# Chapter 1: Essentials of Geometry

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1 Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify, correctly label, and sketch the following geometric figures: point, line, plane, collinear points, coplanar points, segment, ray, opposite rays. 2. Use segment addition to calculate segment lengths. 3. Justify segment congruence on the 4. Use the definitions of midpoint and segment bisector to calculate segment lengths. 5. Calculate the coordinates of the midpoint of a segment using the midpoint formula. 6. Calculate the length of a segment using the distance formula. 1.4 Measure and Classify Angles 7. Identify, correctly label, and sketch the following: acute, right, obtuse, and straight angles, congruent angles, and angle bisectors. 8. Use angle addition to calculate angle measures. 9. Use the angle bisector definition to calculate angle measures. 1.5 Describe Angle Pair Relationships 10. Use the definitions of complementary, supplementary, and adjacent angles to calculate angle measures. 11. Identify and solve for angle measures using linear pairs. 12. Identify and solve for angle measures using vertical angles. Chapter 2A: Reasoning 2.1 Use Inductive Reasoning 1. Describe and find terms in patterns 2. Make and test conjectures 3. Find a counterexample 2.2 Analyze Conditional Statements 4. Rewrite a statement in if-then form 5. Write biconditional and related conditional statements (converse, inverse, contrapositive) 2.3 Apply Deductive Reasoning 6. Use the Laws of Detachment and Syllogism 7. Use inductive and deductive reasoning 2.4 Use Postulates and Diagrams 8. Identify postulates from a diagram 9. Sketch and interpret diagrams 2.5 Reason Using Properties from Algebra 2.6 Prove Statements about Segments and Angles 2.7 Prove Angle Pair Relationships Chapter 2B: Proof 1. Use the distributive property and properties of equality 2. Write algebraic proofs 3. Identify and use properties (reflexive, symmetric, transitive) 4. Write two-column proofs for segments 5. Write two-column proofs for angles 6. Use vertical angles congruence to find angle measures in diagrams

2 3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals Chapter 3A: Parallel Lines 1. Identify angle pairs formed by three intersecting lines 2. Use angles formed by parallel lines and transversals 3.3 Prove Lines are Parallel 3. Use angle relationships to prove that lines are parallel 3.6 Prove Theorems about Perpendicular Lines 4. Draw conclusions about parallel lines, transversals, and the angles they create 3.4 (day1) Chapter 3B: Write and Graph Linear Equations Find and Use Slopes of Lines 1. Find slope of a line given two points, graph 2. Classify lines given the slope 3.4 (day2) (day1) (day2) (day3) Find and Use Slopes of Lines 3. Find slopes of parallel and perpendicular lines 4. Write the equation of a line given point and slope, two points, graph 5. Write the equation of parallel and perpendicular lines 6. Graph equations of lines Chapter 4: Congruent Triangles 4.1 Apply Triangle Sum Properties 1. Classify triangles 2. Find measures of angles in a triangle 4.7 Use Isosceles and Equilateral Triangles 4.2 Apply Congruence and Triangles Prove Triangles Congruent: SSS, SAS, HL, ASA, AAS 4.6 Use Congruent Triangles: CPCTC 3. Use theorems about isosceles and equilateral triangles 4. Identify congruent figures 5. Solve for variables in congruent figures 6. Prove triangles are congruent 7. Use congruent triangles to prove corresponding parts congruent.

