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Investigating Geometry Online (IGO)
Objectives with Glencoe References
Unit 1: Fundamentals
Lesson 1-1: Point, Line, Plane (Glencoe 1-2)
Objective: The student will be able to make and describe fundamental
sketches. The student will also be able to understand basic concepts such
as intersect, horizontal, vertical, collinear and coplanar.
Lesson 1-2: Segments and Rays (Glencoe 1-4, 1-5, number line distance
and midpoint only)
Objective: The student will be able to define segment, ray, opposite rays,
congruent, midpoint, bisect, length and postulate. The "Ruler Postulate"
and "Segment Addition Postulate" will be introduced.
Lesson 1-3: Formulas (Glencoe 1-4, 1-5, 3-3)
Objective: SOL G.2: The student will use pictorial representations,
including computer software and coordinate methods to solve problems
that relate to the distance, midpoint, and slope formulas.
Lesson 1-4: Angles (Glencoe 1-6)
Objective: The students will be able to define four types of angles (acute,
right, obtuse, and straight) and will solve algebraic problems associated
with them. In addition, the student will sketch these angles using computer
software and/or a protractor. The students will be able to define “angle
bisector” and solve problems using the “Angle Addition Postulate”.
Lesson 1-5: Pairs of Angles (Glencoe 1-7)
Objective: SOL G.3: The student will solve practical problems involving
complementary, supplementary, and congruent angles that include vertical
angles.
Lesson 1-6: Pairs of Angles (See also Lesson 10-1) Glencoe page:
31 (congruent segment)
39 (perpendicular bisector)
47 (congruent angles)
48 (angle bisector)
56 (perpendicular to a point on a line, perpendicular to a point off a line)
Objective: SOL G.11: The student will be able to perform six basic
constructions using a compass and straight edge and/or computer
software.
Unit 2: Lines
Lesson 2-1: Conditional Statements (Glencoe 2-2)
Objective: SOL G.1: The student will construct and judge the validity of a
logical argument consisting of a set of premises and a conclusion. This will
include (a) identifying the converse, inverse, and contrapositive of a
conditional statement and (b) translating a short verbal argument into
symbolic form.
Lesson 2-2: Logic (Glencoe 2-4)
Objective: SOL G.1: The student will construct and judge the validity of a
logical argument consisting of a set of premises and a conclusion. This will
include (c) using Venn diagrams to represent set relationship and (d) using
deductive reasoning, including the law of syllogism.
Lesson 2-3: Pairs of Lines (Glencoe 3-3)
Objective: The student will be able to determine if a pair of lines are
parallel, perpendicular, skew or oblique.
Lesson 2-4: Angles and Parallel Lines (Glencoe 3-1, 3-2)
Objective: The student will be able to determine the measures of angles
formed by parallel lines and a transversal.
Lesson 2-5: Proving Lines Parallel (Glencoe 3-4)
Objective: SOL G.4: The student will use the relationships between angles
formed by two lines cut by a transversal to determine if two lines are
parallel and verify, using algebraic and coordinate methods as well as
deductive proofs.
Unit 3: Polygons
Lesson 3-1: Triangle Fundamentals (Glencoe 4-1, 4-2, 5-1)
Objective: The student will be able to describe triangles based on their
angles and sides. The student will also be able to determine the measures
of interior and exterior angles of triangles.
Lesson 3-2: Isosceles Triangles (Glencoe 4-6)
Objective: The student will be able to apply the Isosceles Triangle
Theorem in determining angle and side measurements.
Lesson 3-3: Triangle Inequalities (Glencoe 5-4, 5-5, 5-6)
Objective: SOL G.6: The student, given information concerning the lengths
of sides and/or measures of angles, will apply the triangle inequality
properties to determine whether a triangle exists and to order sides and
angles. These concepts will be considered in the context of practical
situations.
Lesson 3-4: Polygons (Glencoe 10-1)
Objective: SOL G.9: The student will use measures of interior and exterior
angles of polygons to solve problems. Tiling problems will be used to make
connections to art, construction, and nature.
Unit 4; Proof
Lesson 4-1: Using Properties (Glencoe 2-4, 2-5, 2-6)
Objective: The student will be able to use algebraic properties to explain a
series of logical statements.
