Dual Enrollment Program Pre-DE Course: Geometry
[Description?]
Topics and Objectives
Chapter and section numbers refer to Geometry in MyMathLab
1.2 Geometry — A Mathematical System
(32 exercises)
- Understand how a mathematical system, like geometry, is formed
1.3 Points, Lines, and Planes
(49 exercises)
- Learn the basic terms and postulates of geometry
1.4 Segments and Their Measures
(35 exercises)
- Determine where a point is on a line
- Understand the measure of segments
- Determine whether segments are congruent
- Use segment postulates and algebra to find segment lengths
1.5 Angles and Their Measures
(35 exercises)
- Understand the measure of angles
- Use algebra and the Angle Addition Postulate to solve applications
1.6 Angle Pairs and Their Relationships
(52 exercises)
- Learn special relationships between pairs of angles
- Use algebra to find angle measures
1.7 Midpoint and Distance Formulas
(39 exercises)
- Find the midpoint of a segment
- Find the endpoint of a segment
- Find the distance between two points on the coordinate plane
- Find the midpoint and distance of two points
1.8 Basic Geometry Constructions
(25 exercises)
- Make basic constructions using a straight edge and a compass
2.1 Perimeter, Circumference, and Area
(44 exercises)
- Find the perimeter of circumference of basic shapes
- Find the area of basic shapes
- Determine whether a situation is discussing area or perimeter
- Determine the perimeter and area
- Understand the concepts of perimeter and area
2.6 Properties of Equality and Two-Column Proofs
(41 exercises)
- Use properties of equality to justify reasons for steps
- Write a two-column proof
2.7 Proving Theorems About Angles
(37 exercises)
- Prove and uses theorems about angles
3.1 Lines and Angles
(61 exercises)
- Identify relationships between lines and planes
- Learn the names of angles formed by lines and a transversal
3.2 Proving Lines are Parallel
(57 exercises)
- Use theorems to prove that two lines are parallel
- Use algebra to find the measures of angles needed so that lines are parallel
- Understand the concepts of proofs
3.3 Parallel Lines and Angles Formed by Transversals
(45 exercises)
- Prove and use theorems about parallel lines cut by a transversal
- Use algebra to find measures of angles formed by parallel lines
3.4 Proving Theorems: Parallel and Perpendicular Lines
(30 exercises)
- Use and prove theorems about parallel and perpendicular lines
- Use algebra to find measures of angles related to perpendicular lines
3.5 Constructing Parallel an Perpendicular Lines
(28 exercises)
- Construct parallel and perpendicular lines
- Construct geometric shapes
3.6 Coordinate Geometry — The Slope of a Line
(30 exercises)
- Find the slope of a line
- Interpret the slope-intercept form in an application
- Compare the slopes of parallel and perpendicular lines
3.7 Coordinate Geometry — Equations of Lines
(21 exercises)
- Use the slope-intercept form
- Use the point-slope form
- Write the equations of vertical and horizontal lines
- Find the equations of parallel and perpendicular lines
- Understand the concepts of parallel and perpendicular lines
- Find the equation of the perpendicular bisector of a line segment
4.1 Types of Triangles
(63 exercises)
- Learn the vocabulary of triangles
- Classify triangles by angles and sides
- Find angle measures of triangles
4.2 Congruent Figures
(40 exercises)
- Identify corresponding parts in congruent figures
- Prove triangles are congruent
4.3 Congruent Triangles by SSS and SAS
(35 exercises)
- Determine parts of a triangle using a drawing
- Prove two triangles are congruent using the SSS and SAS postulates
- Use the distance formula to determine if two triangles are congruent
- Understand the meaning of the SSS and SAS postulates
4.4 Congruent Triangles by ASA and AAS
(47 exercises)
- Prove two triangles are congruent using ASA postulates and the AAS theorem
- Identify when to use SSS, SAS, ASA, or AAS to prove triangles congruent
- Use postulates and theorems of congruence to find missing values in a triangle
4.5 Proofs Using Congruent Triangles
(45 exercises)
- Identify common parts of overlapping triangles
- Use triangle congruence and corresponding parts of congruent triangles
- Prove two triangles are congruent using other congruent triangles
- Determine the measure of missing angles and sides of congruent triangles
4.6 Isosceles, Equilateral, and Right Triangles
(71 exercises)
- Determine if triangles are congruent
- Use properties of isosceles and equilateral triangles
