Chapter/ Lesson 1/1 Indiana Standard(s) Centerville Jr. High School Curriculum Mapping Geometry 1 st Nine Weeks Matthew A. Lung Key Questions Resources/Activities Vocabulary Assessments What is inductive reasoning? What is a conjecture? What is a counterexample? 1/2 What is a point? What is a line? What are collinear points? What is a plane? What are coplanar objects? What is a postulate? What is an axiom? 1/3 G.1.2a What is a segment? What is a ray? What are parallel lines? What are skew lines? 1/4 G.1.1b, G.1.1d, G.1.2a What are parallel planes? What are congruent segments? What is the midpoint of a segment? Calculate the midpoint of a segment. Define an angle. Classify an angle as acute, obtuse, right, or straight. What are congruent angles? 1/6 G.1.1a, G.1.1c What is the distance formula? What is the midpoint formula? Calculate the distance between coordinates. Calculate the midpoint between two coordinates 1/7 G.2.5a, G.2.5c, G.3.3c, G.4.7a, G.4.7c, SMP2, SMP4 What is perimeter? What is circumference? What is area? Calculate the perimeter/circumference/area of a figure. vocabulary/formula organizers, Inductive reasoning, conjecture, counterexample Point, line, collinear points, plane, coplanar, postulate, axiom Segment, ray, parallel lines, skew lines, parallel planes Congruent segments; midpoint; angle: acute, obtuse, right, straight; congruent angles Distance formula, midpoint formula Perimeter, circumference, area 1
1/5 G.1.2b, G.1.2c, G.1.2e G.1.2f, G.1.2g G.8.9a, G.8.9b G.8.9c, SMP5 What are perpendicular lines? What is a perpendicular bisector? What is an angle bisector? Construct congruent segments/angles. Construct perp. Lines. Construct a perp. bisector. Construct an angle bisector Compass, straight edge, textbook, notes Perpendicular lines, perpendicular bisector, angle bisector 2/1 2/2 What is a conditional statement? What is the converse of a conditional statement? What is a biconditional? What is a good definition? Conditional, hypothesis, conclusion, truth value, converse Biconditional, 2/4 2/5 3/1 G.1.3a, G.1.3b, G.1.3c, G.1.3d, SMP1, SMP3, SMP6, SMP7, Justify the steps in a proof or solution to an equation. Classify the angles as vertical, adjacent, complementary, or supplementary. Prove and apply theorems of angles. Classify two angles given two lines and a transversal. Prove/use properties of parallel lines and transversals. Find the value of the labeled angles. Properties of Congruence, Properties of Equality Vertical angles, Adjacent angles, Complementary angles, supplementary angles Transversal, Alternate interior angles, same-side interior angles, corresponding angles. 3/2 G.1.3c, G.1.3d, SMP7, SMP8 Use a transversal to prove that two lines are parallel. Describe the relationship between parallel and perpendicular lines. Find the value of the variable in the diagram. Parallel lines, Perpendicular Lines 2
3/3 G.4.1a, G.4.1b, SMP3 3/4 G.2.1a, G.2.1b, G.2.2a, G.2.2b, G.2.2c Find the measure of the angles in the triangle. Classify the triangle. Find the exterior angles of the triangle. Classify the polygon as concave or convex. Classify the polygon by the number of sides. Find the sum of the interior and exterior angles of the polygon. Investigation: The sum of three angle measures Triangles: Equiangular, Acute, Right, Obtuse, Equilateral, Isosceles, Scalene; Exterior Angle of a polygon, remote interior angle Polygon, Convex polygon, concave polygon, Regular polygon Handout: Sum of polygon angle measures 3/5 G.1.4a, G.1.4b Graph the line given its equation. Write an equation for the line given its graph. Linear Equations: Slope-Intercept Form, Standard Form, Point- Slope Form. 3
