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Boyd - Geometry
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Topic 11
Answer Key for Practice 12-4
Answer Key for Practice 12-4
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Answer Key for Practice 12-4.pdf
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Textbook Resources
Geometry videos and extra resources
Free math tutorials and practice problems on Khan Academy
Video for Lesson 1-2: Points, Lines, and Planes
Notes for lesson 1-2
Practice worksheet for lesson 1-2
Answer key for 1-2 practice worksheet
Video for lesson 1-3: Segments, Rays, and Distance
Notes for Lesson 1-3
Example problems for lesson 1-3
Practice worksheet for lesson 1-3
Answer key for 1-3 practice worksheet
Video for lesson 1-4: Angles (Naming Angles)
Video for lesson 1-4: Angles (Measuring Angles with a Protractor)
Video for lesson 1-4: Angles (types of angles)
Notes for lesson 1-4
Example Problems for lesson 1-4
Practice worksheet for lesson 1-4
Answer key for 1-4 practice worksheet
Notes for lesson 1-5
Practice worksheet for lesson 1-5
Answer Key for 1-5 practice worksheet
Chapter 1: Naming points, lines, planes, and angles
Chapter 1 review
Unit 2 practice worksheet answer keys
Video for lesson 2-1: If-Then Statements; Converses
Notes for lesson 2-1
Practice worksheet for lesson 2-1
Answer key for 2-1 practice worksheet
Notes for lesson 2-2
Practice worksheet for lesson 2-2
Answer key for 2-2 practice worksheet
Notes for lesson 2-3
Practice worksheet for lesson 2-3
Answer key for 2-3 practice worksheet
Review of lessons 2-1 through 2-3
Video for lesson 2-4: Special Pairs of Angles (Vertical Angles)
Video for Lesson 2-4: Special Pairs of Angles (Complementary and Supplementary Angles)
Notes for lesson 2-4
Practice worksheet for lesson 2-4
Practice worksheet for lesson 2-4 part II
Answer keys for 2-4 and 2-4 part II Practice Worksheets
Video for Lesson 2-5: Perpendicular Lines
Lesson 2-5 Activity
Notes for lesson 2-5
Practice worksheet for lesson 2-5
Answer key for 2-5 Practice worksheet
Notes for lesson 2-6
Practice proofs for lesson 2-6
Answer key for practice proofs
Chapter 2 review
Extra Chapter 2 practice sheet
Video for Lesson 3-1: Definitions (Parallel and Skew Lines)
Parallel Lines Activity
Notes for lesson 3-1
Practice worksheet for lesson 3-1
Answer Key for Practice 3-1
Video for Lesson 3-2: Properties of Parallel Lines (adjacent angles, vertical angles, and corresponding angles)
Video for lesson 3-2: Properties of Parallel Lines (alternate and same side interior angles)
Notes for lesson 3-2
Practice worksheet for lesson 3-2
Answer key for 3-2 practice worksheet
Notes for lesson 3-3
Practice worksheet for lesson 3-3
Answer key for 3-3 practice worksheet
Practice worksheet for lessons 3-2 and 3-3
Answer key for 3-2 and 3-3 worksheet
Review for lessons 3-1 through 3-3
Video for Lesson 3-4: Angles of a Triangle (Types of Triangles)
Notes for lesson 3-4 (part I)
Practice worksheet for lesson 3-4 (part I)
Answer Key for 3-4 practice worksheet (part I)
Video for Lesson 3-4: Angles of Triangle (Triangle sum theorem)
Video for Lesson 3-4: Angles of a Triangle (exterior angles)
Notes for lesson 3-4 (part II)
Practice worksheet for lesson 3-4 (part II)
Answer key for 3-4 practice worksheet (part II)
Video for Lesson 6-4: Inequalities for One Triangle (Triangle Inequality Theorem)
Activity and notes for lesson 6-4
Practice worksheet for lesson 6-4
Answer key for 6-4 practice worksheet
Video for lesson 3-5: Angles of Polygons (types of polygons)
Video for Lesson 3-5: Angles of Polygons (formulas for interior and exterior angles)
Notes for lesson 3-5
Practice worksheet for lesson 3-5
Answer key for 3-5 practice worksheet
Notes for lesson 3-6
Practice worksheet for lesson 3-6
Answer key for 3-6 practice worksheet
Chapter 3 and lesson 6-4 review
Video for lesson 4-1: Congruent Figures
Notes for lesson 4-1
Practice worksheet for lesson 4-1
Answer key for 4-1 practice worksheet
Video for Lesson 4-2: Some Ways to Prove Triangles Congruent (SSS, SAS, ASA)
Notes for lesson 4-2
Practice worksheet for lesson 4-2
Answer key for 4-2 practice worksheet
Lesson 4-3 Proofs for congruent triangles
Triangle congruence practice
Video for Lesson 4-4: The Isoceles Triangle Theorems