3 6.1 Ratios, Proportions, and the Geometric Mean 6.2 Use Proportions to Solve Geometry Problems Chapter 6: Similarity 1. Write, simplify and use ratios 2. Set up, solve, and use proportions 3. Use proportions to find missing segments in triangles and quadrilaterals 6.3 Use Similar Polygons 4. Use proportions to find missing parts of similar polygons Prove Triangles Similar 5. Prove that triangles are similar 7.1 Apply the Pythagorean Theorem 7.2 Use the Converse of the Pythagorean Theorem Chapter 7: Right Triangles and Trigonometry 1. Use the Pythagorean Theorem to find missing side lengths in right triangles 2. Apply the Pythagorean Theorem to area of a triangle and real world problems 3. Classify triangles as acute, obtuse, or right when three sides are given 7.4 Special Right Triangles 4. Find missing sides and angles in triangles 5. Find missing sides and angles in triangles Sine, Cosine, and Tangent Ratios for Right Triangles 6. Find trigonometric ratios for angles in right triangles 7. Use trigonometric ratios to find missing sides in right triangles 7.7 Solve Right Triangles 8. Use inverse trigonometric ratios to find missing angles in right triangles 9. Use trigonometric ratios to solve right triangles (find all sides and angles) Chapter 8: Quadrilaterals 1.6 Classify Polygons 1. Identify and classify polygons 2. Find side lengths of polygons 8.1 Find Angle Measures in Polygons 8.2 Use Properties of Parallelograms 8.3 Show that a Quadrilateral is a Parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 3. Find interior angle measures in polygons 4. Find interior and exterior angle measures in polygons 5. Find side and angle measures in parallelograms 6. Show that a quadrilateral is a parallelogram 7. Use algebra to find missing sides and angles in a parallelogram 8. Identify special parallelograms: rhombuses, rectangles, and squares 9. Use algebra to find missing sides and angles in special parallelograms

4 8.5 Use Properties of Trapezoids and Kites Geometry Learning Targets 10. Identify special quadrilaterals: trapezoids and kites 11. Use algebra to find missing sides and angles in special quadrilaterals 8.6 Identify Special Quadrilaterals 12. Use the properties of quadrilaterals to identify and classify quadrilaterals using characteristics of the 7 types of quadrilaterals 11.1 Areas of Triangles and Parallelograms Chapter 11: Measuring Length and Area 1. Find areas of parallelograms and triangles Areas of Trapezoids, Rhombuses, and Kites 11.3 Perimeter and Area of Similar Figures 2. Find areas of trapezoids, rhombuses, and kites. 3. Use ratios to find area and perimeter of similar figures Circumference and Arc length 4. Find circumference and arc length for a circle Areas of Circles and Sectors 5. Find area and sector area of circles Areas of Regular Polygons 6. Find area and perimeter of regular polygons Use Geometric Probability 7. Find geometric probabilities. Chapter 12: Surface Area and Volume of Solids 12.1 Explore Solids 1. Identify, classify, and describe solids Surface Area of Prisms and Cylinders 12.3 Surface Area of Pyramids and Cones 12.4 Volume of Prisms and Cylinders 12.5 Volume of Pyramids and Cones 12.6 Surface Area and Volume of Spheres 2. Solve problems using surface area of prisms and cylinders. 3. Solve problems using surface area of pyramids and cones. 4. Solve problems using volume of prisms and cylinders. 5. Solve problems using volume of pyramids and cones. 6. Solve problems using surface area and volume of spheres Explore Similar Solids 7. Apply similarity properties to solids.

5 9.1 Translate Figures and Use Vectors Chapter 9: Properties of Transformations 1. Produce an image of the translation (slide) a preimage on a 9.3 Perform Reflections 2. Produce an image after the reflection of a preimage on a 9.4 Perform Rotations 4. Produce an image after the rotation of a preimage on a 9.5 Apply Compositions of Transformations 5. Produce an image after more than one transformation of a preimage on a 9.6 Identify Symmetry 6. Determine if a figure has line symmetry and find its line of symmetry. 7. Determine if a figure has rotational symmetry and find its degree of rotation. 9.7 Identify and Perform Dilations 8. Produce an image after the dilation of a preimage on a

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# Chapter 1: Essentials of Geometry

