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Year at a Glance First Semester Geometry Pre-AP Three Weeks Topics/ Concepts 1st 3 weeks Foundations Vocabulary 2nd 3 weeks Geometric Reasoning Vocabulary 3rd 3 weeks Lines and Planes Vocabulary 4th 3 weeks Triangles Vocabulary 5th 3 weeks More Triangles Vocabulary 6th 3 weeks Similar Triangles Vocabulary Mathematical Systems Logical Reasoning Parallel Lines and Angles Triangle Classification Construction Ratio and Proportion Structure Conjecture and Justification Congruence Segments in a Triangle Similar Triangles Measurement Perpendicular Lines and Angles Applications Applications Applications Resource: HOLT Geometry Chapter 1 TEKS: G1A, G2A, G3B, G7A, G8A, G5C, G1B, G2B, G7C, G8C Lines in the Coordinate Plane Chapter 2 TEKS: G3D, G3A, G3E, G4A, G1A Chapter 3 TEKS: G9A, G3C, G1A, G8A, G7B, G2A, G7A, G7C Topics/ Concepts Chapter 4 TEKS: G1A, G9B, G2B, G10B, G2A Vocabulary Vocabulary Vocabulary 4th 3 weeks Space Measurement Vocabulary Pythagorean Theorem and the Converse Polygons Perimeter and Circumference 2-D/3-D Representation Area Surface Area 1st 3 weeks Right Triangles Ratios in Right Triangles Special Right Triangles Trigonometry Applications Resource: HOLT Geometry Applications Chapter 5 TEKS: G3B, G2A, G7B, G9B, G8C, G5D Chapter 7 TEKS: G11B, G5B, G11A, G11D Second Semester Geometry Pre-AP Three Weeks Applications Triangle Inequalities Chapter 8 TEKS: G11C, G2A, G7A, G11A 2nd 3 weeks Polygons Special Types of Quadrilaterals rd 3 3 weeks Planar Measurement 5th 3 weeks Transformation 6th 3 weeks Circles Vocabulary Vocabulary Isometrics Angles and Segments Related to Circles Dilations Applications Applications Similarity of Polygons Applications Applications Chapter 6 TEKS: G2A, G5B, G9B, G3B Volume Applications Chapter 9 TEKS: G5A, G8A, G7A, G11D Chapter 10 TEKS: G6A, G9D, G6B, G7C, G8D, G11D, G1C Chapter 12 TEKS: G10A, G5C, G11A Chapter 11 TEKS: G9C, G1A, G8B, G5B, G2A, G9C, G5A, G2B First Semester First Semester, 1st and 3rd 3 Weeks Structure of a Mathematical System (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -identify and model points, lines, and planes. -identify collinear and coplanar points and intersecting lines and planes in space. -find segment and angle measures using segment and angle postulates. -describe relationships between segments and angles (congruent, midpoint, segment bisector, angle bisector, perpendicular) and use the relationships to solve problems. -identify special pairs of angles (vertical, linear pair, complementary, supplementary) and use their relationships to solve problems. -develop midpoint and distance formulas using the coordinate plane. G1A G2A G3B G7A G8A G5C G1B G2B G7C G8C G9A G3C G7B Suggested Resources Mathematical Systems Investigate the process and purpose of developing a geometric system Holt Geometry Structure Analyze the structure of a mathematical system, connecting definitions, algebraic properties, postulates, theorems, and corollaries LTF Geometry Resources Lines and Planes Investigate properties of parallel and perpendicular lines using exploration and concrete models Use coordinate systems by: deriving and using formulas to evaluate slope, distance, and midpoint; evaluating slope, distance, and midpoint; investigating properties of lines using their slopes and equations Measurement Measure segments and angles concretely, numerically, and analytically Chapters 1 and 3 Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic units 1&2 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 First Semester, 2nd 3 Weeks Logical Reasoning and Conjecture (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -make conjectures based on inductive reasoning. -analyze statements in if-then form (conditional statements). -write the converse, inverse, and contra positive of a conditional statement and determine the truth value of the statements. -use properties of algebra and congruence to make and justify conclusions. -use deductive reasoning with different styles of proofs to verify segment and angle relationships. G3D G3A G3E G4A G1A Logical Reasoning Apply reasoning and logic by: testing validity of a conditional statement, its converse, inverse, and contra positive, using inductive reasoning to formulate a conjecture, using deductive reasoning to prove a statement., using logical reasoning to prove statements are true and finding counter examples to disprove statements that are false, and constructing and justifying statements about geometric figures and their properties Conjecture and Justifications Formulate conjectures based on investigations and explorations Determine the validity of conjectures by using a variety of approaches (coordinate, axiomatic) to provide justification Suggested Resources Chapter 2 Suggested Assessments Teacher Assessments LTF Geometry Resources Geometry Assessments Holt Geometry LTF Diagnostic unit 1 TAKS Objectives TAKS Obj. 2 TAKS Obj. 3 TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 First Semester, 4th 3 Weeks Triangles (Approximate Time: 3 weeks) ELOs TEKS The student will: -identify and classify triangles by side and angle measures. -determine the relationships among the measures of the interior and exterior angles of a triangle and apply these relationships. -identify and use properties of isosceles and equilateral triangles. -identify congruent triangles and their corresponding parts. -identify methods (SSS, SAS, ASA, AAS, HL) of proving triangles congruent. -find missing sides of triangles