Chapter/ Lesson Indiana Standard(s) 3/6 G.1.4b, G.1.4c, Are the slopes of two parallel lines different or equal? What is the relationship between the slopes of perpendicular lines? Are the lines parallel? Are the lines perpendicular? 3/7 G.1.2d, G.1.2e, Construct a line parallel to the given line. Construct a lines perpendicular to the given line. Curriculum Mapping Geometry 2 nd Nine Weeks Key Questions Resources/Activities Vocabulary Assessments Compass, straight edge, textbook, notes Slopes of parallel lines, slopes of perpendicular lines Parallel lines, perpendicular lines 4/1 Are the figures congruent? List the corresponding parts of the congruent figures. Congruent polygons, Corresponding parts, 4/2 G.4.6c, G.8.8a, SMP1, SMP3, SMP6, SMP8 4/3 G.4.6c, G.8.8a, SMP1, SMP3, SMP6, SMP8 4/4 G.4.6b, G.4.6c, G.8.8a, SMP1, SMP3, SMP6, SMP8 Prove that the triangles are congruent by either SSS or SAS postulates. Prove that the triangles are congruent by ASA Postulate or AAS Theorem. Show that parts of triangles are congruent by CPCTC. Side-Side-Side Postulate, Side-Angle-Side Postulate, congruency statement Angle-Side-Angle Postulate, Angle-Angle-Side Theorem, congruency statement Corresponding Parts of Congruent Triangles are Congruent(CPCTC) 4
4/5 G.4.1a, G.4.1b, G.4.7c 4/6 G.4.6c, G.8.8a SMP1, SMP2, SMP3, SMP6, SMP8 Find the base angles in an isosceles triangle. If the base angles in a triangle are congruent, what is true about their opposite sides? What is an equilateral triangle? Prove the triangles congruent by the Hypotenuse-Leg Theorem. Legs of a Triangle, Base of a Triangle, Base Angles, Vertex Angle Hypotenuse-Leg Theorem 4/7 G.4.6b, SMP1, SMP3, SMP4, SMP6, SMP8 Identify the corresponding overlapping triangles. Use congruent triangles to show that two overlapping triangles are congruent. 5/1 5/2 What is a midsegment? Find the length of a side of a triangle given a midsegment. Prove the Triangle midsegment theorem using a coordinate proof. Find the length of a segment using the perpendicular bisector theorem. Find the measure of an angle using the Angle bisector theorem. Midsegment of a triangle, Coordinate proof Perpendicular Bisector, Angle Bisector, Distance from a point to a line 5
5/3 G.4.2a, G.4.2b, G.4.2g, G.4.2h, G.4.2i, G.4.2j, G.4.2k, G.6.4b What is a point of concurrency? What is a median of a triangle? What is an altitude of a triangle? Identify a median and an altitude of the triangle. What is the difference between circumscribed and inscribed? Find the circumcenter, incenter, centriod, and orthocenter of the triangle. Point of concurrency, Circumcenter of a triangle, Incenter of a triangle, Circumscribed, Inscribed, Median of a triangle, Centroid, Altitude of a triangle, Orthocenter of a triangle 5/3A G.4.2c, G.4.2d, G.4.2e, G.4.2f, G.4.3a, SMP5 5/4 5/5 G.4.8a, G.4.8b, G.4.8c, Construct a circle circumscribed about the triangle. Construct a circle inscribed in the triangle. Construct a triangle congruent to the given triangle Write the negation of the statement. Write the inverse and contrapositive of the conditional statement. Use properties of inequalities in triangles. List the angles of a triangle in order from least to greatest, given its side lengths. List the sides of a triangle from least to greatest given the angle measures. Is it possible for the given measurements to make a triangle? Compass, Straightedge Circumscribed, inscribed, circumcenter, incenter, orthocenter, centroid Negation, Inverse, Contrapositive, Equivalent statements, Indirect reasoning, Indirect proof. 6
6/1 G.3.1a, G.3.1b, G.3.1c, G.3.1d, G.3.1e, G.3.1f, G.3.1g G.3.1h, G.3.3d What is the best classification for the quadrilateral? Classify the quadrilateral using coordinate geometry. Use properties of special quadrilaterals to find side lengths. 6/2 G.3.1c, G.3.3d, Find the measure of the angles in a parallelogram. Calculate the lengths of sides in a parallelogram. Find the length of the diagonals in a parallelogram. 6/3 G.8.8a Prove that the quadrilateral is a parallelogram. Find the value of each variable for which the quadrilateral must be a parallelogram. 6/4 G.3.1d, G.3.1e Find the measure of the diagonals in a rhombus/rectangle. Find the measure of the missing angles in a rhombus or rectangle. Are the diagonals in a rhombus perpendicular? Are the diagonals in a rectangle congruent? 6/5 G.3.1b, G.3.1g What is special about the diagonals in a kite? What is special about the base angles in an Isosceles Trapezoid? Find the labeled angles in the kite. Find the labeled angles in the trapezoid. Find the length of the diagonals in the isosceles trapezoid. s Handout: Classifying Quadrilaterals s Handout: Classifying Quadrilaterals Quadrilateral, Parallelogram, Rhombus, Rectangle, Square, Kite, Trapezoid/Isosceles Trap. Consecutive angles, diagonals Parallelogram Rhombus, Rectangle Kite, Trapezoid, Isosceles Trapezoid 7
