Mathematics 10, 20: Aids for Planning (Geometry)

Scope and Sequence (by strand)
Geometry

The code in the column under the course of study refers to the Concept (capital letter) and the specific learning objective (number) under the Concept in that course of study.

For example, if the code C.6 appears in the 10 column under the course of study, this would indicate that it is in the Math 10 curriculum guide, the sixth learning objective in Concept C.

A in the Grade 9 column indicates this topic has been introduced in the middle level program.

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

1.   To define: line segment, ray, line, bisector, perpendicular line, perpendicular bisector, transversal, alternate interior angles, corresponding angles, same-side interior angles. D.1

2.   To identify and calculate the measures of the following angles formed by parallel lines, corresponding angles, alternate interior angles, and same-side interior angles. D.2

3.   To solve word problems involving angles formed by parallel lines. D.3

4.   To informally construct a line parallel to a given line through a point not on the line. D.4

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

5.   To informally construct a line perpendicular to a given line from a point not on the line. D.5

6.   To informally construct a line perpendicular to a given line through a point on the line. D.6

7.   To informally construct the perpendicular bisector of a line segment. D.7

8.   To define and illustrate by drawing the following: acute angle, right angle, obtuse angle, straight angle, reflex angle, complementary angles, supplementary angles, adjacent angles, vertically opposite angles, congruent angles, central angles of a regular polygon. E.1

9.   To solve word problems involving the angles stated in E.1. E.2

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

10.   To define and illustrate the following polygons: convex, non-convex, regular, quadrilateral parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid. E.3

11.   To classify quadrilaterals as trapezoids, isosceles trapezoids, parallelograms, rectangles, rhombuses, and squares. E.4

12.   To informally construct parallelograms, rectangles, rhombuses, and squares. E.5

13.   To state and apply the properties of parallelograms. E.6

14.   To determine the sum of the measures of the interior and exterior angles of a convex polygon of n sides. E.7

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

15.   To determine the measure of a central angle in a regular n-gon. E.8

16.   To determine the measures of the interior and exterior angles of regular n-gons. E.9

17.   To determine the number of diagonals in a polygon of n sides. E.10

18.   To define the measure of a minor arc, and to calculate the measure of a central angle. H.1

19.   To determine the relationship that exists between the following:
the radius of a circle and a tangent line drawn to it      at the point of tangency;
two tangents drawn to a circle from the same      point;
chords and arcs in the same circle or in congruent      circles;
a diameter and a chord bisected by the diameter;      and,
two chords that intersect inside a circle.
H.2

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

20.   To solve problems based on the relationships state in G.2. H.3

21.   To informally and formally construct congruent angles, and congruent triangles. G.1

22.   To determine the properties of congruent triangles. G.2

23.   To identify and state corresponding parts of congruent triangles. G.3

24.   To determine whether triangles are congruent by SSS, SAS, ASA, AAS, or HL. G.4

25.   To prove that two triangles are congruent by supplying the statements and reasons in a guided deductive proof. G.5

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

26.   To prove triangles congruent by SSS, SAS, AAS, ASA, or HL in a two-column deductive proof or paragraph form. G.6

27.   To prove corresponding parts of congruent triangles are congruent. G.7

28.   Locus
a)   To define and illustrate a locus in a number of       situations.
b)   To sketch and identify a locus given its description. B.1

29.   Circle
a)   To determine the equation of a circle in the general       form Ax ² +By ² +Cx+Dy+E=0, when given the centre       and radius.
b)   To change a given equation of a circle in the general       form to the centre-radius form r ² =(x-h) ² +(y-k) ² , and       to sketch and analyze its graph.
c)   To determine the equation of a circle in either of the       forms x ² +y ² =r ² , or (r ² =(x-h) ² +(y-k) ² from the given       data: centre and intercepts, end points of diameter,       and centre and a point on the circumference, centre       and the equation of a tangent line, etc. B.2

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

30.   Parabola
a)   To determine the equation of a parabola in the       general form y-k=a(x-h) ² or x-h=a(y-k) ² given the       focus and directrix.
b)   To find the equation of a parabola with its vertex at       the point (h,k) by replacing x by x¹=x-h and       replacing y by y¹ = y-k in the equation x ² =4py.
c)   To determine the equation of a parabola from the       given data: focus and directrix, vertex and directrix,       focus and vertex. B.3

31.   Ellipse
a)   To define and illustrate the following terms: ellipse,       foci, focal radii, major axis, minor axis, vertices, axis       of symmetry.
b)   To determine the equation of an ellipse in the       intercept form when given the foci and the sum of the       focal radii, x ² /a ² +y ² /b ² =1.
c)   To convert a given general equation for an ellipse to       the intercept form and sketch and analyze its graph. B.4

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

32.   Hyperbola
a)   To define and illustrate the following terms:       hyperbola, foci, focal radii, major axis, minor axis,       axis of symmetry, asymptotes, vertices, rectangular       hyperbola.
b)   To determine the equation of a hyperbola in the       intercept form when given the foci and the difference       of the focal radii.
c)   To convert a given general equation for a hyperbola       to the intercept form, and sketch and analyze its       graph. B.5

33.
a)   To determine the equation of a hyperbola or an       ellipse, given sufficient information.
b)   To solve word problems involving ellipses or       hyperbolas. B.6

Learning Objectives Course of Study

9 10 20 A 30 B 30 C 30

34.   To examine the coefficients of the second degree equation Ax ² +By ² +Cx+Dy+E=0, and identify the conic section it represents. B.7