Notes for lesson 4-4
Practice worksheet for lesson 4-4
Answer key for 4-4 practice worksheet
Video for Lesson 4-5: Other Methods of Proving Triangles Congruent (AAS)
Video for Lesson 4-5: Other Methods of Proving Triangles Congruent (HL)
Notes for lesson 4-5
Practice worksheet for lesson 4-5
Answer key for 4-5 practice worksheet
Virtual practice with congruent triangles
Review for lessons 4-1, 4-2, and 4-5
Video for lesson 4-7: Angle bisectors, medians, and altitudes
Notes for lesson 4-7 (part I)
Practice worksheet for lesson 4-7 (part I)
Answer key for 4-7 practice worksheet (part I)
Notes for lesson 4-7 (part II)
Practice worksheet for lesson 4-7 (part II)
Answer key for 4-7 practice worksheet (part II)
Chapter 4 review
Online practice for triangle congruence proofs
Video for lesson 5-1: Parallelograms
The quadrilateral family tree (5-1)
The quadrilateral properties chart (5-1)
Practice worksheet for lesson 5-1 and 5-2
Answer key for 5-1 and 5-2 practice worksheet
Video for lesson 5-3: Midsegments of trapezoids and triangles
Notes for lesson 5-3
Practice worksheet for lesson 5-3
Answer key for 5-3 practice worksheet
Video for lesson 5-4: Properties of rhombuses, rectangles, and squares
Notes for lesson 5-4
Practice worksheet for lesson 5-4
Answer key for Practice Worksheet 5-4
Review for lessons 5-1, 5-2, and 5-4
Song about parallelograms for review of properties
Video for lesson 5-5: Properties of trapezoids
Notes for lesson 5-5
Practice worksheet for lesson 5-5
Answer key for 5-5 practice worksheet
Chapter 5 review
Link to the website for enrichment practice proofs
Video for lessons 7-1 and 7-2: Ratios and Proportions
Notes for lesson 7-1 and 7-2
Practice worksheet for lessons 7-1 and 7-2
Notes for lesson 7-1
Practice worksheet for lesson 7-1
Notes for lesson 7-2
Practice worksheet for lesson 7-2
Answer key for 7-1 and 7-2 practice worksheet
Video for Lesson 7-3: Similar Triangles and Polygons
Notes for lesson 7-3
Practice worksheet for lesson 7-3
Answer key for 7-3 practice worksheet
Review for lessons 7-1 through 7-3
Notes for lesson 7-4
Practice worksheet for lesson 7-4
Answer key for 7-4 worksheet
Video for lesson 7-6: Proportional lengths for similar triangles
Notes for lessson 7-6
Practice worksheet for lesson 7-6
Answer key for 7-6 practice worksheet
Review of 7-1, 7-2, 7-3, and 7-6
Video for lesson 8-1: Similar triangles from an altitude drawn from the right angle of a right triangle
Notes for lesson 8-1
Practice worksheet for lesson 8-1
Answer Key for 8-1 (part I) worksheet
Notes for lesson 8-1 (part II)
Practice worksheet for lesson 8-1 (part II)
Answer Key for Practice Worksheet 8-1 (part II)
Video for lesson 8-2: The Pythagorean theorem
Notes for lesson 8-2
Practice worksheet for lesson 8-2
Answer key for 8-2 practice worksheet
Algebra problems for the Pythagorean Theorem
Video for lesson 8-3: The converse of the Pythagorean theorem
Activity and notes for lesson 8-3
Practice worksheet for lesson 8-3
Answer key for 8-3 practice worksheet
Video for lesson 8-4: working with 45-45-90 and 30-60-90 triangle ratios
Notes for lesson 8-4
Practice worksheet for lesson 8-4
Answer Key for Practice Worksheet 8-4
Review for lessons 8-1 through 8-4
Video for lesson 8-5 and 8-6: using the Tangent, Sine, and Cosine ratios
Activity and notes for lesson 8-5
Notes for cosine function
Notes for sine function
Practice worksheet for lesson 8-5 and 8-6
Answer Key for Practice Worksheet 8-5 and 8-6
Video for lesson 8-7: Applications of trig functions
Video for lesson 8-7: Angles of elevation and depression
Notes for lesson 8-7
Practice worksheet for lesson 8-7
Answer Key for 8-7 worksheet
Review for chapter 8
Virtual practice with Pythagorean Theorem and using Trig Functions
Video for lesson 9-1: Basic Terms of Circles
Notes for lesson 9-1
Practice worksheet for lesson 9-1
Answer Key for Practice 9-1
Video for lesson 9-2: Tangents of a circle
Notes for lesson 9-2
Practice worksheet for lesson 9-2
Answer Key for Lesson 9-2
Video for lesson 9-3: Arcs and central angles of circles
Notes for lesson 9-3
Practice worksheet for lesson 9-3
Answer Key for Lesson 9-3
Review worksheet for lessons 9-1 through 9-3
Video for lesson 9-4: Arcs and chords
Notes for lesson 9-4
Practice worksheet for lesson 9-4
Answer Key for Practice Worksheet 9-4