Curriculum Mapping Geometry rd Nine Weeks 3 Chapter/ Lesson Indiana Standard(s) Key Questions Resources/Activities Vocabulary Assessments 6/6 6/7 G.2.6a, G.2.6b, G.2.6c, G.4.9a, G.4.9b, G.4.9c, G.3.4a, G.3.4b, G.3.4c, G.1.1a, G.1.1c, SMP1, SMP4, SMP5, SMP6 Use coordinate geometry to identify the missing coordinates of the figure on the coordinate plane. Prove the theorem by placing the figure in the coordinate plane. What is a midsegment of a trapezoid? Packet: Coordinate Proofs Distance formula, Midpoint formula Midsegment of a trapezoid, distance formula, midsegment formula 7/1 G.3.1c, G.4.7b, What is the formula for the area of a parallelogram? Find the area of the parallelogram. What is the formula for the area of a triangle? Find the area of the triangle. Formula sheet, Area formulas: Parallelogram, triangle; base of a parallelogram, altitude, height, Base of a triangle 7/2 G.5.1a, G.5.1b, G.5.1c, G.5.1d 7/3 G.5.3a, G.5.3b, G.5.3c, G.5.3d, SMP7, SMP8 What is the Pythagorean Theorem? Prove the Pythagorean Theorem. What is a Pythagorean Triple? Classify the triangle as acute, obtuse, or right using the Pythagorean Theorem. Fill in the side lengths of the 45-45-90 triangle. Fill in the side lengths of the 30-60-90 triangle. Find the missing side lenghts using relationships in the special right triangles. Pythagorean Theorem, Pythagorean triple 45-45-90 Triangle, 30-60- 90 Triangle 8
7/4 G.3.1g, G.3.1b, G.3.1e, G.3.3b 7/5 G.2.5a, G.2.5b, G.2.5d, G.4.4a 7/6 G.6.6a, G.6.6b, G.6.7a, G.6.7b 7/7 G.6.7c, G.6.7d, G.6.7e, G.6.7f 8/2 G.3.2a, G.3.2b, G.2.3a, G.2.3b 8/3 G.4.4b, G.4.5a, G.4.6a, SMP2, SMP3 What is the formula for the area of a trapezoid? What is the formula for the area of a kite/rhombus? Find the area of the trapezoid. Find the area of the kite/rhombus? What is the formula for the area of a regular polygon? Identify the radius in the regular polygon. What is an apothem? Calculate the area of the regular polygon. Define a circle. What makes two circles congruent? What are concentric circle? What is a central angle? What is a semicircle/major arc/minor arc? What are adjacent arcs? Calculate the circumference of the circle. What is the formula for arc length? Calculate the arc length. Calculate the area of the circle. What is a sector of a circle? What is a segment of a circle? Calculate the area of the sector. Calculate the area of the segment. What makes two polygons similar? Tell if the two polygons are similar. Identify the corresponding parts of the similar polygons. Find the missing sides on the similar polygons. Prove that the triangles are similar by AA, SAS, or SSS similarity. Determine whether the triangles are similar, and then find a missing value. Formula sheet, Area of a Trapezoid, Height of a trapezoid, Bases of a trapezoid, Diagonal Area of a Regular Polygon, Radius of a regular polygon, Apothem, Perimeter Concentric Circles, central angle, semicircle, major arc, minor arc, circumference, arc length Area of a circle, sector of a circle, segment of a circle. Similarity, Similarity ratio, Similarity statement Angle-Angle Similarity Postulate, Side- Angle-Side Similarity, Side- Side-Side Similarity 9