- Use properties of right triangles
- Use multiple properties of triangles to solve
- Construct triangles
5.1 Perpendicular and Angle Bisectors
(42 exercises)
- Use perpendicular bisectors to solve problems
- Use angle bisectors to solve problems
5.2 Bisectors of a Triangle
(44 exercises)
- Identify the differences between the circumcenter and the incenter of a triangle
- Use properties of perpendicular bisectors of sides of a triangle
- Use properties of angle bisectors of the angles of a triangle
- Use properties of both perpendicular bisectors and angle bisectors
5.3 Medians and Altitudes of a Triangle
(42 exercises)
- Identify differences between medians and altitudes of triangles
- Use properties of the medians of a triangle
- Use properties of the altitudes of a triangle
5.4 Midsegments of Triangles
(35 exercises)
- Use properties of midsegments of triangles
- Use coordinate geometry with midsegments
- Solve applications of midsegments
5.5 Indirect Proofs and Inequalities in One Triangle
(47 exercises)
- Use indirect reasoning to write proofs
- Learn the triangle relationship between length of a side and size of its opposite angle
- Use the triangle inequality theorem
5.6 Inequalities in Two Triangles
(26 exercises)
- Use the Hinge Theorem and its converse to compare measures of sides and angles
6.2 Parallelograms
(51 exercises)
- Use relationships among sides and angles of parallelograms
- Use relationships among consecutive angles and diagonals of parallelograms
6.3 Proving that a Quadrilateral is a Parallelogram
(24 exercises)
- Determine whether quadrilaterals are parallelograms
- Use coordinate geometry with parallelograms
6.4 Rhombuses, Rectangles, and Squares
(39 exercises)
- Define and classify special types of parallelograms
- Use properties of diagonals of rhombuses, rectangles, and squares
- Use properties of diagonals to form rhombuses, rectangles, and squares
6.5 Trapezoids and Kites
(36 exercises)
- Use properties of trapezoids
- Use properties of kites
7.3 Similar Polygons
(51 exercises)
- Identify similar polygons
- Use similar polygons to solve applications
- Understand the concepts of similar polygons
- Make scaled drawings
7.4 Proving Triangles are Similar
(48 exercises)
- Use the AA~ Postulate and the SAS~ and SSS~ Theorem
- Use similarity to find indirect measurements
- Find the measurements of similar figures
7.5 Geometric Mean and Similarity in Right Triangles
(43 exercises)
- Use altitudes of right triangles to prove similarity
- Find the geometric mean of the lengths of segments in a right triangle
- Solve applications involving right triangles
- Understand the concepts of right triangles
7.6 Additional Proportions in Triangles
(45 exercises)
- Use the Side-Splitter Theorem
- Use the Triangle-Angle-Bisector Theorem
- Understand the properties of parallelograms
8.1 Rigid Transformations
(18 exercises)
- Identify rigid transformations of isometries
- Name images and corresponding parts
- Use isometries to determine values of variables
8.2 Translations
(20 exercises)
- Find translation images of figures
- Write ordered-pair translation rules
- Solve application problems involving translations
- Solve conceptual problems involving translations
8.3 Reflections
(26 exercises)
- Find reflection images of figures
- Identify and use line symmetry
- Solve application problems involving reflections
- Solve conceptual problems involving reflections
8.4 Rotations
(27 exercises)
- Draw and identify rotation images of figures
- Find angles of rotation
- Identify symmetries
8.5 Dilations
(22 exercises)
- Understand dilation images of figures
8.6 Compositions of Reflections
(21 exercises)
- Find compositions of reflections, including glide reflections
- Classify isometries
- Work with kaleidoscope images
- Prove properties of transformations
9.1 Pythagorean Theorem and its Converse
(36 exercises)
- Use the Pythagorean Theorem
- Use the converse of the Pythagorean Theorem
- Solve application problems
9.2 Special Right Triangles
(27 exercises)
- Use the properties of 45°-45°-90° triangles
- Use the properties of 30°-60°-90° triangles
- Use the properties of special triangles to find the missing parts of figures
- Solve application problems
9.3 Trigonometric Ratios
(47 exercises)
- Write the ratios for sine, cosine, and tangent given a right triangle
- Approximate values for the sine, cosine, and tangent of an angle
- Use sine, cosine, and tangent ratios to determine side lengths in right triangles