Lesson 4-2: Congruent Triangles (Glencoe 4-3)
Objective: SOL G.5: The student will (a) investigate and identify
congruence relationships between triangles.
Lesson 4-3: Proofs (SSS, SAS, ASA) (Glencoe 4-4)
Objective: SOL G.5: The student will (b) prove two triangles are congruent
given information in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
Lesson 4-4: Proofs (AAS, HL) (Glencoe 4-5, 5-2)
Objective: SOL G.5: The student will (b) prove two triangles are congruent
given information in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
Unit 5: Quadrilaterals
Lesson 5-1: Parallelograms (Glencoe 6-1)
Objective: SOL G.8: The student will (a) investigate and identify properties
of parallelograms involving opposite sides and angles, consecutive sides
and angles, and diagonals; (b) prove these properties of parallelograms,
using algebraic and coordinate methods as well as deductive reasoning;
and (c) use properties of parallelograms to solve practical problems.
Lesson 5-2: Tests for Parallelograms (Glencoe 6-2)
Objective: The student will be able to determine if a quadrilateral has the
characteristics of a parallelogram based on given information.
Lesson 5-3: Rectangles (Glencoe 6-3)
Objective: SOL G.8: The student will (a) investigate and identify properties
of rectangles involving opposite sides and angles, consecutive sides and
angles, and diagonals; (b) prove these properties of rectangles, using
algebraic and coordinate methods as well as deductive reasoning; and (c)
use properties of rectangles to solve practical problems.
Lesson 5-4: Rhombi and Squares (Glencoe 6-4)
Objective: SOL G.8: The student will (a) investigate and identify properties
of rhombi and squares involving opposite sides and angles, consecutive
sides and angles, and diagonals; (b) prove these properties of rhombi and
squares, using algebraic and coordinate methods as well as deductive
reasoning; and (c) use properties of rhombi and squares to solve practical
problems.
Lesson 5-5: Trapezoids and Kites (Glencoe 6-5)
Objective: SOL G.8: The student will (a) investigate and identify properties
of trapezoids and kites involving opposite sides and angles, consecutive
sides and angles, and diagonals; (b) prove these properties of trapezoids
and kites, using algebraic and coordinate methods as well as deductive
reasoning; and (c) use properties of trapezoids and kites to solve practical
problems.
Unit 6: Similarity
Lesson 6-1: Using Proportions (Glencoe 7-1)
Objective: The student will be able to use ratios and proportions to solve a
variety of problems.
Lesson 6-2: Exploring Similar Polygons (Glencoe 7-2)
Objective: SOL G.14: The student will (a) use proportional reasoning to
solve practical problems, given similar geometric objects.
Lesson 6-3: Identifying Similar Triangles (Glencoe 7-3)
Objective: SOL G.5: The student will (a) investigate and identify similarity
relationships between triangles; and (b) prove two triangles are similar
given information in the form of a figure or statement, using algebraic and
coordinate as well as deductive proofs.
Lesson 6-4: Proportional Parts (Glencoe 7-4, 7-5)
Objective: The student will be able to use proportional reasoning in
determining segment lengths when (a) parallel lines are intersected by
more than one transversal, (b) an angle bisector of a triangle intersects the
opposite side of the triangle, and (c) the altitude of a right triangle is drawn
from the right angle to the hypotenuse.
Unit 7: Right Triangles
Lesson 7-1: Geometric Mean (Glencoe 8-1)
Objective: The student will be able to determine the geometric mean of
two values. These values will be random, or determined when the altitude
of a right triangle is drawn from the right angle to the hypotenuse.
Lesson 7-2: The Pythagorean Theorem (Glencoe 8-1)
Objective: SOL G.7: The student will solve practical problems involving
right triangles by using the Pythagorean Theorem. Solutions will be
expressed in radical form or as decimal approximations.
Lesson 7-3: Special Right Triangles (Glencoe 8-2)
Objective: SOL G.7: The student will solve practical problems involving
right triangles by using properties of special right triangles. Solutions will be
expressed in radical form or as decimal approximations.
