# Introduction to Geometry

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1 Introduction to Geometry This course covers the topics outlined below. You can customize the scope and sequence of this course to meet your curricular needs. Curriculum (211 topics + 6 additional topics) Algebra and Deductive Reasoning (47 topics) Numbers (21 topics) Order of operations with whole numbers Order of operations with whole numbers and grouping symbols Factors Least common multiple of 2 numbers Finding the next terms of a sequence with whole numbers Equivalent fractions Simplifying a fraction Addition or subtraction of fractions with different denominators Product of a fraction and a whole number: Problem type 1 Fraction multiplication Fraction division Writing ratios for real world situations Writing an improper fraction as a mixed number Decimal place value: Hundreds to ten thousandths Rounding decimals Finding a percentage of a whole number without a calculator: Basic Integer addition: Problem type 1 Integer addition: Problem type 2 Integer subtraction Integer multiplication and division Absolute value of a number Equations (17 topics) Evaluating a linear expression: Integer multiplication with addition or subtraction Evaluating a quadratic expression: Integers Translating a sentence into a one step equation Distributive property: Whole number coefficients Combining like terms: Integer coefficients Additive property of equality: Problem type 3 Multiplicative property of equality with signed fractions Solving a two step equation with integers Solving a two step equation with signed fractions Solving a linear equation with several occurrences of the variable: Variables on the same side and distribution Solving a linear inequality: Problem type 1 Graphing a linear inequality on the number line Graphing a compound inequality on the number line Solving a rational equation that simplifies to linear: Denominator x Solving a proportion of the form x/a = b/c Solving a proportion of the form a/(x+b) = c/x Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 1/6

2 Word problem on proportions: Problem type 1 Exponents and Radicals (4 topics) Evaluating expressions with exponents: Problem type 1 Square root of a perfect square Simplifying the square root of a whole number less than 100 Rationalizing the denominator of a radical expression Deductive Reasoning (5 topics) Interpreting a Venn diagram of 2 sets Interpreting a Venn diagram of 3 sets Conditional statements and negations The converse, inverse, and contrapositive of a conditional statement Conditional statements and deductive reasoning Lines and Angles (26 topics) Segments (7 topics) Naming segments, rays, and lines Measuring length to the nearest quarter or half inch Computing distances between decimals on the number line Midpoint of a number line segment Segment addition and midpoints Introduction to proofs: Justifying statements Proofs involving segment congruence Lines (6 topics) Identifying parallel and perpendicular lines Constructing the perpendicular bisector of a line segment Constructing a pair of perpendicular lines Constructing a pair of parallel lines Introduction to proofs involving parallel lines Proofs involving parallel lines Angles (13 topics) Measuring an angle with the protractor Drawing an angle with the protractor Acute, obtuse, and right angles Finding supplementary and complementary angles Identifying corresponding and alternate angles Identifying linear pairs and vertical angles Solving equations involving vertical angles and linear pairs Solving equations involving angles and two pairs of parallel lines Constructing congruent angles Constructing an angle bisector Angle addition with relationships between angles Angle addition and angle bisectors Proofs involving angle congruence Triangles (29 topics) Properties of Triangles (14 topics) Acute, obtuse, and right triangles Classifying scalene, isosceles, and equilateral triangles by side lengths or angles Area of a triangle Finding an angle measure of a triangle given two angles Finding an angle measure given extended triangles Finding an angle measure given a triangle and parallel lines Finding angle measures of a right or isosceles triangle given angles with variables Finding an angle measure for a triangle with an extended side Finding an angle measure for a triangle sharing a side with another triangle Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 2/6

3 Using triangle inequality to determine if side lengths form a triangle Using triangle inequality to determine possible lengths of a third side Relationship between angle measures and side lengths in a triangle Relationship between angle measures and side lengths in two triangles Indirect proof (proof by contradiction) Congruent Triangles (6 topics) Identifying and naming congruent triangles Proofs involving congruent triangles and vertical angles or the reflexive property Proofs involving congruent triangles and segment or angle bisectors Proofs involving congruent triangles that overlap: Basic Proofs involving congruent triangles, parallel or perpendicular segments, and CPCTC Proofs involving congruent triangles that overlap: Advanced Right Triangles (4 topics) Pythagorean Theorem Computing an area using the Pythagorean Theorem Special right triangles: Exact answers Circles inscribed in and circumscribed about regular polygons Trigonometric Ratios (5 topics) Sine, cosine, and tangent ratios: Variables for side lengths Using a trigonometric ratio to find a side length in a right triangle Using trigonometry to find a length in a word problem with one right triangle Using a trigonometric ratio to find an angle measure in a right triangle Using trigonometry to find angles of elevation or depression in a word problem Polygons and Circles (43 topics) Polygons and Quadrilaterals (9 topics) Properties of quadrilaterals Conditions for quadrilaterals Classifying parallelograms Finding measures involving diagonals of parallelograms Conditions for parallelograms Finding measures involving diagonals of rectangles Finding measures involving diagonals of rhombi The sum of interior angle measures in a convex polygon Interior and exterior angle measures in a regular polygon Perimeters and Areas of Polygons (16 topics) Perimeter of a polygon Perimeter of a square or a rectangle Perimeter of a piecewise rectangular figure Sides of polygons having the same perimeter Finding a side length given the perimeter and side lengths with variables Area of a square or a rectangle Distinguishing between the area and perimeter of a rectangle Areas of rectangles with the same perimeter Area of a piecewise rectangular figure Finding the side length of a rectangle given its perimeter or area Finding the perimeter or area of a rectangle given one of these values Area of a parallelogram Area of a trapezoid Word problem involving the area between two rectangles Area involving rectangles and triangles Area of a regular polygon Circles (9 topics) Introduction to a circle: Diameter, radius, and chord Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 3/6