8/4 G.5.2a, G.5.2b, Determine relationships between sides of similar right triangles. What is the geometric mean? Find the geometric mean of two numbers. Use the geometric mean to find missing side lengths in similar right triangles. 8/5 G.4.5b, G.4.5a, G.4.6a, G.4.4b Use the Side-Splitter Theorem to find side lengths in similar triangles. Apply the Side-Splitter Theorem to parallel lines and transversals. Use the Triangle- Angle Bisector Theorem to find side lengths in similar triangles. 8/6 G.4.7d, Calculate perimeters and areas of similar polygons. Geometric mean, hypotenuse, altitude Side-Splitter Theorem, Triangle-Angle Bisector Theorem Similarity ratio, Ratio of areas 10
Curriculum Mapping Geometry 4 th Nine Weeks Chapter/ Lesson Indiana Standard(s) Key Questions Resources/Activities Vocabulary Assessments 9/1 G.5.4a, G.5.4b, G.5.4d, G.5.4e, SMP8 9/2 G.5.4a, G.5.4b, G.5.4d, G.5.4e, SMP8 What is the tangent ratio? Identify the hypotenuse of the right triangle. What are the opposite and adjacent sides from angle A in the right triangle? Calculate the tangent of an angle given the sides of the triangle. Find the measure of an angle using the inverse of the tangent ratio. What is the sine ratio? What is the cosine ratio? Find the sine and cosine ratios of an angle in a right triangle. Find the measure of an angle using the sine inverse and cosine inverse. 9/2A G.5.4c, SMP8 How do secant, cosecant, and cotangent relate to sine, cosine, and tangent? What are the secant, cosecant, and contangent of the angle? 9/2B G.5.5a, G.5.5b, SMP8 9/3 G.5.6a, G.5.6b, SMP4 9/4, SMP7 What is sin 2 x+cos 2 x equal to? What is an angle of elevation? What is an angle of depression? Determine whether the angle is an elevation or depression. Find the magnitude of the vector. Describe the vector as a set of ordered pairs. Find the resultant vector., formula sheet Tangent Ratio, Opposite side, Adjacent side Sine ration, cosine ration, Sine inverse, cosine inverse Secant, Cosecant, Cotangent Trigonometric identity Angle of elevation, Angle of Depression Vector, Magnitude, Initial point, terminal point, resultant vector 11
9/5, SMP1 10/1 G.7.1a, G.7.1b, G.7.1c, G.7.2a, G.7.2b, G.7.3a, G.7.3b, SMP1, SMP6 10/3 G.3.3a, G.3.3b, G.4.7a, G.4.7b, G.4.7d, G.7.7a, G.7.7c, SMP6 10/4 G.7.7a, G.7.7c, SMP6 10/5 G.7.7b, G.7.7c, SMP6 10/6 G.7.7b, G.7.7c, SMP6 Use trigonometry to calculate the area of the regular polygon. Determine the formula for the area of a triangle using an altitude and trigonometric ratios. Find the area of a triangle. What is a polyhedron? Draw a net for the figure. Classify the figure using the given net. What is the relationship between faces, edges, and vertices in polyhedral? Use Euler s Formula to find the number of faces/edges/vertices in the polyhedron. What is a prism? What is a cylinder? Define surface area. Identify the bases of the prism. Find the lateral area of the prism/cylinder. What is the formula for the surface area of a prism/cylinder? Find the surface area of the prism/cylinder. What is a pyramid? What is a cone? Identify the slant height of the pyramid/cone. What are the formulas for the lateral and surface areas of pyramids/cones? Find the lateral and surface areas of the pyramid/cone. What is volume? What is the volume formula for a prism/cylinder? Find the volume of the prism/cylinder. Find the volume of the composite space figure. What is a cross section? What is the volume formula for a pyramid/cone? Identify the height of the pyramid/cone. What is the difference between a slant height and the actual height? Find the volume of the pyramid/cone., formula sheet, formula sheet Sine ratio, cosine ration, tangent ratio, Area of a regular polygon Net, Polyhedron, face, edge, vertex Prism, Cylinder, lateral face, altitude, height, right prism/cylinder, oblique prism/cylinder, lateral area, surface area, Lateral and Surface area formulas for prisms and cylinders Pyramid, cone, vertex, slant height, Lateral and surface area formulas for pyramids and cones Volume, Cross section, Cavalieri s principle, composite space figure, Volume formulas for Prisms and cylinders Height of a pyramid/cone, Volume formulas for pyramids and cones 12