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1 Section Section Title 1.1 Identify Points, Lines, and Planes 1.2 Use Segments and Congruence 1.3 Use Midpoint and Distance Formulas Chapter 1: Essentials of Geometry Learning Targets I Can 1. Identify, correctly label, and sketch the following geometric figures: point, line, plane, collinear points, coplanar points, segment, ray, opposite rays. 2. Use segment addition to calculate segment lengths. 3. Justify segment congruence on the 4. Use the definitions of midpoint and segment bisector to calculate segment lengths. 5. Calculate the coordinates of the midpoint of a segment using the midpoint formula. 6. Calculate the length of a segment using the distance formula. 1.4 Measure and Classify Angles 7. Identify, correctly label, and sketch the following: acute, right, obtuse, and straight angles, congruent angles, and angle bisectors. 8. Use angle addition to calculate angle measures. 9. Use the angle bisector definition to calculate angle measures. 1.5 Describe Angle Pair Relationships 10. Use the definitions of complementary, supplementary, and adjacent angles to calculate angle measures. 11. Identify and solve for angle measures using linear pairs. 12. Identify and solve for angle measures using vertical angles. Chapter 2A: Reasoning 2.1 Use Inductive Reasoning 1. Describe and find terms in patterns 2. Make and test conjectures 3. Find a counterexample 2.2 Analyze Conditional Statements 4. Rewrite a statement in if-then form 5. Write biconditional and related conditional statements (converse, inverse, contrapositive) 2.3 Apply Deductive Reasoning 6. Use the Laws of Detachment and Syllogism 7. Use inductive and deductive reasoning 2.4 Use Postulates and Diagrams 8. Identify postulates from a diagram 9. Sketch and interpret diagrams 2.5 Reason Using Properties from Algebra 2.6 Prove Statements about Segments and Angles 2.7 Prove Angle Pair Relationships Chapter 2B: Proof 1. Use the distributive property and properties of equality 2. Write algebraic proofs 3. Identify and use properties (reflexive, symmetric, transitive) 4. Write two-column proofs for segments 5. Write two-column proofs for angles 6. Use vertical angles congruence to find angle measures in diagrams

2 3.1 Identify Pairs of Lines and Angles 3.2 Use Parallel Lines and Transversals Chapter 3A: Parallel Lines 1. Identify angle pairs formed by three intersecting lines 2. Use angles formed by parallel lines and transversals 3.3 Prove Lines are Parallel 3. Use angle relationships to prove that lines are parallel 3.6 Prove Theorems about Perpendicular Lines 4. Draw conclusions about parallel lines, transversals, and the angles they create 3.4 (day1) Chapter 3B: Write and Graph Linear Equations Find and Use Slopes of Lines 1. Find slope of a line given two points, graph 2. Classify lines given the slope 3.4 (day2) (day1) (day2) (day3) Find and Use Slopes of Lines 3. Find slopes of parallel and perpendicular lines 4. Write the equation of a line given point and slope, two points, graph 5. Write the equation of parallel and perpendicular lines 6. Graph equations of lines Chapter 4: Congruent Triangles 4.1 Apply Triangle Sum Properties 1. Classify triangles 2. Find measures of angles in a triangle 4.7 Use Isosceles and Equilateral Triangles 4.2 Apply Congruence and Triangles Prove Triangles Congruent: SSS, SAS, HL, ASA, AAS 4.6 Use Congruent Triangles: CPCTC 3. Use theorems about isosceles and equilateral triangles 4. Identify congruent figures 5. Solve for variables in congruent figures 6. Prove triangles are congruent 7. Use congruent triangles to prove corresponding parts congruent.

3 6.1 Ratios, Proportions, and the Geometric Mean 6.2 Use Proportions to Solve Geometry Problems Chapter 6: Similarity 1. Write, simplify and use ratios 2. Set up, solve, and use proportions 3. Use proportions to find missing segments in triangles and quadrilaterals 6.3 Use Similar Polygons 4. Use proportions to find missing parts of similar polygons Prove Triangles Similar 5. Prove that triangles are similar 7.1 Apply the Pythagorean Theorem 7.2 Use the Converse of the Pythagorean Theorem Chapter 7: Right Triangles and Trigonometry 1. Use the Pythagorean Theorem to find missing side lengths in right triangles 2. Apply the Pythagorean Theorem to area of a triangle and real world problems 3. Classify triangles as acute, obtuse, or right when three sides are given 7.4 Special Right Triangles 4. Find missing sides and angles in triangles 5. Find missing sides and angles in triangles Sine, Cosine, and Tangent Ratios for Right Triangles 6. Find trigonometric ratios for angles in right triangles 7. Use trigonometric ratios to find missing sides in right triangles 7.7 Solve Right Triangles 8. Use inverse trigonometric ratios to find missing angles in right triangles 9. Use trigonometric ratios to solve right triangles (find all sides and angles) Chapter 8: Quadrilaterals 1.6 Classify Polygons 1. Identify and classify polygons 2. Find side lengths of polygons 8.1 Find Angle Measures in Polygons 8.2 Use Properties of Parallelograms 8.3 Show that a Quadrilateral is a Parallelogram 8.4 Properties of Rhombuses, Rectangles, and Squares 3. Find interior angle measures in polygons 4. Find interior and exterior angle measures in polygons 5. Find side and angle measures in parallelograms 6. Show that a quadrilateral is a parallelogram 7. Use algebra to find missing sides and angles in a parallelogram 8. Identify special parallelograms: rhombuses, rectangles, and squares 9. Use algebra to find missing sides and angles in special parallelograms