Video for lesson 9-5: Inscribed angles
Notes for lesson 9-5
Practice worksheet for lesson 9-5
Answer Key for Practice Worksheet 9-5
Review for quiz on 9-1, 9-2, 9-3, and 9-5
Video for lesson 9-6: Angles formed inside a circle but not at the center
Video for lesson 9-6: Angles formed outside a circle
Notes for lesson 9-6
Practice worksheet for lesson 9-6
Answer Key for Practice Worksheet 9-6
Video for lesson 9-7: Finding lengths of intersecting chords
Video for lesson 9-7: Finding lengths of secants
Video for lesson 9-7: Finding the lengths of intersecting tangents and secants
Notes for lesson 9-7
Practice worksheet for lesson 9-7
Answer Key for 9-7
Chapter 9 circle dilemma problem (diagram)
Chapter 9 circle dilemma problem (info and answer sheet)
Review for chapter 9
Video for lesson 11-1: Finding perimeters of irregular shapes
Video for lesson 11-1: Area of rectangles
Notes for lesson 11-1
Practice worksheet for lesson 11-1
Answer Key for Practice Worksheet 11-1
Video for lesson 11-2: Areas of parallelograms
Video for lesson 11-2: Areas of triangles
Video for lesson 11-2: Areas of rhombuses
Video for lesson 11-2: Finding the area of irregular shapes (rectangles and triangles)
Video for lesson 11-3: Areas of trapezoids
Notes for lesson 11-2 and 11-3
Practice worksheet for lessons 11-2 and 11-3
Answer Key for 11-2 and 11-3
Video for lesson 11-4: Areas of regular polygons
Notes for lesson 11-4
Practice worksheet for lesson 11-4
Answer Key for Lesson 11-4
Video for lesson 11-5: Circumference of circles
Video for lesson 11-5: Areas of circles
Video for lesson 11-5: Areas between circles and squares
Video for lesson 11-5: Finding the area of irregular figures (circles and trapezoids)
Video for lesson 11-6: Arc lengths
Video for lesson 11-6: Areas of sectors
Notes for lesson 11-5 and 11-6
Practice worksheet for lessons 11-5 and 11-6
Answer Key for 11-5 and 11-6
Video for lesson 11-7: Ratios of perimeters and areas
Notes for lesson 11-7
Practice worksheet for lesson 11-7
Answer Key for Lesson 11-7
Video for lesson 11-8: Finding geometric probabilities using area
Video for lesson 12-1: Finding surface area of a rectangular prism
Video for lesson 12-1: Finding the surface area of a triangular prism
Video for lesson 12-1: Finding the volume of prisms
Video for lesson 12-2: Applications for finding the volume of a prism
Notes for lesson 12-1
Practice worksheet for lesson 12-1
Video for lesson 12-2: Finding the surface area of a pyramid
Video for lesson 12-2: Finding the volume of a pyramid
Notes for lesson 12-2
Practice worksheet for lesson 12-2
Answer Key for 12-2
Video for lesson 12-3: Finding the surface area of a cylinder
Video for lesson 12-3: Finding the volume of a cylinder
Video for lesson 12-3: Finding the surface area of cones
Video for lesson 12-3: Finding the volume of a cone
Notes for lesson 12-3
Practice worksheet for lesson 12-3
Answer Key for 12-3 and 12-4
Video for lesson 12-4: Finding the surface area and volume of a sphere
Video for lesson 12-4: Finding the surface area of composite figures
Notes for 12-4
Practice worksheet for 12-4
Video for lesson 12-5: Finding area and volume of similar figures
Notes for lesson 12-5
Practice worksheet for lesson 12-5
Answer Key for Practice 12-5
Answer Key for Pyramid Worksheet
Answer Key for Prism Worksheet
Video for lesson 13-1: Using the distance formula to find length
Video for lesson 13-1: Finding the center and radius of a circle using its equation
Video for lesson 13-5: Finding the midpoint of a segment using the midpoint formula
Practice worksheet for lessons 13-1 and 13-5 (due Friday, January 20)
Extra practice with 13-1 and 13-5 (due Tuesday, January 24)
Video for lesson 13-2: Finding the slope of a line given two points
Video for lesson 13-3: Identifying parallel and perpendicular lines by their slopes
Practice worksheet for lessons 13-2 and 13-3 (due Wednesday, January 25)
Video for lesson 13-6: Graphing a linear equation in standard form
Video for lesson 13-6: Graphing lines using slope-intercept form of an equation
Application problems for 13-2, 13-3, and 13-6 (due Monday, January 30)
Review for unit 8 (Test A Monday)
Answer key for the unit 8 review
Formula sheet for unit 8 test
Video for lesson 12-5: Finding area and volume of similar figures ►