10/7 G.7.7b, G.7.7c, G.7.5a, G.7.5b, SMP6 10/8 G.7.6a, G.7.6c, G.7.6b, G.7.6d, G.4.7d, SMP2 11/1 G.6.2a, G.6.2b, G.6.3a, SMP2, SMP3 11/2 G.6.2a, G.6.2b, G.6.3a What is a sphere? What is the great circle in a sphere? Define a hemisphere. What is the formula for the surface area of a sphere? What is the formula for the volume of a sphere? Find the surface area and volume of the sphere. What are the relationships between the surface areas and volumes of similar solids? Given the volume/surface area of a smaller figure, find the volume/surface area of a larger similar figure using their similarity ratios. What is a tangent line? What is a point of tangency? What is the relationship between a tangent line and a radius at the point of tangency? Show that the line is tangent to the circle. Find the missing length using what you know about tangent lines and circles. What is a chord? Use properties of chords to find missing values., formula sheet, formula sheet Sphere, surface area and volume formulas for spheres, great circle, hemisphere Similarity ratio, surface areas and volumes of similar solids Tangent line, point of tangency Chord 11/3 G.6.3a, G.6.5a, G.6.5b, G.6.5c, SMP1 11/4 G.6.2a, G.6.2b, G.6.3a, G.6.5b, G.6.5c, SMP1 What is an inscribed angle? Find the value of the inscribed angle given its intercepted arc. Find the measure of the intercepted arc given the inscribed angle. What is a secant line? Find the measure of the angles created by the secants in the circle. Find the lengths of the segments created by the secants and the circle. Inscribed angle, intercepted arc Secant 13
14 11/5 G.6.3a, G.6.8a, G.6.8b, G.6.8c, SMP2 11/6 G.6.1a, G.6.1b, SMP5 Derive the formula for a circle using the distance formula. What is the standard form equation for a circle? Find the center of the circle given the equation of the circle. Graph the circle given its equation. Write and equation for the circle given its graph. Write an equation for the circle given its center and a point on the circle. Find the center of the circle using a compass and straight edge. Construct a circle through three nonconliniear points. Construct a common tangent to two circles. 12/1 G.2.4a What is a transformation? What is a reflection? What is a preimage? What is an image? What is an isometry? Is the transformation an isometry? Draw a reflection of the figure across the x- axis/y-axis 12/2 G.2.4a What is a translation? Translate the figure using vectors. Write a matrix that represents the translation of the figure. 12/3 G.8.9a, G.8.9b, What is a rotation? Rotate the figure x o about a given point. Find the angle of rotation given an image and preimage. 12/4 G.2.4a, SMP1 Identify the type of transformation. Use a composition of reflections. What is a glide reflection? Draw an image of a figure using a glide reflection. 12/5 G.2.4c What is symmetry? What is reflectional symmetry (line symmetry)? What is rotational symmetry? What is point symmetry? Is the figure symmetric? What type of symmetry does the figure have? compass, straightedge protractor, compass, straightedge protractor, compass, straightedge Standard form equation for a circle, distance formula Common tangents Transformation, reflection, preimage, image, isometry Translation, matrix Rotation, angle of rotation Composition of reflections, glide reflection Symmetry, reflectional symmetry (line symmetry), rotational symmetry, point symmetry
12/5A G.7.4a, G.7.4b What are the types of symmetries for solid figures? What type of symmetry does the solid have? 12/6 G.2.4a, G.2.4d, G.2.4e What is a tessellation? What is tiling? Will the figure tessellate? Create a tessellation. 12/7 G.2.4b What is a dilation? Is the dilation an enlargement or a reduction? Describe the dilation. Find the scale factor of the dilation. What is scalar multiplication? Use scalar multiplication with matrices to draw the image of the figure. s Rotational symmetry, reflectional symmetry Tessellation, tiling, Dilation, enlargement, reduction, scalar multiplication 15