Accelerated Geometry Syllabus
Date: Spring 2011
Authors: D. Busa, M.J. Gonzalez, H. Hewitt, W. Kolc
Text: Merrill Geometry Applications and Connections
Unit 1 – Lines & Angles Defined.
Topics: definitions of point, line, plane, segment, ray; collinear vs. non-collinear points;
coplanar vs. non-coplanar points, lines, segments, rays; the Segment Addition Postulate;
definition of between; the Midpoint Formula; definition of segment bisector; definition of
angle; formal notation for angles; parts of an angle (vertex, sides); measure of an angle; the
Angle Addition Postulate; classifying angles by their measures; complementary angles;
supplementary angles; the Linear Pair Postulate; the Vertical Angles Theorem; introduction
to coordinate geometry (parallel lines, perpendicular lines, etc.); Pythagorean Theorem
and/or distance formula
Textbook sections: 1.1, 1.2, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 12.1, 12.2., 8.2
Unit 2 – Two-Dimensional Figures.
Topics: identifying a figure as a polygon or non-polygon; identifying a polygon as concave or
convex; identifying regular, equilateral and equiangular polygons; formal notation for
names of polygons and parts of polygons; classifying polygons by their number of sides;
interior angles in polygons; perimeter and circumference, including composite shapes; given
perimeter find a missing measurement; area of squares, rectangles, composite shapes,
triangles, trapezoids, parallelograms; given perimeter find area; given area find missing
measurement; word problems for all above (see CAPT released items); area of circles,
sectors; given circumference find area; identifying special quadrilaterals by sight; identifying
special quadrilaterals with given information marked on a sketch; reasoning about special
quadrilaterals (such as "every square is a rectangle"); properties of special quadrilaterals;
coordinate geometry (such as identifying a parallelogram by the slope of its sides)
Textbook sections: 10.1, 10.2, 6.1, 6.3, 6.4, 6.5, 10.4, 6.6, 10.5, 9.1, 9.2, 9.3, 10.7
Unit 3 – Three-Dimensional Figures and Volume.
Topics: nets of cylinders, rectangular prisms, triangular prisms, rectangular pyramids,
triangular pyramids, cones; volume of cylinders, rectangular prisms, triangular prisms,
rectangular pyramids, triangular pyramids, cones, spheres; identifying a solid as a
polyhedron or non-polyhedron; counting faces, vertices and edges of a polyhedron; Euler's
Theorem; volume of composite solids (multiple prisms and a cylinder cut out of a cylinder,
"holes" cut out of solids, etc.); word problems for all above (see CAPT released items)
Textbook sections: 10.1, 11.5, 11.6, 11.7
Unit 4 – Transformations and Symmetry
Topics: line symmetry, rotational symmetry, rotations, reflections, translations
Textbook sections: 13.4, 13.5, 13.6, 13.7
MIDTERM EXAM
Unit 5 – Similarity and Proportions.
Topics: word problems that can be solved using proportions, including rate questions and
"shadow" questions for which similar triangles can be sketched
Textbook sections: 7.1, 7.2, 7.3, 7.4, 7.5, 7.6
Unit 6 – Surface Area.
Topics: surface area of rectangular prisms, triangular prisms, cubes, cylinders, rectangular
pyramids, triangular pyramids, cones, spheres; lateral area of triangular prisms, cylinders,
rectangular pyramids, triangular pyramids, cones; word problems for all above, such as
painting a room (also see CAPT released items)
Textbook sections: 11.2, 11.3, 11.4
Unit 7 – Logical Reasoning and Proofs.
Topics: conditional statements, inverse, converse, contrapositive, two-column algebraic
proofs
Textbook sections: 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7
Unit 8 – Transversal Lines & Special Angles.
Topics: the Corresponding Angles Postulate; the Alternate Interior Angles Theorem; the
Alternate Exterior Angles Theorem; the Same-Side Interior Angles Theorem; proving that
lines are parallel (converses); two-column proofs with all above
Textbook sections: 3.1, 3.2, 3.3, 3.4, 3.5
Unit 9 – Triangles.
Topics: classifying triangles by their sides or angles; inequalities in one triangle; Triangle
Sum Theorem; the Base Angles Theorem; special segments in triangles; congruent triangles;
two-column proofs with all above; special right triangles; introduction to trigonometry as
time allows
Textbook sections: 4.1, 4.2, 4.3, 4.4, 4.5, 4.7, 5.1, 5.2, 5.5, 5.6, 5.7, 8.1, 8.3, 8.4, 8.5, 8.6, 8.7
FINAL EXAM