Lesson 7-4: Trigonometry (Glencoe 8-3, 8-4)
Objective: SOL G.7: The student will solve practical problems involving
right triangles by using right triangle trigonometry. Solutions will be
expressed in radical form or as decimal approximations.
Unit 8: Circles
Lesson 8-1: Terminology (Glencoe 9-1, 9-2)
Objective: The student will be able to define and sketch the following circle
related objects: circle, radius, chord, diameter, secant, tangent, point of
tangency, common tangents, congruent circles, concentric circles,
inscribed/circumscribed objects, arc, minor arc, semicircle, major arc, arc
length, circumference, sphere, and great circle.
Lesson 8-2: Area and Circumference (Glencoe 9-1, 10-5)
The student will be able to determine the area, sector, circumference and
arc length of a circle.
Lesson 8-3: Tangents (Glencoe 9-5)
Objective: SOL G.10: The student will investigate and solve practical
problems involving circles, using properties of tangents. Problems will
include applications of architecture, art, and construction.
Lesson 8-4: Arcs and Chords (Glencoe 9-3)
Objective: SOL G.10: The student will investigate and solve practical
problems involving circles, using properties of arcs and chords. Problems
will include applications of architecture, art, and construction.
Lesson 8-5: Angle Formulas (Glencoe 9-4, 9-6)
Objective: SOL G.10: The student will investigate and solve practical
problems involving circles, using properties of angles and arcs. Problems
will include applications of architecture, art, and construction.
Lesson 8-6: Segment Formulas (Glencoe 9-7)
Objective: SOL G.10: The student will investigate and solve practical
problems involving circles, using properties of chords, tangents, secants
and arcs. Problems will include applications of architecture, art, and
construction.
Unit 9: Area & Volume
Lesson 9-1: Area of 2D Shapes (Glencoe 10-3, 10-4, 10-5)
Objective: The student will be able to determine the area of a variety of
shapes including polygons, circles, and sectors of circles.
Lesson 9-2: Prisms and Pyramids (Glencoe 11-2, 11-3, 11-4, 11-5, 11-6)
Objective: SOL G.13: The student will use formulas for surface area and
volume of prisms and pyramids to solve practical problems. Calculators will
be used to find decimal approximations for results.
Lesson 9-3: Cylinders and Cones (Glencoe 11-3, 11-4, 11-5, 11-6)
Objective: SOL G.13: The student will use formulas for surface area and
volume of cylinders and cones to solve practical problems. Calculators will
be used to find decimal approximations for results.
Lesson 9-4: Spheres (Glencoe 11-7)
Objective: SOL G.13: The student will use formulas for surface area and
volume of spheres to solve practical problems. Calculators will be used to
find decimal approximations for results.
Lesson 9-5: Similar Objects (Glencoe 11-8)
Objective: SOL G.14: The student will (b) determine how changes in one
dimension of an object affect area and/or volume of the object.
Unit 10: Special Topics
Lesson 10-1: Constructions (See Lesson 1-6)
Objective: SOL G.11: The student will be able to perform six basic
constructions using a compass and straight edge and/or computer
software.
Lesson 10-2: 3-D Views (Glencoe 11-1)
Objective: SOL G.12: The student will make a model of a threedimensional figure from a two-dimensional drawing and make a twodimensional representation of a three-dimensional object. Models and
representations will include scale drawings, blueprints, or computer
simulations.
Lesson 10-3: Perspective Drawings (Glencoe 11-1)
Objective: SOL G.12: The student will make a model of a threedimensional figure from a two-dimensional drawing and make a twodimensional representation of a three-dimensional object. Models and
representations will include perspective drawings.
Lesson 10-4: Tessellations (Glencoe 10-2)
Objective: SOL G.9: Tessellations and tiling problems will be used to make
connections to art, construction, and nature.
Lesson 10-5: Transformations (Glencoe 13-4, 13-5, 13-6, 13-7)
Objective: SOL G.2: The student will use pictorial representations,
including computer software, constructions, and coordinate methods, to
solve problems involving symmetry and transformation. This will include
(a) investigating and using formulas for finding distance, midpoint, and
slope; (b) investigating symmetry and determining whether a figure is
symmetric with respect to a line or a point; and (c) determining whether a
figure has been translated, reflected, or rotated.