Download Semester One - Chicago High School for Agricultural Sciences

CHICAGO HIGH SCHOOL FOR AGRICULTURAL SCIENCES
GEOMETRY COURSE OUTLINE
2009-2010
Semester One
POINTS, LINES, PLANES, AND ANGLES
 Identify and model points, lines, and planes. 9B1a
 Identify collinear and coplanar points and intersecting lines and planes in space. 9B1a
 Measure segments and determine accuracy of measurement and compute with measures. 6C5, 7B3
 Find the distance between two points. 7A4b, 9C3b
 Find the midpoint of a segment. 9C3b
 Measure and classify angles. 7A3b, 9B1b
 Identify and use congruent angles and the bisector of an angle. 9B1a
 Identify and use special pairs of angles. 9B1a
 Identify perpendicular lines. 9B1a
 Identify and name polygons and find their perimeters. 7A4b, 9B1a
As result of the above, the student will be able to have the basic building blocks used in geometry and use these blocks to
describe real-world objects.
REASONING AND PROOF
 Make conjectures, determine whether a statement is true or false, and find counterexamples for statements. 9C4a & b
 Use deductive reasoning to reach valid conclusions. 9C4a & b
 Verify algebraic and geometric conjectures using informal and formal proof. 9C4c, 8A3c
 Write proofs involving segment and angle theorems. 9C4c
As result of the above, the student will be able to solve problems and reach conclusions using logic and reasoning.
PARALLEL AND PERPENDICULAR LINES
 Identify angle relationships that occur with parallel lines and a transversal.9B2
 Identify and prove lines parallel from given angle relationships.9B2
 Use slope to analyze a line and to write its equation. 8B4a
 Find the distance between a point and a line and between two parallel lines.9C3b
As result of the above, the student will be able to identify special angle relationships, review slope and forms for the equation of
a line, solve problems by writing linear equations, use slope to determine whether lines are parallel, perpendicular or neither
and find the distance between a point and a line.
CONGRUENT TRIANGLES
 Classify triangles. 9B4
 Apply the Angle Sum Theorem and the Exterior Angle Theorem.9B1b
 Identify corresponding parts of congruent triangles. 9C4b
 Test for triangle congruence using SSS, SAS, ASA, and AAS. 9B4
 Use properties of isosceles and equilateral triangles. 9C4c
 Write proofs.
As result of the above, the student will be able to learn about the properties of congruent triangles & properties of isosceles and
equilateral triangles, apply the angle sum and exterior angle theorems and prove triangles are congruent using SSS, SAS, ASA
and AAS.
RELATIONSHIPS IN TRIANGLES
 Identify and use perpendicular bisectors, angle bisectors, medians and altitudes in triangles. 9B2
 Apply properties of inequalities relating to the measures of angles and sides of triangles. 9B2
 Apply the Triangle Inequality Theorem. 9B2
As result of the above, the student will be able to expand their knowledge of triangles and their properties, identify bisectors,
medians, and altitudes and apply properties of inequalities related to the measure of angles and sides and the theorem of
Triangle Inequality.
PROPORTIONS AND SIMILARITY 6D4
 Review the terms, ratio and proportions, and how to solve equations with proportions. 6D3 & 4
 Identify similar figures and similar triangles. 6D4, 9A3c
 Solve problems involving scale factors. 6D4, 9A3c
 Use similar triangles to solve problems. 6D4, 8D3b, 9B4
 Use proportional parts of triangles. 6D4, 9A3c
As result of the above, the student will be able to develop and solve proportions using similar figures or triangles.
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Semester Two
RIGHT TRIANGLES AND TRIGONOMETRY
 Find the geometric mean between two numbers. 7A4b, 10A4a
 Solve problems involving relationships between parts of a right triangle and the altitude to its hypotenuse. 9C3b
 Use the Pythagorean theorem and its converse. 9D3
 Identify Pythagorean Triples. 9D3
 Use the properties of 45-45-90 and 30-60-90 triangles. 9C3b
 Find trigonometric ratios using right triangles and solve problems using trigonometric ratios. 9D4
As result of the above, the student will be able to find the geometric mean between two numbers and work with right triangles
to find the measure of missing sides or angles using the geometric mean, the Pythagorean Theorem, the properties of the special
right triangles and/or Trigonometry.
QUADRILATERALS
 Find the sum of the interior angles and the sum of the exterior angles of a polygon. 7A3b
 Recognize and apply properties of the sides, angles and diagonals of parallelograms, rectangles, squares, rhombi and
trapezoids. 9B4
 Solve problems involving the medians of trapezoids. 9B4
As result of the above, the student will be able to solve problems involving the interior angles and exterior angles of polygons
and will be able to determine what type of quadrilateral is given by using properties given.
CIRCLES
 Identify parts of a circle and solve problems involving circumference. 9B4
 Find arc and angle measures in a circle. 7A4b
 Find measures of segments in a circle. 7A4b
 Write an equation of a circle. 8B2
As result of the above, the student will be able to identify and solve problems involving circles.
AREAS OF POLYGONS AND CIRCLES
 Find areas of rectangles, squares, parallelograms, triangles, rhombi, trapezoids, regular polygons, and circles. 7A4b
 Find areas of irregular figures. 7B5b
 Find geometric probability and areas of sectors and segments of circles. 7A4b, 10C4a
As result of the above, the student will be able to find the areas of: polygons, circles, circle sectors and irregular figures and will
determine the geometric probability.
SURFACE AREA
 Identify three-dimensional figures and their parts. 9A4a
 Find the lateral area and surface area of prisms, cylinders, pyramids, and cones. 7A4b
 Find the surface area of spheres and hemispheres.
 As result of the above, the student will be able to identify and find the surface areas of three-dimensional figures.
7A4b
VOLUME
 Find the volumes of prisms, cylinders, pyramids, cones, and spheres. 7A4b, 7B5
 Graph solids in space. 9C5b
 Use the Distance and Midpoint Formulas for points in space. 7A4b
As result of the above, the student will be able to find the volume of three-dimensional figures and find the distance or
midpoints of points in space.
TRANSFORMATIONS
 Name, draw, and recognize figures that have been reflected, translated, or rotated. 7B5, 10A4a, 10B4
Textbooks:
Glencoe Mathematics Geometry - Illinois Edition 2005
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