4 8.5 Use Properties of Trapezoids and Kites Geometry Learning Targets 10. Identify special quadrilaterals: trapezoids and kites 11. Use algebra to find missing sides and angles in special quadrilaterals 8.6 Identify Special Quadrilaterals 12. Use the properties of quadrilaterals to identify and classify quadrilaterals using characteristics of the 7 types of quadrilaterals 11.1 Areas of Triangles and Parallelograms Chapter 11: Measuring Length and Area 1. Find areas of parallelograms and triangles Areas of Trapezoids, Rhombuses, and Kites 11.3 Perimeter and Area of Similar Figures 2. Find areas of trapezoids, rhombuses, and kites. 3. Use ratios to find area and perimeter of similar figures Circumference and Arc length 4. Find circumference and arc length for a circle Areas of Circles and Sectors 5. Find area and sector area of circles Areas of Regular Polygons 6. Find area and perimeter of regular polygons Use Geometric Probability 7. Find geometric probabilities. Chapter 12: Surface Area and Volume of Solids 12.1 Explore Solids 1. Identify, classify, and describe solids Surface Area of Prisms and Cylinders 12.3 Surface Area of Pyramids and Cones 12.4 Volume of Prisms and Cylinders 12.5 Volume of Pyramids and Cones 12.6 Surface Area and Volume of Spheres 2. Solve problems using surface area of prisms and cylinders. 3. Solve problems using surface area of pyramids and cones. 4. Solve problems using volume of prisms and cylinders. 5. Solve problems using volume of pyramids and cones. 6. Solve problems using surface area and volume of spheres Explore Similar Solids 7. Apply similarity properties to solids.

5 9.1 Translate Figures and Use Vectors Chapter 9: Properties of Transformations 1. Produce an image of the translation (slide) a preimage on a 9.3 Perform Reflections 2. Produce an image after the reflection of a preimage on a 9.4 Perform Rotations 4. Produce an image after the rotation of a preimage on a 9.5 Apply Compositions of Transformations 5. Produce an image after more than one transformation of a preimage on a 9.6 Identify Symmetry 6. Determine if a figure has line symmetry and find its line of symmetry. 7. Determine if a figure has rotational symmetry and find its degree of rotation. 9.7 Identify and Perform Dilations 8. Produce an image after the dilation of a preimage on a

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### Content Structure

Content Structure The geometry course is centered on the beliefs that: The ability to construct a valid argument is the basis of logical communication, in both mathematics and the real-world. There is a need to use segments and congruence, understand midpoint and distance formulas, measure and classify angles, and describe angle pair relationships. The course covers the following topics:

1. **Fundamental Concepts and Patterns in Geometry**
   - Points, lines, and planes
   - Segments and congruence
   - Midpoint and distance formulas
   - Angles and their measures
   - Angle pair relationships

2. **Reasoning and Proof**
   - Inductive reasoning
   - Conditional statements
   - Deductive reasoning
   - Postulates and diagrams
   - Properties from algebra

3. **Parallel and Perpendicular Lines**
   - Parallel lines and transversals
   - Proving lines parallel
   - Slopes of lines
   - Equations of lines

4. **Congruent Triangles**
   - Classifying triangles
   - Congruence and triangles
   - Proving triangles congruent (SSS, SAS, ASA, AAS, HL)
   - Using congruent triangles (CPCTC)

