Scope & Sequence
 
Topic 1: Foundations of Geometry 1.4: Inductive Reasoning 1.5 Conditional Statements (converse only) 1.6 Deductive Reasoning (concept only) 1.7 Writing Proofs (twocolumn only; emphasize algebra proofs) Standards: HSG.CO.C.9, 10, 11.
Topic 2: Parallel and Perpendicular Lines 1.1 Measuring Segments and Angles 2.1 Properties of Parallel Lines 2.2 Proving Lines are Parallel 2.3 Parallel Lines and Triangles 2.4 Slopes of Parallel and Perpendicular Lines Standards: HSG.CO.A.1, 3; HSG.CO.C.9, 10; HSG.MG.A.1, 3; HSG.GPE.B.5.
Topic 3: Transformations (transform y = x^2 and y = x in tandem) 3.1 Reflections 3.2 Translations 3.3 Rotations (omit Example 4) 3.4 Classification of Rigid Motions 3.5 Symmetry Standards: HSG.CO.A.2, 3, 4, 5; HSG.CO.B.6
Topic 4: Triangle Congruence 4.1 Congruence 4.2 Isosceles and Equilateral Triangles 4.3 Proving and Applying the SAS and SSS Congruence Criteria 4.4 Proving and Applying the ASA and AAS Congruence Criteria 4.5 Congruence in Right Triangles 4.6 Congruence in Overlapping Triangles Standards: HSG.CO.A.5; HSG.CO.B.6, 7, 8; HSG.SRT.B.5
Topic 6A: Quadrilaterals and Other Polygons 1.3 Midpoint & Distance 9.1 Polygons in the Coodinate Plane 6.1 Polygon AngleSum Theorems 6.2 Kites and Trapezoids Standards: HSG.GPE.B.4, 6, 7; HSG.SRT.B.5
 Topic 6B: Quadrilaterals and Other Polygons 6.3 Properties of Parallelograms 6.4 Proving a Quadrilateral is a Parallelogram 6.5 Properties of Special Parallelograms 6.6 Identifying Special Parallelograms Standards: HSG.CO.C11; HSG.SRT.B.5
7.1 Dilations 7.2 Similarity Transformations 7.3 Proving Triangles are Similar 7.4 Similarity in Right Triangles 7.5 Proportions in Triangles Standards: HSG.CO.A.2, 5; HSG.CO.C.10; HSG.SRT.A.1, 2, 3; HSG.SRT.B.4, 5
Topic 8: Right Triangles and Trigonometry Topic 11: Two and ThreeDimensional Models 11.2 Volumes of Prisms and Cylinders (also cross sections: concept only) 11.3 Pyramids and Cones (omit Example 1) 11.4 Spheres Standards: HSG.GMD.A.1, 2(+), 3; HSG.MG.A.1, 2
Topic 5: Relationships in Triangles (as time allows) 1.2 Basic Constructions 5.1 Perpendicular and Angle Bisectors 5.2 Bisectors in Triangles 5.3 Medians and Altitudes 5.4/5 Inequalities in Triangles Standards: HSG.C.A.3; HSG.CO.C.9, 10; HSG.CO.D.12; HSG.SRT.B.5

Essential Learning
Semester 1
Topic 1: Foundations of Geometry
1.4 Inductive Reasoning
 Use inductive reasoning to identify patterns and make predictions based on data.
 Use inductive reasoning to provide evidence that conjectures are true or provide counterexamples to disprove them.
1.5 Conditional Statements (converse only)
 Write conditional and biconditional statements.
1.6 Deductive Reasoning (concept only)
 Use deductive reasoning to draw a valid conclusion based on a set of given facts.
1.7 Writing Proofs
 Use deductive reasoning to prove geometric theorems about lines and angles.
Topic 2: Parallel and Perpendicular Lines
1.1 Measuring Segments and Angles
 Use the ruler and segment addition postulates.
 Use the protractor and the angle addition postulates.
 Identify congruent segments and congruent angles.
2.1 Properties of Parallel Lines
 Define parallel lines using the undefined terms point and line.
 Prove theorems about lines and angles.
 Use theorems to find the measures of angles formed by parallel lines and a transversal.
2.2 Proving Lines Parallel
 Prove that two lines cut by a transversal are parallel using the converses of parallel line angle relationship theorems.
 Use properties of parallel lines and transversals to solve realworld and mathematical problems.
 Write and use flow proofs.