and other figures based on congruence relationships. -use deductive reasoning to prove corresponding parts of congruent triangles congruent. -use triangle congruence to solve problems in real-life situations. G1A G9B G2B G10B G2A Topics (not in sequential order) Suggested Resources Triangle Classification Classify triangles by angle and side measures Validate classification of triangles by using a variety of approaches (coordinate, axiomatic) to provide justification Holt Geometry Congruence Investigate properties of congruent triangles Construct statements related to triangle congruence relationships Determine necessary and sufficient conditions in order for triangles to be congruent Use logical reasoning to justify triangle congruence from a variety of perspectives Formulate and test conjectures about the properties of equilateral, equiangular, isosceles, and right triangles based on explorations and concrete models Apply properties of congruent triangles to solve meaningful problems by modeling, representing, and analyzing relationships Chapter 4 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 3&4 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 10 First Semester, 5th 3 Weeks Triangles (Approximate Time: 3 weeks) ELOs TEKS The student will: -identify and use properties of perpendicular bisectors and angle bisectors. -identify special segments (angle bisectors, perpendicular bisectors, medians, altitudes, midsegments) of a triangle, determine their relationships and apply those relationships to solve problems. -recognize and apply properties of inequalities to the relationships between the sides and angles of a triangle. -recognize and apply properties of inequalities between the sides and angles of two triangles G3B G2A G7B G9B G8C G5D Topics (not in sequential order) Suggested Resources Construction Use a variety of techniques and tools (concrete, graphical, technological) to recreate geometric figures based on a given set of information Validate construction of geometric figures by using a logical reasoning and a variety of approaches (coordinate, axiomatic) to provide justification Holt Geometry Special Segments in a Triangle Identify bisectors, medians, altitudes and midsegments of triangles Use a variety of techniques and tools to construct special segments in triangles Identify points of concurrency for bisectors, medians, and altitudes (circumcenter, incenter, centroid, orthocenter) Make conjectures about the properties and relationships of special segments and points of concurrency in triangles Use logical reasoning to justify these properties from a variety of perspectives Apply the properties of special segments and points of concurrency to solve meaningful problems by modeling, representing, and analyzing relationships Triangle Inequalities Investigate situations involving inequalities within and among triangles Compare and order sides and angles within one triangle or among several triangles Apply triangle inequality properties to solve meaningful problems by modeling, representing, and analyzing relationships Chapter 5 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 5 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 10 First Semester, 6th 3 Weeks Polygons (Approximate Time: 3 weeks) ELOs TEKS The student will: -compute ratios and use proportions to solve problems. -solve percent and probability problems. -identify the conditions that ensure two polygons are similar. -use properties of similar polygons to solve problems. -recognize the conditions that ensure two triangles are similar. -use similar triangles to solve reallife problems. -identify proportional parts of a triangle and use them to solve problems. -recognize and use proportional relationships of perimeters and other corresponding segments of similar triangles. G11B G5B G11A G11D Topics (not in sequential order) Suggested Resources Ratio and Proportion Identify proportional and non-proportional relationships in problem situations Use ratios as scale factors for similar figures Holt Geometry Similar Triangles Investigate properties of similar triangles Construct statements related to triangle similarity relationships Determine necessary and sufficient conditions in order for triangles to be similar Use logical reasoning to justify triangle similarity from a variety of perspectives Apply properties of similar triangles to solve meaningful problems by modeling, representing, and analyzing relationships Chapter 7 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 4 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10 Second Semester Second Semester, 1st 3 Weeks Similar Triangles (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -identify the geometric mean of two numbers. -solve problems involving relationships between parts of a right triangle and the altitude to the hypotenuse. -use the Pythagorean Theorem and its converse to solve problems. -use the Pythagorean theorem to classify a triangle as acute, right, or obtuse. -identify a pattern in the side lengths of special right triangles (45-4590, 30-60-90) and use special right triangles to solve problems. -find trigonometric ratios (sine, cosine, tangent) using right triangles and solve problems using these trigonometric ratios. -solve problems involving angles of elevation and depression. G11C G2A G7A G11A Pythagorean Theorem Review the simplification of and operations with radical numbers Derive, extend and use the Pythagorean Theorem in problem situations Apply the Pythagorean Theorem