Standard

Concepts

Lesson(s)

Ancillary Materials

		GE 1.0
		GE 8.0
	GE 13.0

 

 GE 15.0

	GE 16.0
	GE 17.0
	GE 22.0

 

Chapter 1: Foundations For Geometry

·        Demonstrate understanding by identifying and giving examples of undefined terms (points, lines, and planes) and postulates (axioms).

·        Perform basic constructions with a compass and straightedge of segments and angles bisectors.

·        Identify and find measures of adjacent, vertical, complementary, and supplementary angles, and linear pairs.

·        Know and solve problems involving the perimeter, circumference, and area of common geometric figures.

·        Use the distance and midpoint formulas and Pythagorean Theorem to find the distance between two points in a coordinate plane.

·        Identify reflections, rotations, and translations of figures, and be able to graph these transformations in a coordinate plane.  

Lessons 1-1 – 1-7

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

	GE 1.0
	GE 2.0
	GE 3.0

 

Chapter 2: Geometric Reasoning

·        Demonstrate understanding by identifying and giving examples of inductive reasoning to make conjectures; also, provide counterexamples to disprove conjectures.

·        Identify, write, and analyze the truth value of conditional statements; and write the inverse, converse, and contrapositive of a conditional statement.

·        Demonstrate understanding by identifying and giving examples of inductive and deductive reasoning by applying the Law of Detachment and the Law of Syllogism.

·        Write and analyze biconditional statements.

·        Write (algebraic and) geometric proofs by using properties of equality and congruence using two-column, flowchart, and paragraph proofs.

Lessons 2-1 – 2-7

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

	GE 1.0
	GE 2.0
	GE 7.0
	GE 16.0

A1-9.0

GE 17.0

Review:

·        Solve systems of two linear equations in two variables.

Chapter 3: Parallel and Perpendicular Lines

·        Identify parallel, perpendicular, and skew lines.

·        Identify corresponding, alternate interior and exterior, and same-side interior angles cut by a transversal.

·        Prove and use theorems about angles formed by parallel lines and a transversal.

·        Use the angles formed by a transversal to prove lines are parallel

·        Prove and apply theorems about perpendicular lines using geometric proofs.

·        Find the slope of a line in a coordinate plane; and be able to use the slope to identify if lines are parallel or perpendicular.

·        Graph lines and write their equations in slope-intercept and point-slope form.

·        Classify lines as parallel, intersecting, or coinciding.

Lessons 3-1 – 3-6

·        Holt Text:  pp. 152-153 or Alg. 1 textbook on solving equations with two variables (before Lesson 3-2).

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

		A1-20.0
		GE 5.0
		GE 12.0
		G 13.0
		GE 16.0
	GE 17.0

A1-14.0

Review:

·        Solving quadratic equations by factoring or using the quadratic formula for Lesson 4-6.

Chapter 4: Triangle Congruence

·        Classify and solve problems of triangles using their side lengths and interior and exterior angle measures.

·        Apply theorems about the interior and exterior angles of triangles.

·        Prove triangles are congruent using definition of congruence, SSS, SAS, ASA, AAS, and HL.

·        Apply the definition of congruence, SSS, SAS, ASA, AAS, and HL to solve problems.

·        Use corresponding parts of congruent triangles 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; also, apply properties of isosceles and equilateral triangles to solve problems.

Lessons 4-1 – 4-8

·        Holt Text:  p. 266 or Alg. 1 textbook on solving quad. equations (before Lesson 4-7). 

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

		A1-2.0
		A1-5.0
		GE 1.0
			GE 2.0
			GE 6.0
		GE 12.0
		GE 14.0
	GE 15.0
		GE 16.0

 

GE 17.0

GE 20.0

Review:

·        Write expressions in simplest radical form for Lesson 5-6.

·        Solve multistep problems involving linear inequalities in one variable for Lesson 5-5.

Chapter 5: Properties and Attributes of Triangles

·        Write geometric proofs by applying theorems about perpendicular and angle bisectors.

·        Write geometric proofs by applying theorems involving perpendicular bisectors and angle bisectors of triangles.

·        Apply properties of medians and altitudes of a triangle.

·        Perform basic constructions with a compass and straightedge of the sides of a triangle to find the centroid.

·        Prove and use properties of triangle midsegments using coordinate geometry.

·        Write geometric proofs by using proof of contradiction.

