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Key to Geometry, Book 7: Perpendiculars and Parallels, Chords and Tangents, Circles
Key to Geometry introduces students to a wide range of geometric discoveries as they do step-by-step constructions. Using only a pencil, compass, and straightedge, students begin by drawing lines, bisecting angles, and reproducing segments. Later they do sophisticated constructions involving over a dozen steps. When they finish, students will have been introduced to 134 geometric terms and will be ready to tackle formal proofs. Book 7 of Key to Geometry
168 pages, Paperback
First published January 1, 1
2 people want to read
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McGraw-Hill Education
23.7k books151 followersMcGraw-Hill Education traces its history back to 1888 when James H. McGraw, co-founder of the company, purchased the American Journal of Railway Appliances. He continued to add further publications, eventually establishing The McGraw Publishing Company in 1899. His co-founder, John A. Hill, had also produced several technical and trade publications and in 1902 formed his own business, The Hill Publishing Company.
In 1909 both men agreed upon an alliance and combined the book departments of their publishing companies into The McGraw-Hill Book Company. John Hill served as President, with James McGraw as Vice-President. 1917 saw the merger of the remaining parts of each business into The McGraw-Hill Publishing Company, Inc.
In 1909 both men agreed upon an alliance and combined the book departments of their publishing companies into The McGraw-Hill Book Company. John Hill served as President, with James McGraw as Vice-President. 1917 saw the merger of the remaining parts of each business into The McGraw-Hill Publishing Company, Inc.
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February 18, 2023Book 7 in the "Key to" series of workbooks for practical geometry. Expectations pick up here! Until now, workbooks have run about 50 pages; this one is 154.
In addition to much deeper work with perpendiculars and parallels, this text spends a good amount of time working with circles beyond the radius/diameter work of earlier books. There is a "practice test" at the end of each chapter
This text is full of complicated objectives more in line with producing real life construction and patterned artwork without use of arithmetic. It is assumed that the student has mastered the work of previous texts.
Like all books in the series, work is performed using only a straightedge and compass. Standard measures (on a ruler or protractor) are not used.
N.B. Reference to "sum" in the contents list below does not mean adding degrees of an angle arithmetically -- it is geometrically constructing multiple adjacent angles in order to produce a larger angle.
CHAPTER I: PERPENDICULARS AND PARALLELS
... comparing angles
... definition and exploration of vertical angles, corresponding angles, alternate interior angles
... analyzing the sides and angles of a triangle
... introduction of isosceles triangle, including construction of same using perpendicular line segment
... using a triangle's length of sides and size of angles to test for isosceles
... perpendicular bisector of base of a triangle; using this to test isosceles and equilateral status
... bisector of angles; testing perpendicular and parallel (covered in prior books, expanded here)
... testing and constructing parallelograms; properties of parallelograms
... same same rhombus
... midpoints of a quadrilateral, using those to construct nested shape
... determining and constructing the sum of two angles
... exterior angles of a triangle; constructing sum of same
... sum of exterior angles of a polygon (quadrilateral, pentagon)
... sum of angles of a triangle
... sum of angles of a quadrilateral
CHAPTER II: CHORDS AND TANGENTS
... definition of chord, constructing a chord, comparing chords with radius
... constructing a circle through the endpoints of a line segment
... definition of tangent, constructing a tangent to a circle, perpendicular relationship between radius and tangent touching the same point on a circle
... constructing a circle tangent to a line segment
... definition of tangent circles; construction of same
CHAPTER THREE
... circumscribing a triangle
... inscribing a triangle inside a circle
... drawing a circle through three points
... circumscribing a polygon (quadrilateral, pentagon, hexagon)
... inscribing a polygon (square, regular octagon, regular hexagon, regular dodecagon, regular pentagon, regular decagon)
... inscribing a circle in a triangle
... inscribing a circle in a regular polygon
For information about the Key to Geometry series as a whole, see my review of book one here:
https://www.goodreads.com/book/show/8...
In addition to much deeper work with perpendiculars and parallels, this text spends a good amount of time working with circles beyond the radius/diameter work of earlier books. There is a "practice test" at the end of each chapter
This text is full of complicated objectives more in line with producing real life construction and patterned artwork without use of arithmetic. It is assumed that the student has mastered the work of previous texts.
Like all books in the series, work is performed using only a straightedge and compass. Standard measures (on a ruler or protractor) are not used.
N.B. Reference to "sum" in the contents list below does not mean adding degrees of an angle arithmetically -- it is geometrically constructing multiple adjacent angles in order to produce a larger angle.
CHAPTER I: PERPENDICULARS AND PARALLELS
... comparing angles
... definition and exploration of vertical angles, corresponding angles, alternate interior angles
... analyzing the sides and angles of a triangle
... introduction of isosceles triangle, including construction of same using perpendicular line segment
... using a triangle's length of sides and size of angles to test for isosceles
... perpendicular bisector of base of a triangle; using this to test isosceles and equilateral status
... bisector of angles; testing perpendicular and parallel (covered in prior books, expanded here)
... testing and constructing parallelograms; properties of parallelograms
... same same rhombus
... midpoints of a quadrilateral, using those to construct nested shape
... determining and constructing the sum of two angles
... exterior angles of a triangle; constructing sum of same
... sum of exterior angles of a polygon (quadrilateral, pentagon)
... sum of angles of a triangle
... sum of angles of a quadrilateral
CHAPTER II: CHORDS AND TANGENTS
... definition of chord, constructing a chord, comparing chords with radius
... constructing a circle through the endpoints of a line segment
... definition of tangent, constructing a tangent to a circle, perpendicular relationship between radius and tangent touching the same point on a circle
... constructing a circle tangent to a line segment
... definition of tangent circles; construction of same
CHAPTER THREE
... circumscribing a triangle
... inscribing a triangle inside a circle
... drawing a circle through three points
... circumscribing a polygon (quadrilateral, pentagon, hexagon)
... inscribing a polygon (square, regular octagon, regular hexagon, regular dodecagon, regular pentagon, regular decagon)
... inscribing a circle in a triangle
... inscribing a circle in a regular polygon
For information about the Key to Geometry series as a whole, see my review of book one here:
https://www.goodreads.com/book/show/8...
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