- Approximate angle measures given the sine, cosine, or tangent value
- Use the sine, cosine, and tangent ratios to determine angle measure in right triangles
- Write the ratios for secant, cosecant, and cotangent given a right triangle
- Solve application problems
9.4 Solving Right Triangles
(29 exercises)
- Solve right triangles
- Use angle of elevation and depression to solve problems
- Solve application problems
10.1 Angles: Polygons & Regular Polygon Tessellations
(38 exercises)
- Find and use the measures of interior angles of polygons
- Find and use the measures of exterior angles of polygons
- Solve problems related to the measures of interior and exterior angles of polygons
- Determine whether a tessellation of regular polygons is formed
- Prove theorems related to the measures of interior and exterior angles of polygons
10.2 Areas of Triangles and Quadrilaterals
(47 exercises)
- Find the areas of squares, rectangles, parallelograms, and triangles
- Find the areas of trapezoids, rhombuses, and kites
- Find the areas of irregular figures
10.3 Areas of Regular Polygons
(36 exercises)
- Find the measures of angles formed between radii and the apothem in regular polygons
- Find areas of regular polygons
- Find areas of regular polygons using trigonometric ratios
- Solve problems involving geometric constructions or proofs
- Understand the relationships among radii, apothems, side lengths, and areas of regular polygons
10.4 Perimeters and Areas of Similar Figures
(33 exercises)
- Find scale factors and ratios of perimeters and areas of similar figures
- Find side lengths, perimeters, and areas of similar figures
- Solve application problems
- Solve problems involving geometric constructions
- Complete statements about similar figures
10.5 Arc Measure, Circumference, and Arc Lengths of Circles
(40 exercises)
- Identify and name semicircles, major arcs, and minor arcs
- Find measures of central angles and arcs
- Find circumferences and arc lengths
10.6 Areas of Circles and Sectors
(33 exercises)
- Find areas of circles, sectors, and segments of circles
- Find radii of circles
- Solve problems relating regular polygons and circles
10.7 Geometric Probability
(33 exercises)
- Use segment models to find the probabilities of events
- Use are models to find the probabilities of events
11.1 Solids and Cross Sections
(35 exercises)
- Recognize polyhedra and their parts
- Visualize cross sections of solids
- Visualize solids formed by revolving a region about a line
11.4 Volume of Prisms and Cylinders
(32 exercises)
- Find the volume of a prism
- Find the volume of a cylinder
- Find the volume of a composite solids
11.5 Volume of Pyramids and Cones
(20 exercises)
- Find the volume of a pyramid
- Find the volume of a cone
11.6 Volume of Spheres
(16 exercises)
- Find the volume of a sphere
12.1 Circle Review and Tangent Lines
(33 exercises)
- Review circles and arcs
- Use properties of a tangent line to a circle
- Solve problems involving geometric proofs or constructions
12.2 Chords and Arcs
(18 exercises)
- Use congruent chords, arcs, and central angles
- Use perpendicular bisectors to chords
- Solve problems involving geometric proofs or constructions
12.3 Inscribed Angles
(18 exercises)
- Find measures of inscribed angles and/or intercepted arcs
- Find measures of angles and/or arcs formed by tangent and chords
- Solve problems involving geometric proofs or constructions
12.4 Additional Angle Measure and Segment Lengths
(17 exercises)
- Find measures of angles formed by chords, secants, and tangents
- Find the lengths of segments associated with circles
- Solve application problems
- Solve problems involving geometric proofs
12.5 Circles in the Coordinate Plane
(19 exercises)
- Write an equation of a circle
- Find the center and radius of a circle written in standard form
- Complete the square to find the center and radius of a circle
- Find quantities related to circles
13.1 Fundamentals of Probability
(18 exercises)
- Compute theoretical probability
- Compute empirical probability
13.2 Events Involving “Not” and “Or”
(16 exercises)
- Find the probability that an event will not occur
- Find the probability of one event or a second event occurring
13.3 Events Involving “And”; Conditional Probability
(19 exercises)
- Find the probability of one event and a second event occurring
- Compute conditional probabilities
Course Profile
| Name | Last Modified |
|---|---|
| Geometry COURSE PROFILE with Supplemental Activities 7-13-2022 [docx] | 2022-07-13 |