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August
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September
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October
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November
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December
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January
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February
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March
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April
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1.1 Understanding Points, Lines, and Planes
1.2 Measuring and Constructing Segments
1.3 Measuring and Constructing Angles
1.4 Pairs of Angles.
1.5 Using Formulas in Geometry
1.6 Midpoint and Distance in the Coordinate Plane
1.7 Transformations in the Coordinate Plane
2.1 Using Inductive Reasoning to Make Conjectures.
2.2 Conditional Statements
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2.3 Using Deductive Reasoning to Verify Conjectures
2.4 Bi-conditional Statements and Definitions
2.5 Algebraic Proof
2.6 Geometric Proof
2.7 Flowchart and Paragraph Proofs
3.1 Lines and Angles
3.2 Angles Formed by Parallel Lines and Transversals
3.3 Proving Lines Parallel
3.4 Perpendicular Lines
3.5 Slopes of Lines
3.6 Lines in the Coordinate Plane
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4.1 Classifying Triangles
4.2 Angle Relationships in Triangles
4.3 Congruent Triangles
4.4 Triangle Congruence
4.5 Triangle Congruence: ASA, AAS, and HL
4.6 Triangle Congruence: CPCTC
4.7 Introduction to Coordinate Proof
4.8 Isosceles and Equilateral Triangles
5.1 Perpendicular and Angle Bisectors
5.2 Bisectors of Triangles
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5.3 Medians and Altitudes of Triangles
5.4 The Triangle Mid-segment Theorem
5.5 Indirect Proof and Inequalities in One Triangle
5.6 Inequalities in Two Triangles
5.7 The Pythagorean Theorem
5.8 Applying Special Right Triangles
6.1 Properties and Attributes of Polygons
6.2 Properties of Parallelograms
6.3 Conditions for Parallelograms
6.4 Properties of Special Parallelograms
6.5 Conditions for Special Parallelograms
6.6 Properties of Kites and Trapezoids
7.1 Ratio and Proportion
7.2 Ratios in Similar Polygons
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7.3 Triangle Similarity: AA, SSS, and SAS
7.4 Applying Properties of Similar Triangles
7.5 Using Proportional Relationships
7.6 Dilations and Similarity in the Coordinate Plane
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8.1 Similarity in Right Triangles
8.2 Trigonometric Ratios
8.3 Solving Right Triangles
8.4 Angles of Elevation and Depression
8.5 Law of Sines and Law of Cosines
8.6 Vectors
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9.1 Developing Formulas for Triangles and Quadrilaterals
9.2 Developing Formulas for Circles and Regular Polygons
9.3 Composite Figures
9.4 Perimeter and Area in the Coordinate Plane
9.5 Effects of Changing Dimensions Proportionally
9.6 Geometric Probability
10.1 Solid Geometry
10.2 Representations of Three-Dimensional Figures
10.3 Formulas in Three Dimensions
10.4 Surface Area of Prisms and Cylinders
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10.5 Surface Area of Pyramids and Cones
10.6 Volume of Prisms and Cylinders
10.7 Volume of Pyramids and Cones
10.8 Spheres
11.1 Lines That Intersect Circles
11.2 Arcs and Chords
11.3 Sector Area and Arc Length
11.4 Inscribed Angles
11.5 Angle Relationships in Circles
11.6 Segment Relationships in Circles
11.7 Circles in the Coordinate Plane
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12.1 Reflections
12.2 Translations
12.3 Rotations
12.4 Compositions of Transformations
12.5 Symmetry
12.6 Tessellations
12.7 Dilations
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Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.
Use length and midpoint of a segment. Construct midpoints and congruent segments
Name and classify angles. Measure and construct angles and angle bisectors.
Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles.
Apply formulas for perimeter, area, and circumference.
Develop and apply the formula for midpoint. Use the Distance Formula and the Pythagorean Theorem to find the distance between two points.
Identify reflections, rotations, and translations. Graph transformations in the coordinate plane.
Use inductive reasoning to identify patterns and make conjectures. Find counterexamples to disprove conjectures.
Identify, write, and analyze the truth value of conditional statements. Write the inverse, converse, and contra positive of a conditional statement.
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The Law of Detachment and the Law of Syllogism in logical reasoning.
Write and analyze bi-conditional statements.
Review properties of equality and use them to write algebraic proofs. Identify properties of equality and congruence.
Write two-column proofs. Prove geometric theorems by using deductive reasoning.
Write flowchart and paragraph proofs. Prove geometric theorems by using deductive reasoning.
Identify parallel, perpendicular, and skew lines. Identify the angles formed by two lines and a transversal.
Prove and use theorems about the angles formed by parallel lines and a transversal.
Use the angles formed by a transversal to prove two lines are parallel.
Prove and apply theorems about perpendicular lines.
Find the slope of a line. Use slopes to identify parallel and perpendicular lines.
