |
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Page 8
... Hypotenuse ? Arm ? 58. If two right angles have two arms of the one equal respectively to two arms of the other ... hypotenuse and an arm of the one equal respectively to the hypotenuse and an arm of the other , the triangles are ...
... Hypotenuse ? Arm ? 58. If two right angles have two arms of the one equal respectively to two arms of the other ... hypotenuse and an arm of the one equal respectively to the hypotenuse and an arm of the other , the triangles are ...
Page 14
... Hypotenuse ? Arm ? 21. How many times was superposition used in proving triangles congruent ? In what theorems ? 22. How were the other cases of congruent triangles proved ? 23. What two theorems of congruent triangles were proved by ...
... Hypotenuse ? Arm ? 21. How many times was superposition used in proving triangles congruent ? In what theorems ? 22. How were the other cases of congruent triangles proved ? 23. What two theorems of congruent triangles were proved by ...
Page 19
... hypotenuse equals one - half the hypotenuse . SPECIAL RIGHT TRIANGLES 120. The 60-30 right triangle and the 45 ° right triangle are useful in numerical exercises . 121 . EXERCISES 1. A diagonal of a square makes.
... hypotenuse equals one - half the hypotenuse . SPECIAL RIGHT TRIANGLES 120. The 60-30 right triangle and the 45 ° right triangle are useful in numerical exercises . 121 . EXERCISES 1. A diagonal of a square makes.
Page 20
... hypotenuse is twice the shorter arm . 7. If the hypotenuse of a right triangle is twice the shorter arm , the included angle is 60 ° . 8. In right triangle ABC , the hypotenuse AB = 4 and △ A = 60 ° ; what is AC ? 9. In triangle ABC ...
... hypotenuse is twice the shorter arm . 7. If the hypotenuse of a right triangle is twice the shorter arm , the included angle is 60 ° . 8. In right triangle ABC , the hypotenuse AB = 4 and △ A = 60 ° ; what is AC ? 9. In triangle ABC ...
Page 30
... hypotenuse divides the right angle into two parts equal respectively to the other angles of the triangle . 16. If a perpendicular is drawn from the middle point of the base of an isosceles triangle to one of the arms , this line makes ...
... hypotenuse divides the right angle into two parts equal respectively to the other angles of the triangle . 16. If a perpendicular is drawn from the middle point of the base of an isosceles triangle to one of the arms , this line makes ...
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Common terms and phrases
acute angle adjacent angles altitude angle-bisectors angles are equal apothem axiom basic method bisects central angle CHAPTER chord circles are tangent circumference circumscribed circle congruent triangles Construct a square Construct a triangle corresponding sides Define diagonal diameter equal angles equal circles equal respectively equally distant equals one-half equals the product equilateral triangle exterior figure Find a point Find the area Find the locus geometry given line given point given straight line given triangle greater hypotenuse included angle inscribed angle interior angles intersect isosceles triangle line joining lines drawn locus of points median Method is Art methods of proving middle points non-parallel sides number of sides opposite sides parallel lines parallelogram perimeter point of tangency proof proving lines quadrilateral radii ratio rectangle regular inscribed regular polygon rhombus right angle secant similar polygons similar triangles supplementary angles theorem third side transversal trapezoid triangle ABC triangle are equal unequal vertex angle
Popular passages
Page 24 - 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. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.
Page 77 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Page 8 - If two triangles have two angles and the included side of one equal respectively to two angles and the included side of the other, the triangles are congruent.
Page 18 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.
Page 8 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 33 - 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 centre.
Page 73 - 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, minus twice the product of one of these sides and the projection of the other side upon it.
Page 114 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Page 21 - Theorem. —A line perpendicular to one of two parallel lines is perpendicular to the other.
Page 59 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.