35.   To sketch diagrams to show possible relationships and intersections of the following systems: Linear-Quadratic; and Quadratic-Quadratic. B.8

36.   To solve the following systems of equations algebraically: Linear-Quadratic and Quadrati-Quadratic. B.9

Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
1. To define: line segment, ray, line, bisector, perpendicular line, perpendicular bisector, transversal, alternate interior angles, corresponding angles, same-side interior angles.		D.1
2. To identify and calculate the measures of the following angles formed by parallel lines, corresponding angles, alternate interior angles, and same-side interior angles.		D.2
3. To solve word problems involving angles formed by parallel lines.		D.3
4. To informally construct a line parallel to a given line through a point not on the line.		D.4
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
5. To informally construct a line perpendicular to a given line from a point not on the line.		D.5
6. To informally construct a line perpendicular to a given line through a point on the line.		D.6
7. To informally construct the perpendicular bisector of a line segment.		D.7
8. To define and illustrate by drawing the following: acute angle, right angle, obtuse angle, straight angle, reflex angle, complementary angles, supplementary angles, adjacent angles, vertically opposite angles, congruent angles, central angles of a regular polygon.		E.1
9. To solve word problems involving the angles stated in E.1.		E.2
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
10. To define and illustrate the following polygons: convex, non-convex, regular, quadrilateral parallelogram, rectangle, rhombus, square, trapezoid, isosceles trapezoid.		E.3
11. To classify quadrilaterals as trapezoids, isosceles trapezoids, parallelograms, rectangles, rhombuses, and squares.		E.4
12. To informally construct parallelograms, rectangles, rhombuses, and squares.		E.5
13. To state and apply the properties of parallelograms.		E.6
14. To determine the sum of the measures of the interior and exterior angles of a convex polygon of n sides.		E.7
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
15. To determine the measure of a central angle in a regular n-gon.		E.8
16. To determine the measures of the interior and exterior angles of regular n-gons.		E.9
17. To determine the number of diagonals in a polygon of n sides.		E.10
18. To define the measure of a minor arc, and to calculate the measure of a central angle.			H.1
19. To determine the relationship that exists between the following: the radius of a circle and a tangent line drawn to it at the point of tangency; two tangents drawn to a circle from the same point; chords and arcs in the same circle or in congruent circles; a diameter and a chord bisected by the diameter; and, two chords that intersect inside a circle.			H.2
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
20. To solve problems based on the relationships state in G.2.			H.3
21. To informally and formally construct congruent angles, and congruent triangles.			G.1
22. To determine the properties of congruent triangles.			G.2
23. To identify and state corresponding parts of congruent triangles.			G.3
24. To determine whether triangles are congruent by SSS, SAS, ASA, AAS, or HL.			G.4
25. To prove that two triangles are congruent by supplying the statements and reasons in a guided deductive proof.			G.5
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
26. To prove triangles congruent by SSS, SAS, AAS, ASA, or HL in a two-column deductive proof or paragraph form.			G.6
27. To prove corresponding parts of congruent triangles are congruent.			G.7
28. Locus a) To define and illustrate a locus in a number of situations. b) To sketch and identify a locus given its description.						B.1
29. Circle a) To determine the equation of a circle in the general form Ax ² +By ² +Cx+Dy+E=0, when given the centre and radius. b) To change a given equation of a circle in the general form to the centre-radius form r ² =(x-h) ² +(y-k) ² , and to sketch and analyze its graph. c) To determine the equation of a circle in either of the forms x ² +y ² =r ² , or (r ² =(x-h) ² +(y-k) ² from the given data: centre and intercepts, end points of diameter, and centre and a point on the circumference, centre and the equation of a tangent line, etc.						B.2
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
30. Parabola a) To determine the equation of a parabola in the general form y-k=a(x-h) ² or x-h=a(y-k) ² given the focus and directrix. b) To find the equation of a parabola with its vertex at the point (h,k) by replacing x by x¹=x-h and replacing y by y¹ = y-k in the equation x ² =4py. c) To determine the equation of a parabola from the given data: focus and directrix, vertex and directrix, focus and vertex.						B.3
31. Ellipse a) To define and illustrate the following terms: ellipse, foci, focal radii, major axis, minor axis, vertices, axis of symmetry. b) To determine the equation of an ellipse in the intercept form when given the foci and the sum of the focal radii, x ² /a ² +y ² /b ² =1. c) To convert a given general equation for an ellipse to the intercept form and sketch and analyze its graph.						B.4
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
32. Hyperbola a) To define and illustrate the following terms: hyperbola, foci, focal radii, major axis, minor axis, axis of symmetry, asymptotes, vertices, rectangular hyperbola. b) To determine the equation of a hyperbola in the intercept form when given the foci and the difference of the focal radii. c) To convert a given general equation for a hyperbola to the intercept form, and sketch and analyze its graph.						B.5
33. a) To determine the equation of a hyperbola or an ellipse, given sufficient information. b) To solve word problems involving ellipses or hyperbolas.						B.6
Learning Objectives	Course of Study
Learning Objectives	9	10	20	A 30	B 30	C 30
34. To examine the coefficients of the second degree equation Ax ² +By ² +Cx+Dy+E=0, and identify the conic section it represents.						B.7
35. To sketch diagrams to show possible relationships and intersections of the following systems: Linear-Quadratic; and Quadratic-Quadratic.						B.8
36. To solve the following systems of equations algebraically: Linear-Quadratic and Quadrati-Quadratic.						B.9