Geometry Curriculum
Chapter 1: Basics of Geometry
In Chapter 1, we cover the basics of geometry, including a number of definitions and concepts we'll use throughout the rest of the course.
Standard 1.A: I can solve problems involving lines and planes
*Standard 1.B: I can apply midpoint and distance formula.
Standard 1.C: I can solve problems involving angles.
Resources
Tutorials
Distance Formula (applet at the bottom for practice too!)
Practice Problems
Distance Formula **For Station Review
Midpoint **For Station Review
Chapter 2: Reasoning & Proofs
In Chapter 2, we will be discussing logic and begin to write proofs.
Standard 2.A: I can write conditional statements in if-then form.
Standard 2.B: I can recall and use the point, line, and plane postulates.
Standard 2.C: I can write proofs about lines and angles.
*Standard 2.D: I can use reasoning skills to create a logical argument or critique the reasoning of others.
Need to reassess 2.D? Do the following, then meet with Mrs. Hafner before or after school:
The original 2.D assignments (check class calendar)
p.116 #5-8
p.119 #12, 13 (just make & test a conjecture), 14
Complete the 2.D Review Guide (from in class)
Resources
Tutorials
Practice Problems
2-Column Proofs (choose statement & reason from a list) Try those about complementary, supplementary, and vertical angles.
2-Column Proofs (match the reason with the statement) Try the first link, Segment & Angle Relationships
Chapter 3: Parallel & Perpendicular Lines
In Chapter 3, we will be working with parallel and perpendicular lines. We will write proofs about these pairs of lines, as well as find missing measures in diagrams. Writing equations of lines that are parallel or perpendicular to a given line is also covered in this chapter.
Standard 3.A: I can write equations of parallel and perpendicular lines in slope-intercept form or point-slope form.
*Standard 3.B: I can use properties of parallel lines to solve problems.
Standard 3.C: I can prove theorems about parallel and perpendicular lines cut by transversals.
Review Information & Suggested Problems for the test
Resources
Tutorials
Practice Problems
Chapter 4: Transformations
In Chapter 4, we study geometric transformations (rotations, reflections, translations, and dilations) as well as how they relate to congruence and similarity.
*Standard 4.A: I can perform compositions with translations, reflections, and rotations about the origin in the coordinate plane.
*Standard 4.B: I can identify and describe lines of reflection and rotational symmetry.
Standard 4.C: I can perform compositions of transformations, including dilations.
Resources
Tutorials
Overview of Transformations (links to more specific information about each transformation at the bottom of the page)
Rotations, and more rotations
Practice Problems
Transformation worksheets **printable**
Congruence Transformations (doing more that one transformation at once)
Congruence Transformations (identifying what transformations map one figure to another)
Chapter 5: Congruent Triangles
In Chapter 5, we look at different ways to prove that two triangles are congruent. In Chapter 4, you needed to show all pairs of corresponding sides and corresponding angles were congruent for the triangle to be congruent, but now we have shortcuts (SSS, SAS, ASA, AAS, HL).
Standard 5.A: I can use congruence theorems to prove triangle congruence .
Standard 5.B: I can write coordinate proofs to prove that two figures are congruent.
Standard 5.C: I can use the theorems from the chapter to solve problems involving triangles.
Resources
Tutorials
Triangle Exterior Angle Theorem
Overview of all triangle congruence theorems (and CPCF [they call it CPCTC])
Practice Problems
Practice 2-Column Proofs--Try Congruent Triangles, Triangle Sum Theorem, Triangle Exterior Angle Theorem
Chapter 6: Relationships Within Triangles
In Chapter 6, we study what happens in triangles when we draw in different segments: medians, altitudes, perpendicular bisectors, angle bisectors (these will help us find different centers of a triangle). We'll also work with the Triangle Midsegment Theorem, and how different pieces of a triangle are related to each other.
Standard 6.A: I can find and solve problems using circumcenters and orthocenters.
Standard 6.B: I can find and solve problems about incenters and centroids.
Standard 6.C: I can solve problems using the Hinge theorem and triangle midsegments.
Resources
Tutorials
Finding the Circumcenter (diagram is not well drawn in the video, but the steps are helpful)
Practice Problems
Naming the segment (median, altitude, etc.)
Constructing an Angle Bisector ;Here's another for Angle Bisector
Constructing a Perpendicular Bisector (& Finding Midpoint) ;Here's another for Perpendicular Bisector
Constructing an Altitude; Again
Chapter 6 Review
Choose review problems from the sections that you are struggling most.
Writing equations for perpendicular bisectors: p.307 #19-22
Angle Bisectors & Perpendicular Bisectors: p.306 #3-18
Identifying which center to use: p.316 #27, 28
Finding the circumcenter: p.315 #7-10, 33, 34
Finding the centroid: p.324 #15-18
Finding the orthocenter: p.324 #19-22
Midsegments: p.333 #7-19
Relationships among angles & sides of triangles (Triangle Larger Angle, Longer Side, Triangle Inequality Theorem): p.340 #11-24
Chapter 7: Quadrilaterals & Other Polygons
In Chapter 7, we spend a brief time reviewing what a polygon is and how to find measures of its interior and exterior angles. We focus on quadrilaterals in the chapter: parallelograms, rectangles, squares, rhombuses, trapezoids, and kites.