·        Apply inequalities in one and/or two triangles.

·        Prove the Pythagorean Theorem.

·        Use the Pythagorean Theorem and its converse to solve problems.

·        Use Pythagorean inequalities to classify a triangle as right, obtuse, or acute.

·        Justify and apply properties of 30°-60°-90° and 45°-45°-90° triangles.

Lessons 5-1 – 5-8

·        Holt Text:  p. 340 or Alg. 1 textbook on solving compound inequalities (before Lesson 5-5).

·        Holt Text: p. 346 or Alg. 1 textbook on simplifying radical expressions (before Lesson 5-7).

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

GE 1.0

	GE 2.0
	GE 7.0
	GE 12.0

GE 17.0

GE 15.0

GE 16.0

Chapter 6: Polygons and Quadrilaterals

·        Classify polygons using their sides and angles.

·        Find and use the measures of interior and exterior angles of polygons.

·        Prove and apply properties of parallelograms, rectangles, rhombuses, and squares.

·        Use properties of parallelograms, rectangles, rhombuses, and squares to solve problems.

·        Prove that a given quadrilateral is a parallelogram, rectangle, rhombus, or a square.

·        Use properties of kites and trapezoids to solve problems.

Lessons 6-1 – 6-6

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

	GE 1.0

 

GE 5.0

GE 17.0

GE 16.0

GE 12.0

GE 11.0

GE 8.0

GE 7.0

Chapter 7: Similarity

·        Write and simplify ratios; use proportions to solve problems.

·        Identify similar polygons.

·        Apply properties of similar polygons to solve problems.

·        Prove triangles are similar by using AA, SSS, or SAS Similarity.

·        Use triangle similarity to solve problems.

·        Use properties of similar triangles to find segment lengths.

·        Apply proportionality and triangle angle bisector theorems to solve problems.

·        Use ratios to make indirect measurements.

·        Use scale drawings to solve problems involving triangles and polygons.

·        Apply similarity properties in the coordinate plane.

·        Use coordinate proof to prove figures similar.

Lessons 7-1 – 7-6

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

	GE 4.0

 

GE 19.0

Chapter 8: Right Triangles and Trigonometry

·        Use geometric mean to find segment lengths in similar 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 the side lengths in right triangles and to solve real-world problems.

·        Solve problems involving angles of elevation and depression.

·        Use the law of sines and cosines to solve triangles.

·        Find the magnitude and direction of a vector.

·        Use vectors and vector addition to solve real-world problems.

Lessons 8-1 – 8-6

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

	A1-5.0
	GE 1.0
	GE 8.0
	GE 10.0
	GE 11.0
	GE 12.0
		GE 15.0

 

Review:

·        Solve multistep problems, including word problems, involving linear equations.

Chapter 9: Extending Perimeter, Circumference, and Area

·        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.

Lessons 9-1 – 9-6

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

		GE 1.0
		GE 8.0
	GE 9.0
		GE 11.0

 

Chapter 10: Spatial Reasoning

·        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, cylinder, pyramid, cone, and sphere.

·        Learn and apply the formula for the volume of a prism, cylinder, pyramid, cone, and sphere.

Lessons 10-1 – 10-8

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

		GE 1.0
	GE 7.0
		GE 8.0

 

GE 21.0

GE 16.0

Chapter 11: Circles

·        Identify tangents, secants, and chords of circles.

·        Use properties of tangents to solve problems.

·        Use properties of arcs and chords to solve problems.

·        Find the arc length and the area of a sector of a circle.

·        Find the measure of an inscribed angle; use inscribed angles and their properties to solve problems.

·        Find the measures of angles and side lengths formed by lines that intersect circles.

·        Use angle measures and side lengths to solve problems.

·        Write equations and graph circles in the coordinate plane.

·        Use the equation and graph of a circle to solve problems.

Lessons 11-1 – 11-7

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners. 

Standard

Concepts

Lesson(s)

Ancillary Materials

		GE 1.0

A1-21.0

Review:

·        Write a function rule for a given transformation.

Chapter 12: Extending Transformational Geometry

·        Identify and draw reflections, translations, and rotations.

·        Apply theorems about isometries.

·        Identify and draw compositions of 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.

Lessons 12-1 – 12-7

·        Use the On Course Mapping Instruction:  A Teacher’s Guide for Planning to assist benchmark, advance, strategic, special needs students, and English learners.