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PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 14 Days 14 Days 22 Days 10 Days Unit Topic Unit 1 Unit 2 Unit 3 Unit 4 (Specify Reasoning and Proof Spatial Visual Triangles 2-Dimensional skills/information that will be learned.) Enduring In proofs, deductive Geometric figures and The Pythagorean Polygons are categorized Understandings reasoning about given relationships can be Theorem is essential to by the number of sides. (Give and/or information is used to represented in the solving problems Studying patterns can demonstrate reach mathematical coordinate plane. involving right triangles. lead to geometric necessary conclusions. Geometric figures can Congruent figures are formulas and information) Theorems and properties be measured in the also similar figures, but relationships. exist that guarantee two coordinate plane. similar figures are not Rectangles, squares, and triangles are congruent or The slope of a line is the always congruent. rhombi are similar given certain ratio of vertical change Congruency and parallelograms and conditions. (rise) to horizontal similarity have real life belong to the set of Relationships between change (run). applications in art, quadrilaterals. lines, angles and figures Slopes, distances and architecture, and Relationships exist can be used to establish midpoints can be science. between sides, angles additional mathematical determined when a Parallel and and segments in relationships. segment is graphed in perpendicular lines are polygons. Congruent figures are also the coordinate plane. used to prove triangles By using the area similar figures, but similar A line’s direction and congruent or similar. formula of a rectangle, figures are not always steepness are 30º-60º-90º and 45º- we can derive area congruent. determined by its slope. 45º-90º triangles are formulas for other Linear equations can be similar triangles. figures. used to make predictions. PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 14 Days 14 Days 22Days 10 Days Enduring Parallel and perpendicular A line’s slope and x- and Special triangles have Perimeter and Understandings lines are used to prove y-intercepts have real real world applications. circumference are 1- con’t triangles congruent or world applications. Relationships in special dimensional measures, similar. right triangles can be while area is a 2- determined by the dimenionsal measure. Pythagorean Theorem. Measurement of geometric figures is an essential part everyday life. Essential Why write formal proofs? Why is it important to Why is the intersection How can you use Questions Why are properties and learn about geometric point of special segments patterns to find the sum (Steps to check for theorems about parallel figures and relationships in triangles important? of the interior angles of student and perpendicular lines in the coordinate plane? What theorems any polygon? understanding) useful in geometric proofs? How do you determine guarantee two triangles How can you determine How can reasoning about information about a line congruent? the measure of interior geometric situations be or segment graphed in How do congruent and exterior angles in used to solve real life the coordinate plane? figures differ from regular polygons? problems? How does the Distance similar figures? How do you classify If two figures are Formula relate to the Where are parallel and quadrilaterals using congruent or similar, what Pythagorean Theorem? perpendicular lines special segments and else do you know about How do you represent evident in everyday life? properties? their corresponding parts? geometric figures in the How are the angles How do special What theorems or coordinate plane? formed by parallel lines segments in polygons postulates (properties) How do you measure used to prove triangles help solve everyday guarantee two triangles geometric figures using congruent? situations? congruent? the coordinate plane? PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 14 Days 14 Days 22 Days 10 Days Essential How do congruent figures How does slope describe How are properties of How can you derive the Questions con’t differ from similar figures? a line? How can you use perpendicular lines used various area formulas an equation to make a to prove congruent and from the area of a prediction? similar triangles? rectangle? What does the slope of How is the Pythagorean How can you find the the line tell you? Theorem related to the areas of irregular How do you write an lengths of sides of figures? equation for a line? special right triangles? How does finding the How do you write an How does the concept of area of the various equation for a line if you similarity apply to figures apply to everyday are given two points? special right situations?How are How do you determine triangles?How are right perimeter, the x- and y-intercepts triangle relationships circumference, and area graphically and used in the real world? different from one algebraically? How do you find the another? lengths of sides of special right triangles? Standards G-1.1 Demonstrate an G-2.4 Use direct G-3.1 Carry out a G-2.3 Use the understanding of the measurement to procedure to compute congruence of line axiomatic structure of determine the length of a the perimeter of a segments and angles to geometry segment, measure triangle. solve problems. using undefined terms, of an angle, and distance G-3.2 Carry out a G-4.6 Apply congruence definitions, postulates, from a point to a line. procedure to compute and similarity between theorems, and corollaries. G-6.1 Use the distance the area of a triangle. shapes (including formula to solve G-3.3 Analyze how quadrilaterals and problems. changes in dimensions polygons) to solve affect the perimeter or problems. area of triangles. PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 14 Days 14 Days 22 Days 10 Days Standards con’t G-1.2 Communicate G-6.2 Use the midpoint G-3.4 Apply properties of G-2.5 Carry out a knowledge of geometric formula to solve isosceles and equilateral procedure to create relationships using problems. triangles to solve geometric constructions mathematical G-2.2 Apply properties of problems. (including terminology appropriately. parallel lines, G-3.5 Use interior midpoint of a line G-1.7 Understand the intersecting lines, and angles, exterior angles, segment, angle bisector, historical development of parallel lines cut medians, angle bisectors, perpendicular bisector of geometry. by a transversal to solve altitudes, a line segment, line G-1.4 Formulate and test problems. and perpendicular through a given point conjectures using a variety G-2.5 Carry out a bisectors to solve that is parallel to a given of tools such as concrete procedure to create