Standard 7.A: I can find interior and exterior angles of polygons.
*Standard 7.B: I can use and describe properties of special quadrilaterals to make conclusions.
Standard 7.C: I can use theorems and coordinate geometry to write proofs and make conclusions about rhombuses, squares, rectangles, kites and trapezoids.
Resources
Tutorials
Properties of Parallelograms (and quadrilateral vocabulary)
Practice Problems
2014-2015 Notes
Chapter 8: Similarity
In Chapter 8, we revisit the idea of similarity, which we first saw in Chapter 4 when we talked about dilations. We have some theorems (AA, SAS, and SSS) to determine when two triangles are similar. We will also use proportions to find missing measurements in similar triangles.
*Standard 8.A: I can solve problems involving similar polygons.
Standard 8.B: I can write proofs using the SAS, AA, and SSS similarity theorems to show triangles are similar.
Standard 8.C: I can use the triangle proportionality theorem and its converse to find lengths of segments and solve real-world problems.
Resources
Tutorials
Practice Problems
Stations Review Links
Station 2: Triangle Similarity (Do AA & SSS--see links on left side of page)
Station 3: Determining if Polygons Are Similar
Station 4: Finding Missing Side Lengths (watch video, do practice problems)
Station 5: Rep-tiles (Extra Credit) (can print to complete)
Chapter Review
8.1--Similar Polygons
Deciding if polygons are similar: p.434 #5-7, 11; p.425 #25, 26;
Area of similar polygons: p.424 #19-22, 41, 42; p.434 #11; p.457 #12
Perimeter of similar polygons: p.424 #11-16, 39, 40; p.434 #11; p.457 #12
Finding scale factor & missing sides: p.423 #3-10, 28-34, 37, 38; p.434 #3, 4; p.441 #5, 6, 7, 8, 17, 18
8.2--AA Similarity Theorem
Determine if triangles are similar using AA: p.431 #3-6; p.457 #
Show two triangles are similar: p.431 #7-10; p.434 #8-10; p.442 #13-16
Using similar triangles: p.431 #11-18; p.430 #4-5, p.434 #12
8.3--SAS Similarity & SSS Similarity
Determine if triangles are similar using SSS or SAS similarity: p.441 #3, 4, 7-10
8.4--Proportionality Theorem
Using Triangle Proportionality Theorem & Converse: p.450 #3-8, 25, 26; p.457 #4
Three Parallel Lines Theorem: p.450 #13-18; p.457 #8, 9
Triangle Angle Bisector Theorem: p.450 #19-24; p.457 #5, 6
Determine if triangles are similar (using any theorem): p.457 #1-3
Chapter 9: Right Triangles & Trigonometry
In Chapter 9, we learn all about right triangles. We'll start with the Pythagorean Theorem, which should be familiar, and move into something new, Trigonometry (this is sine, cosine, tangent, etc.).
Standard 9.A: I can use the pythagorean theorem and its converse to find side lengths in right triangles and solve real-world problems.
Standard 9.B: I can use the right triangle similarity theorem, geometric mean (altitude) theorem, and geometric mean (leg) theorem to solve problems involving triangles.
*Standard 9.C: I can solve mathematical and real-life problems involving right triangles using the sine, cosine, and tangent ratios.
*Standard 9.D: I can use the law of sines and law of cosines to solve triangles in real-world scenarios.
Resources
Tutorials
Khan Academy link to all things right triangles (Pythagorean Theorem, trigonometry, etc.)
Practice Problems
Pythagorean Inequalities (classify a triangle as acute, right, or obtuse)
Basic Trig: Identify the values of sin, cos, tan of an angle given the side lengths
Completed Law of Sines/Law of Cosines Note Sheet (2016)
Chapter 10: Circles
In Chapter 10, we discuss angles and segments in circles, and how they are related to each other. We also discuss circles in the coordinate plane.
Standard 10.A: I can solve problems involving chords, segments and tangents.
Standard 10.B: I can solve real-world problems involving arcs and angles in circles.
Standard 10.C: Solve real-world problems using graphs of circles.
Chapter 11: Circumference, Area, & Volume
In Chapter 11, we review the formulas learned for circumference, area, and volume, and use those formulas to explore their various applications.
*Standard 11.A: I can solve mathematical and real-world problems involving circles including problems involving distance traveled.
*Standard 11.B: I can find area and surface area of figures.
Standard 11.C: I can solve problems involving cross sections of 3D objects and rotations of 2D objects.
*Standard 11.D: I can solve mathematical and real-life problems using the volume of a 3D figure.