Graph lines and write their equations in slope-intercept and point-slope form. Classify lines as parallel, intersecting, or coinciding.
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Classify triangles by their angle measures and side lengths. Use triangle classification to find angle measures and side lengths.
Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.
Use properties of congruent triangles. Prove triangles congruent by using the definition of congruence.
Apply SSS and SAS to construct triangles and to solve problems. Prove triangles congruent by using SSS and SAS.
Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.
Use CPCTC to prove parts of triangles are congruent.
Position figures in the coordinate plane for use in coordinate proofs. Prove geometric concepts by using coordinate proof.
Prove theorems about isosceles and equilateral triangles. Apply properties of isosceles and equilateral triangles.
Prove and apply theorems about perpendicular bisectors. Prove and apply theorems about angle bisectors.
Prove and apply properties of perpendicular bisectors of a triangle. Prove and apply properties of angle bisectors of a triangle.
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Apply properties of medians of a triangle. Apply properties of altitudes of a triangle.
Prove and use properties of triangle mid-segments.
Write indirect proofs. Apply inequalities in one triangle.
Apply inequalities in two triangles.
Use the Pythagorean Theorem and its converse to solve problems. Use Pythagorean inequalities to classify triangles.
Justify and apply properties of 45°-45°-90° triangles. Justify and apply properties of 30°-60°-90° triangles.
Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons.
Find the measures of interior and exterior angles of triangles. Apply theorems about the interior and exterior angles of triangles.
Prove that a given quadrilateral is a parallelogram.
Prove and apply properties of rectangles, rhombuses, and squares. Use properties of rectangles, rhombuses, and squares to solve problems.
Prove that a given quadrilateral is a rectangle, rhombus, or square.
Use properties of kites to solve problems. Use properties of trapezoids to solve problems.
Write and simplify ratios. Use proportions to solve problems.
Identify similar polygons. Apply properties of similar polygons to solve problems.
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Prove certain triangles are similar by using AA, SSS, and SAS. Use triangle similarity to solve problems.
Use properties of similar triangles to find segment lengths. Apply proportionality and triangle angle bisector theorems.
Use ratios to make indirect measurements. Use scale drawings to solve problems.
Apply similarity properties in the coordinate plane. Use coordinate proof to prove figures similar.
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Use geometric mean to find segment lengths in right triangles. Apply similarity relationships in right triangles to solve problems.
Find the sine, cosine, and tangent of an acute angle. Use trigonometric ratios to find side lengths in right triangles and to solve real-world problems.
Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems.
Solve problems involving angles of elevation and angles of depression.
Use the Law of Sines and the Law of Cosines to solve triangles.
Find the magnitude and direction of a vector. Use vectors and vector addition to solve real-world problems.
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Develop and apply the formulas for the areas of triangles and special quadrilaterals. Solve problems involving perimeters and areas of triangles and special quadrilaterals.
Develop and apply the formulas for the area and circumference of a circle. Develop and apply the formula for the area of a regular polygon.
Use the Area Addition Postulate to find the areas of composite figures. Use composite figures to estimate the areas of irregular shapes.
Find the perimeters and areas of figures in a coordinate plane.
Describe the effect on perimeter and area when one or more dimensions of a figure are changed. Apply the relationship between perimeter and area in problem solving.
Calculate geometric probabilities. Use geometric probability to predict results in real-world situations.
Classify three-dimensional figures according to their properties. Use nets and cross sections to analyze three-dimensional figures.
Draw representations of three-dimensional figures. Recognize a three-dimensional figure from a given representation.
Apply Euler’s formula to find the number of vertices, edges, and faces of a polyhedron. Develop and apply the Distance and Midpoint Formulas in three dimensions.
Learn and apply the formula for the surface area of a prism. Learn and apply the formula for the surface area of a cylinder.
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Learn and apply the formula for the surface area of a cone. Learn and apply the formula for the surface area of a cone.
Learn and apply the formula for the volume of a prism. Learn and apply the formula for the volume of a cylinder.
Learn and apply the formula for the volume of a pyramid. Learn and apply the formula for the volume of a cone.
Learn and apply the formula for the volume of a sphere. Learn and apply the formula for the surface area of a sphere.
Identify tangents, secants, and chords. Use properties of tangents to solve problems.
Apply properties of arcs. Apply properties of chords.
Find the area of sectors. Find arc lengths.
Find the measure of an inscribed angle. Use inscribed angles and their properties to solve problems.
Find the measures of angles formed by lines that intersect circles. Use angle measures to solve problems.
Find the lengths of segments formed by lines that intersect circles. Use the lengths of segments in circles to solve problems.
Write equations and graph circles in the coordinate plane. Use the equation and graph of a circle to solve problems.
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Identify and draw reflections.
Identify and draw translations.
Identify and draw rotations
Apply theorems about isometries. Identify and draw compositions of transformations, such as glide reflections.
Identify and describe symmetry in geometric figures.