to investigate Pythagorean Triples Apply the Converse of the Pythagorean Theorem to determine, with justification, if a triangle is a right triangle Ratios in Right Triangles Apply the definition of geometric mean in situations involving an altitude drawn to the hypotenuse of a right triangle Special Right Triangles (30-60-90 and 45-45-90) Investigate segment relationships in special right triangles Derive statements defining segment relationships in special right triangles Apply properties of special right triangles to solve meaningful problems by modeling, representing, and analyzing relationships Trigonometry Use segment ratios to apply the definitions of sine, cosine, and tangent Determine segment lengths and angle measures using the trigonometric ratios sine, cosine, and tangent Identify angles of elevation or depression using trigonometric ratios Apply trigonometric ratios to solve meaningful problems involving right triangle relationships Suggested Resources Holt Geometry Chapter 8 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 5&6 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10 Second Semester, 2nd 3 Weeks Right Triangles (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -identify, name, and classify polygons. -find measures of interior and exterior angles of polygons. -recognize and apply properties of the sides and angles of parallelograms. -use properties of parallelograms to solve problems. -recognize the conditions that ensure a quadrilateral is a parallelogram. -identify special parallelograms(rectangle, rhombus, square), identify their properties, and apply the properties to solve problems. -recognize and apply properties of trapezoids and special trapezoids. -recognize the conditions that ensure polygons are congruent. G2A G5B G9B G3B Polygons Use appropriate terminology to identify polygons based on the number of their sides or angles. Use a variety of methods to investigate the interior and exterior angle relationships of polygons Make and justify conjectures about component parts of polygons Investigate necessary conditions for polygons to be identified as “regular” Make and justify conjectures about component parts of regular polygons Use properties of polygons to make connections between mathematics and the real world Special Types of Quadrilaterals Use a variety of methods to investigate relationships and make and justify conjectures about angles and segments in a trapezoid Use a variety of methods to investigate relationships and make and justify conjectures about angles and segments in a kite Use a variety of methods to investigate relationships and make and justify conjectures about the component parts of a parallelogram Use the properties of parallelograms and the definitions for rhombus, rectangle, and square to investigate their related properties Make and justify conjectures about properties of rhombi, rectangles, and squares Similarity of Polygons Extend properties of similar triangles to investigate properties of similar polygons Apply these similarity properties to make connections between mathematics and the real world Suggested Resources Holt Geometry Chapter 6 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10 Second Semester, 3rd 3 Weeks Perimeter and Area (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -find perimeters and areas of triangles and quadrilaterals (including rectangles, squares, parallelograms, trapezoids, rhombi, and other quadrilaterals). -identify regular polygons and find their perimeters and areas. -find circumference and area of a circle and use them to find the length of an arc or the area of a sector. -find perimeters and areas of composite figures. -identify properties of areas of similar polygons and use the relationships to solve problems. G5A G8A G7A G11D Perimeter and Circumference Use patterns and algebraic reasoning to derive formulas for finding the perimeter of polygons and the circumference of circles Apply formulas for perimeter and circumference to make connections between mathematics and the real world Use the formula for circumference of a circle and proportional reasoning to determine arc lengths of circles Use a variety of methods to investigate the relationship between perimeters of similar geometric figures Make and justify a conjecture describing the proportionality of perimeters of similar figures Area Use patterns and algebraic reasoning to derive formulas for finding the area of polygons and circles Apply formulas for area to make connections between mathematics and the real world Use the formulas for area of circles and triangles with proportional reasoning to determine area of sectors and segments of circles Use a variety of methods to investigate the relationship between areas of similar geometric figures Make and justify a conjecture describing the proportionality of areas of similar figures Suggested Resources Holt Geometry Chapter 9 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 8 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10 Second Semester, 4th 3 Weeks Surface Area and Volume (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -relate nets to different solids. -identify three dimensional figures, recognize different views of threedimensional figures, and investigate cross sections of three-dimensional figures. -find surface areas of prisms, pyramids, cylinders, cones, and spheres. -use surface areas to solve problems. -find volumes of prisms, pyramids, cylinders, cones, and spheres. -use volumes to solve