problems. line, models, graphing. geometric constructions G-3.6 Apply the Triangle and line through a given calculators, spreadsheets, (including Sum Theorem to solve point that is and dynamic geometry midpoint of a line problems. perpendicular to a given Software segment, angle bisector, G-3.7 Apply the Triangle line). G-1.9 Demonstrate an perpendicular bisector of Inequality Theorem to G-4.6 Apply congruence understanding of how a line segment, line solve problems. and similarity between geometry applies to real through a given point G-3.8 Apply congruence shapes (including world contexts (including that is parallel to a given and similarity between quadrilaterals and architecture, construction, line, triangles to solve polygons) to solve farming, astronomy). and line through a given problems. problems. point that is G-3.9 Apply theorems to G-2.6 Use scale factors perpendicular to a given prove triangles are to solve problems line). similar or congruent. involving scale drawings G-3.10 Use the and Pythagorean Theorem models. and its converse to solve problems. PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 14 Days 14 Days 22 Days 10 Days Standards G-1.10 Understand G-3.11 Use the G-2.7 Use geometric con’t geometric relationships properties of 45-45-90 probability to solve including constructions and 30-60-90 triangles problems. through investigations to solve problems. G-4.1 Carry out a using a variety of tools G-3.12 Use trigonometric procedure to compute such as straightedge, ratios (including sine, the perimeter of compass, cosine, tangent) to solve quadrilaterals, paper folding, dynamic problems involving right regular polygons, and geometry software, and triangles. composite figures. hand-held computing G-4.2 Carry out a devices. procedure to find the G-1.3 Apply basic rules of area of quadrilaterals, logic to determine the regular polygons, and validity of the converse, composite figures. inverse, and contrapositive G-4.3 Apply procedures of a conditional statement to compute measures of G-1.5 Use inductive interior and exterior reasoning to formulate angles of polygons. area conjectures. of quadrilaterals and G-1.6 Use deductive regular polygons. reasoning to validate G-4.4 Analyze how conjectures with formal changes in dimensions and informal proofs, and affect the perimeter or give counterexamples to area of quadrilaterals disprove a statement. and regular polygons PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 14 Days 14 Days 22 Days 10 Days Standards G-4.5 Apply con’t properties and attributes of quadrilaterals and regular polygons and their component parts to solve problems. G-2.1 Infer missing elements of visual or numerical geometric patterns (including triangular numbers, rectangular numbers, and number of diagonals in polygons). G-2.7 Use geometric probability to solve problems. Integrations (with other discipline areas) District Benchmark Exam Assessments (culminating assessments) PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 12 Days 5 Days 13 Days Unit Topic Unit 5 Unit 6 Unit 7 (Specify 3-Dimensional Transformations Circles skills/information that will be learned.) Enduring Three-dimensional Transformations move or Indirect measurement is Understandings figures have properties map figures (preimages) based on the properties (Give and/or similar to those of two- onto their images. of geometric figures. demonstrate dimensional figures. Reflections, rotations, Relationships exist necessary and translations are among angles, segments, information) transformations that lengths, circumference, preserve shape and size and area of circles. (congruency). Dilation is a transformation that preserves shape only (similarity). Essential How are two-dimensional Why do certain How are the areas of Questions relationships connected transformations preserve polygons and circles (Steps to check to the properties of three- shape and size while related and applied? for student dimensional figures? others only preserve How are angles and understanding) shape? intercepted arcs of circles How does combining related and applied? transformations affect the final result? How are the coordinates affected by transformations in the PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 12 Days 5 Days 13 Days Essential coordinate plane? Questions How are scale factors con’t used in transformations? Standards G-7.1 Carry out a G-6.3 Apply G-5.1 Carry out a procedure to compute transformations procedure to compute the surface area of three- (translation, reflection, the circumference of dimensional rotation, and dilation) to circles. objects (including cones, figures in the coordinate G-5.2 Carry out a cylinders, pyramids, plane using sketches and procedure to compute prisms, spheres, and coordinates. the area of circles. hemispheres). G-6.4 Apply G-5.3 Analyze how a G-7.2 Carry out a transformations change in radius affects procedure to compute (including translation the circumference or area the volume of three- and dilation) to figures in of a circle. dimensional the coordinate plane G-5.4 Carry out a objects (including cones, using matrices. procedure to compute arc cylinders, pyramids, G-6.5 Carry out a length or area of a sector prisms, spheres, procedure to represent of a circle. hemispheres, and the sum of two vectors G-5.5 Apply properties of composite objects). geometrically by using component parts of a G-7.3 Analyze how the parallelogram circle (including radii, changes in dimensions method. diameters, chords, affect the volume of G-6.6 Carry out a sectors, arcs, and objects (including procedure to determine segments) to solve cylinders, prisms, and the magnitude and problems. spheres). direction of the resultant by direct measurement using a PACING GUIDES FOR MATH Grade Level: Tenth Big Idea: Geometry Prepared by Union County Schools Time Frame: 12 Days 5 Days 13 Days Standards G-7.4 Apply scale drawing. G-5.6 Apply congruence and G-6.7 Carry out a properties of lines similarity between procedure to that intersect objects to solve compute the circles(including two problems. magnitude of the secants, two G-7.5 Apply a resultant of two tangents, or a secant procedure to draw a perpendicular and a tangent) to top-view, front-view, vectors using the solve problems. and side-view of a Pythagorean G-5.7 Apply three-dimensional Theorem. properties of central object. G-6.8 Carry out a angles, inscribed G-7.6 Apply a procedure to angles, and arcs of procedure to draw determine the circles to solve an isometric view of direction of the problems. a three-dimensional resultant of two G-2.7 Use geometric object perpendicular probability to solve vectors using direct problems. measurement. Integrations (with other discipline areas) District Final Exam Assessments (culminating assessments)