Use transformations to draw tessellations. Identify regular and semiregular tessellations and figures that will tessellate.
Identify and draw dilations.
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The contents of this lesson go beyond the scope of the Arizona Content Standards.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.6 Solve problems related to complementary, supplementary or congruent angle concepts.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.3 Make a net to represent a 3-dimensional object;
PO.4 Make a 3-dimensional model from a net;
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels
PO.3 Make a net to represent a 3-dimensional object;
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.9 Solve problems using the triangle inequality property; PO.10 Solve problems using special case right triangles.
PO.1 Identify the attributes of special triangles;
PO.11 Determine when triangles are congruent by applying SSS, ASA, AAS, or SAS;
PO.12 Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates.
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PO.3 Make a net to represent a 3-dimensional object;
PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
PO.4 Make a 3-dimensional model from a net;
PO.10 Solve problems using special case right triangles.
PO.2 Identify the hierarchy of quadrilaterals;
PO.13 Construct a triangle congruent to a given triangle.
PO.13 Construct a triangle congruent to a given triangle.
PO.13 Construct a triangle congruent to a given triangle.
PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
PO.13 Construct a simple formal or informal deductive proof.
PO.13 Construct a simple formal or informal deductive proof.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.2 Identify the hierarchy of quadrilaterals; PO.4 Make a 3-dimensional model from a net.
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PO.1 Identify the attributes of special triangles.
PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants;
PO.11 Determine when triangles are congruent by applying SSS, ASA, AAS, or SAS;
PO.13 Construct a triangle congruent to a given triangle.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants;
PO.11 Determine when triangles are congruent by applying SSS, ASA, AAS, or SAS;
PO.13 Construct a triangle congruent to a given triangle.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.14 Solve contextual situations using angle and side length relationships.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.14 Solve contextual situations using angle and side length relationships.
PO.13 Construct a simple formal or informal deductive proof.
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PO.14 Solve contextual situations using angle and side length relationships.
PO.14 Solve contextual situations using angle and side length relationships.
PO.14 Solve contextual situations using angle and side length relationships.
PO.9 Solve problems using the triangle inequality property.
PO.14 Solve contextual situations using angle and side length relationships.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants;
PO.14 Solve contextual situations using angle and side length relationships.
PO.14 Solve contextual situations using angle and side length relationships.
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants.
PO.2 Identify the hierarchy of quadrilaterals.
PO.2 Identify the hierarchy of quadrilaterals.
PO.2 Identify the hierarchy of quadrilaterals.
PO.2 Identify the hierarchy of quadrilaterals.
PO.2 Identify the hierarchy of quadrilaterals; PO.14 Solve contextual situations using angle and side length relationships.
PO.9 Solve scale factor problems using ratios and proportions.
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PO.9 Solve scale factor problems using ratios and proportions.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants;
PO.12 Determine when triangles are similar by applying SAS, SSS, or AA similarity postulates.
PO.10 Solve problems using special case right triangles.
PO.9 Solve problems using the triangle inequality property; PO.10 Solve problems using special case right triangles.
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PO.3 Make a net to represent a 3-dimensional object;
PO.4 Make a 3-dimensional model from a net;
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.9 Solve problems using the triangle inequality property.
PO.14 Solve contextual situations using angle and side length relationships.
PO.10 Solve problems using special case right triangles.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.14 Solve contextual situations using angle and side length relationships.
PO.14 Solve contextual situations using angle and side length relationships.
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The contents of this lesson go beyond the scope of the Arizona Content Standards.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.10 Solve problems using special case right triangles.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.4 Make a 3-dimensional model from a net.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
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PO.3 Make a net to represent a 3-dimensional object; PO.4 Make a 3-dimensional model from a net.
PO.3 Make a net to represent a 3-dimensional object;
PO.4 Make a 3-dimensional model from a net;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.2 Identify the hierarchy of quadrilaterals;
PO.4 Make a 3-dimensional model from a net.
PO.2 Identify the hierarchy of quadrilaterals; PO.4 Make a 3-dimensional model from a net.
PO.2 Identify the hierarchy of quadrilaterals;
PO.3 Make a net to represent a 3-dimensional object;
PO.4 Make a 3-dimensional model from a net;
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels;
PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs;
PO.8 Solve problems by applying the relationship between radii, diameters, chords, tangents, or secants.
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PO.7 Solve problems by applying the relationship between circles, angles, and intercepted arcs.
PO.4 Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation.
PO.4 Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation.
PO.4 Determine whether a given pair of figures on a coordinate plane represents a translation, reflection, rotation, or dilation.
PO.1 Identify the attributes of special triangles.
The contents of this lesson go beyond the scope of the Arizona Content Standards.
PO.2 Identify the hierarchy of quadrilaterals.
PO.5 Draw 2-dimensional and 3-dimensional figures with appropriate labels; PO.6 Solve problems related to complementary, supplementary, or congruent angle concepts.
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