problems. -identify properties of surface areas and volumes of similar figures and use the relationships to solve problems. G6A G9D G6B G7C G8D G11D G1C 2-D/3-D Representation Use concrete and pictorial representations to identify three-dimensional objects such as prisms, cylinders, pyramids, cones, cylinders, and composites of these figures Use concrete objects, isometric and orthographic paper, drawing tools, and/or technology to represent three dimensional geometric figures Analyze, describe, and draw the intersection of a plane with three-dimensional geometric figures Draw nets of three-dimensional objects and draw three dimensional views of objects using their nets Surface Area Make and justify conjectures about surface area using concrete objects, measuring tools, patterns, and algebraic reasoning Derive formulas for the surface area of various solid geometric figures using area formulas for twodimensional figures Apply formulas for surface area to make connections between mathematics and the real world Volume Make and justify conjectures about volume using concrete objects, measuring tools, patterns, and algebraic reasoning Use formulas to find volume of various solid geometric figures and composites of those figures Apply formulas for volume to make connections between mathematics and the real world Use a variety of methods to investigate the relationship between volumes of similar threedimensional geometric figures Make and justify a conjecture describing the proportionality of volumes of similar threedimensional geometric figures Suggested Resources Holt Geometry Chapter 10 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 9 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10 Second Semester, 5tht 3 Weeks Transformations (Approximate Time: 3 weeks) ELOs TEKS Topics (not in sequential order) The student will: -identify translation, reflection, rotation, and dilation transformations. -use properties of reflections to find reflection images and relate reflections and line symmetry. -use properties of rotations to find rotation images and identify figures with rotational symmetry. -use properties of translations to find translation images. -use algebra notation to define translations, reflections, and rotations. -identify tessellations. -use compositions of transformations and identify their properties. -identify, use properties of, and determine the scale factor of dilations. G10A G5C G11A Isometrics Investigate the congruence transformations of reflection, rotation, and translation of geometric figures concretely and with technology Use coordinates to investigate reflection, rotation, and translation of geometric figures, using technology when appropriate Use patterns to derive symbolic representations of geometric transformations Make conjectures about congruence transformations of geometric figures and determine their validity Investigate composition of congruence transformations, including tessellations, concretely and symbolically Apply the properties of congruence transformations to make connections between mathematics and the real world Dilations Use a center of dilation and scale factors to investigate dilation of geometric figures using appropriate concrete, coordinate and technological methods Extend properties of similar figures, scale factors and ratios to investigate properties of dilated geometric figures analytically Make conjectures about dilated geometric figures and determine their validity Apply similarity properties to dilated geometric figures to make connections between mathematics and the real world Suggested Resources Holt Geometry Chapter 12 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 6 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10 Second Semester, 6th 3 Weeks Circles (Approximate Time: 3 weeks) ELOs TEKS The student will: -identify and use parts of circles. -recognize major arcs, minor arcs, semicircles, and central angles, find their measures and use their measures to solve problems. -recognize and use relationships between arcs and chords to solve problems. -recognize inscribed angles and use their properties to solve problems including inscribed polygons. -identify and use properties of tangents to solve problems including circumscribed polygons. -find measures of angles formed by segments or lines intersecting on a circle, inside a circle, or outside a circle (chords, secants, tangents). -determine the equation of a circle. G9C G1A G8B G5B G2A G9C G5A G2B Topics (not in sequential order) Suggested Resources Angles and Segments Related to Circles Describe and identify, using appropriate geometric terms, the lines and segments that intersect circles Describe and identify, using appropriate geometric terms, the angles formed by the intersection of lines or segments when the intersection occurs in the interior, exterior or on a circle Use exploration, concrete objects, drawing and measuring tools, technology, patterns, and algebraic reasoning to determine relationships between angles and segments with circles Make and justify conjectures to describe angle and segment relationships in circle situations Use symbolic notation to derive formulas describing angle and segment relationships in circle situations Apply formulas to make connections between mathematics and the real world Holt Geometry Chapter 11 LTF Geometry Resources Suggested Assessments Teacher Assessments Geometry Assessments LTF Diagnostic unit 7 TAKS Objectives TAKS Obj. 6 TAKS Obj. 7 TAKS Obj. 8 TAKS Obj. 9 TAKS Obj. 10