4 Identifying central angles, inscribed angles, arcs, chords, and tangents of a circle Tangents of a circle: Problem type 1 Tangents of a circle: Problem type 2 Lengths of chords, secants, and tangents Inscribed angles of a circle Central angles and inscribed angles of a circle Angles of intersecting secants and tangents Angle measure in a circle graph Circumferences and Areas of Circles (9 topics) Finding the radius or the diameter of a circle given its circumference Circumference and area of a circle Perimeter involving rectangles and circles Circumference ratios Arc length and area of a sector of a circle Word problem involving the area between two concentric circles Area involving rectangles and circles Area involving rectangles and circles: Advanced problem Area as probability Similarities and Transformations (19 topics) Similarities (9 topics) Identifying congruent shapes on a grid Identifying similar or congruent shapes on a grid Similar polygons Triangles and parallel lines Similar right triangles Right triangles and geometric mean Indirect measurement Computing ratios of side lengths, surface areas, and volumes for similar solids Similar solids: Problem type 2 Transformations (10 topics) Identifying transformations Translating a polygon Using a translated point to find coordinates of other translated points Reflecting a polygon over a vertical or horizontal line Finding the coordinates of three points reflected over an axis Drawing lines of symmetry Rotating a figure about the origin Finding an angle of rotation Rotational and point symmetries Dilating a figure Volumes and Surface Areas (20 topics) Volumes (11 topics) Counting the cubes in a solid made of cubes Volume of a rectangular prism made of unit cubes Volume of a rectangular prism Volume of a piecewise rectangular prism Volume of a triangular prism Volume of a pyramid Volume of a cylinder Volume of a cone: Exact answers in terms of pi Volume of a sphere Word problem involving the rate of filling or emptying a cylinder Ratio of volumes Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 4/6

5 Surface Areas (9 topics) Vertices, edges, and faces of a solid Nets of solids Side views of a solid made of cubes Surface area of a piecewise rectangular prism made of unit cubes Surface area of a cube or a rectangular prism Surface area of a triangular prism Surface area of a cylinder: Exact answers in terms of pi Surface area involving prisms or cylinders Surface area of a sphere Coordinate Geometry (27 topics) Coordinate Plane (6 topics) Plotting a point in the coordinate plane Midpoint of a line segment in the plane Distance between two points in the plane: Exact answers Finding coordinates of vertices of polygons Finding the coordinates of a point to make a parallelogram Area of quadrilaterals in the coordinate plane Equations of Lines (12 topics) Graphing a line given its x and y intercepts Graphing a line given its equation in slope intercept form Finding x and y intercepts of a line given the equation: Advanced Graphing a line given its equation in standard form Graphing a line through a given point with a given slope Determining the slope of a line given its graph Finding the slope of a line given its equation Finding slopes of lines parallel and perpendicular to a line given in the form Ax + By = C Writing equations of lines parallel and perpendicular to a given line through a point Writing an equation of a line given the y intercept and another point Writing the equation of a line given the slope and a point on the line Writing the equation of the line through two given points Equations of Circles (3 topics) Graphing a circle given its equation in standard form Writing an equation of a circle given its center and a point on the circle Writing an equation of a circle given the endpoints of a diameter Vectors (6 topics) Scalar multiplication of a vector: Geometric Approach Vector addition: Geometric approach Vector addition and scalar multiplication: Component form Magnitude of a vector given in component form Finding the magnitude and direction of a vector given its graph Finding the components of a vector given its graph Other Topics Available(*) (6 additional topics) Triangles (3 topics) Solving a triangle with the law of sines: Problem type 1 Solving a triangle with the law of sines: Problem type 2 Solving a triangle with the law of cosines Coordinate Geometry (3 topics) Translation of a vector Addition or subtraction of matrices Scalar multiplication of a matrix Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 5/6

6 *Other Topics Available By default, these topics are NOT included in the course, but can be added using the content editor in the Teacher Module. Copyright 2018 UC Regents and ALEKS Corporation. ALEKS is a registered trademark of ALEKS Corporation. 6/6

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