2.3 Parallel Lines and Triangles
 Use line constructed parallel to another line to solve problems and prove theorems.
 Use the sum of the angle measures in a triangle to solve problems.
2.4 Slopes of Parallel and Perpendicular Lines
 Show that two lines in the coordinate plane are parallel by comparing their slopes, and solve problems.
 Show that two line in the coordinate plane are perpendicular by comparing their slopes, and use that information to solve problems.
Topic 3: Transformations
3.1 Reflections
 Find a reflected image and write a rule for a reflection.
 Define reflection as a transformation across a line or reflection with given properties and perform reflections on and off a coordinate grid.
3.2 Translations
 Translate a figure and write a rule for a translation.
3.3 Rotations
 Rotate a figure and write a rule for a rotation.
 Find the image of a figure after a composition of rigid motions.
3.4 Classification of Rigid Motions
 Specify a sequence of transformations that will carry a given figure onto another.
 Use geometric descriptions of rigid motions to transform figures.
3.5 Symmetry
 Describe the rotation and/or reflections that carry a polygon onto itself.
 Predict the effect of a given rigid motion on a figure.
 Identify types of symmetry in a figure.
Topic 4: Triangle Congruence
4.1 Congruence
 Relate congruence to rigid motions.
 Demonstrate that two figure are congruent by using one or more rigid motions to map one onto the other.
4.2 Isosceles and Equilateral Triangles
 Use properties of and theorems about isosceles and equilateral triangles to solve problems.
 Identify congruent triangles using properties of isosceles and equilateral triangles.
4.3 Proving and Applying the SAS and SSS Congruence Criteria
 Prove triangle congruence by SAS and SSS criteria and use triangle congruence to solve problems.
 Understand that corresponding parts of congruent triangles are congruent and use CPCTC to prove theorems and solve problems.
4.4 Proving and Applying the ASA and AAS Congruence Criteria
 Prove that two triangles are congruent using ASA and AAS criteria and apply ASA to solve problems.
 Prove that when all corresponding sides and angles of two polygons are congruent, the polygons are congruent.
4.5 Congruence in Right Triangles
 Prove and use the HL Theorem.
 Use congruence criteria for triangles to solve problems and to prove relationships in geometric figures.
4.6 Congruence in Overlapping Triangles
 Apply congruence criteria to increasingly difficult problems involving overlapping triangles and multiple triangles.
 Prove triangles are congruent by identifying corresponding parts and using theorems.
Topic 6A: Quadrilaterals and Other Polygons, plus 9.1 Polygons in the Coordinate Plan
1.3 Midpoint & Distance
 Use the midpoint formula to find the midpoint of a segment drawn on a coordinate plane.
 Use the distance formula to find the length of a segment drawn on the coordinate plane.
9.1 Polygons in the Coordinate Plane
 Use coordinate geometry to classify triangles and quadrilaterals on the coordinate plane.
 Solve problems involving triangles and polygons on the coordinate plane
6.1 Polygon AngleSum Theorems
 Show that the sum of the exterior angles of a polygon is 360 degrees and use that to solve problems.
 Show that the um of the interior angles of a polygon is the product of 180 degrees and two less than the number of sides, and use that to solve problems.
6.2 Kites and Trapezoids
 Use properties of the diagonals of a kite to solve problems.
 Use properties of isosceles trapezoids to solve problems.
 Use the relationship between the lengths of the bases and the midsegment of a trapezoid to solve problems.
Semester 2
Topic 6B: Quadrilaterals and Other Polygons, plus 9.1 Coordinates in the Coordinate Plane
6.3 Properties of Parallelograms
 Show that the consecutive angles of a parallelogram are supplementary and opposite angle are congruent.
 Show that opposite sides of a parallelogram are congruent.
 Show that diagonals of a parallelogram bisect each other.
6.4 Proving a Quadrilateral is a Parallelogram
 Demonstrate that a quadrilateral is a parallelogram based on its sides and diagonals.
 Demonstrate that a quadrilateral is a parallelogram based on its angles.
6.5 Properties of Special Parallelograms
 Prove that the diagonals of rhombuses are perpendicular bisectors of each other and angle bisectors of the angles of the rhombus.
 Prove that the diagonals of a rectangle are congruent.
 Use properties of rhombuses, rectangles, and squares to solve problems.
6.6 Conditions of Special Parallelograms
 Identify rhombuses, rectangles, and squares by the characteristics of diagonals of parallelograms.
Topic 7: Transformations
7.1 Dilations
 Dilate figures on and off the coordinate plane.
 Understand how distances and links in a dilation are related to the scale factor and center of dilation
7.2 Similarity Transformations
 Understand that two figures are similar if there is a similarity transformation that maps one figure to the other.
 Identify a combination of rigid motions and dilation that maps one figure to a similar figure.
 Identify the coordinates of an image under a similarity transformation.
7.3 Proving Triangles Similar
 Use dilations and rigid motions to prove triangles are similar.
 Prove and do use the AA~,SSS ~, and SAS ~ theorems to prove triangles are similar.
7.4 Similarity in Right Triangles
 Use similarity of right triangles to solve problems.
 Use length relationships of the sides of right triangles and an altitude drawn to the hypotenuse to solve problems.
7.5 Proportions in Triangles
 Use the side splitter theorem in the triangle midsegment theorem to find lengths of sides in segments of triangles.
 Use the triangle angle bisector theorem to find length of side in segments of triangles
Topic 8: Right Triangles and Trigonometry
8.1 Right Triangles and Pythagorean Theorem
 Prove the Pythagorean theorem using similar right triangles.
 Understand and apply the relationship between side links in a 454590 and a 306090 triangle.
8.2 Trigonometric Ratios
 Define and calculate sine, cosine, and tangent ratios.
 Use trigonometric ratios to solve problems.
8.5 Problem Solving with Trigonometry
 Distinguish between angles of elevation and depression.
Topic 10: Circles
10.1 Arcs and Sectors
 Calculate the length of an arc when the central angle is given in degrees calculate the length of an arc when the central angle is given in degrees or radians.
 Calculate the area of sectors and segments of circles.
10.2 Tangent Lines to a Circle
 Identify lines that are tangent to a circle using angle measures and segment lengths.
 Solve problems involving tangent lines.
10.3 Chords
 Prove and apply relationships between chords, arcs, and central angles.
 Find links of chords given the distance from the center of the circle and use this information to solve problems
10.4 Inscribed Angles
 Identify and apply relationships between the measures of inscribed angles, arcs, and central angles.
 Identify and apply the relationships between an angle formed by a chord and a tangent to its intercepted arc.
Topic 11: Two and ThreeDimensional Models
11.2 Volumes of Prisms & Cylinders
 Do use Euler’s formula to calculate the number of vertices, faces, and edges in polyhedrons.
 Describe cross sections of polyhedrons.
 Describe rotations of polygons about an axis.
11.3 Pyramids & Cones
 Understand how the volume formulas for pyramids and cones apply to oblique pyramids and cones.
 Model three dimensional figures as pyramids and cones to solve problems.
11.4 Spheres
 Use Cavalieri’s Principle to show how the volume of a hemisphere is related to the volume of a cone and a cylinder.
 Calculate volumes and surface areas of spheres and composite figures.
Topic 5: Relationships in Triangles
1.2 Basic Constructions
 Construct copies of segments and angles, perpendicular bisectors of segments, and bisectors of angles.
 Apply construction to solve problems.
5.1 Perpendicular and Angle Bisectors
 Prove the Perpendicular Bisector Theorem, the Angle Bisector Theorem, and their converses.
 Use the Perpendicular Bisector Theorem to solve problems.
 Use the Angle Bisector Theorem to solve problems.
5.2 Bisectors in Triangles
 Prove that the point of concurrency of the perpendicular bisectors of a triangle, called the circumcenter, is equidistant from the vertices.
 Prove that the point of concurrency of the angle bisectors of a triangle, called the incenter is equidistant form the sides.
5.3 Medians and Altitudes
 Identify special segments in triangles and understand theorems about them.
 Find and use the point of concurrency of the medians of a triangle to solve problems and prove relationships in triangles.
 Find the point of concurrency of the altitudes of a triangle.
5.4 Inequalities in One Triangle
 Prove that the side lengths of a triangle are related to the angle measures of the triangle.
 Use the angle measures of a triangle to compare the side lengths of the triangle.
 Use the Triangle Inequality Theorem to determine if three given side lengths will form a triangle and to find a range of possible side lengths for a third side given two side lengths.
5.5 Inequalities in Two Triangles
 Prove the Hinge Theorem and use the Hinge Theorem to compare side lengths.
 Prove the Converse of the Hinge Theorem and use the Converse of the Hinge Theorem to compare angle measures.