Geometry. Patterns and Inductive Reasoning 8.A.4b, 9.C.4b, 9.C.4c Find and describe pattern Use inductive reasoning to make real-life conjectures
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1 Geometry Basics of Geometry Patterns and Inductive Reasoning 8.A.4b, 9.C.4b, 9.C.4c Find and describe pattern Use inductive reasoning to make real-life conjectures Points, Lines, and Planes - 9.B.4 Understand and use the basic undefined terms and defined terms of geometry Sketch the intersections of lines and planes Segment and their Measures - 7.A.4b, 9.B.4 Use segment postulates Use the distance formula to measure distances Angles and their Measures - 7.A.4b, 7.B.4, 9.B.4, 9.C.4b Use angle postulates Classify angles as acute, right, obtuse, or straight Segment and Angle Bisectors - 7.A.4b, 9.B.4 Bisect a segment and an angle Angle Pair Relationships - 7.A.4b, 9.B.4 Identify vertical angles and linear pairs Identify complementary and supplementary angles Introduction to Perimeter, Circumference, and Area - 7.A.4b, 9.B.4 Find the perimeter and area of common plane figures Use a general problem-solving plan Reasoning and Proof Conditional Statements - 9.B.4, 9.C.4b, 9.C.4c Recognize and analyze a conditional statement Write postulates about points, lines, and planes using conditional statements Definitions and Biconditional Statements - 9.B.4, 9.C.4c Recognize and use definitions and biconditional statements Deductive Reasoning - 8.A.4b, 9.C.4a, 9.C.4b Use symbolic notation to represent logical statements Form conclusions by applying the laws of logic of true statements Reasoning with Properties from Algebra - 6.A.4, 8.A.4b, 9.C.4c Use properties from algebra Use properties of length and measure to justify segment and angle relationships
2 Proving Statements about Segments - 9.B.4, 9.C.4c Justify statements about congruent segments Write reasons for steps in a proof Proving Statements about Angles - 9.B.4, 9.C.4c Use angle congruence properties Prove properties about special pairs of angles Perpendicular and Parallel Lines Lines and Angles - 9.B.4, 9.C.4b Identify relationships between lines Identify angles formed by transversals Proof and Perpendicular Lines - 9.B.4, 9.C.4c Write different types of proofs Prove results about perpendicular lines Parallel Lines and Transversals - 9.B.4, 9.C.4c Prove and use results about parallel lines and transversals Use properties about parallel lines to solve real-life problems Proving lines are parallel - 9.B.4, 9.C.4c Prove that two lines are parallel Use properties of parallel lines to solve real-life problems Using Properties of Parallel Lines - 9.B.4, 9.C.4c Use properties of parallel lines in real-life situations Construct Parallel lines using straightedge and compass Parallel Lines in the Coordinate Plane - 7.A.4b, 8.B.4a, 9.B.4 Find slopes of lines and use slope to identify parallel lines in a coordinate plane Write equations of parallel lines in a coordinate plane Perpendicular Lines in the Coordinate Plane - 7.A.4b, 8.B.4a, 9.B.4 Use slope to identify perpendicular lines in a coordinate plane Write equations of perpendicular lines Congruent Triangles Triangles and Angles - 9.B.4, 9.C.4c Classify triangles by their sides and angles Find angle measures in triangles Congruence and Triangles - 9.B.4, 9.C.4c Identify congruent figures and corresponding parts Prove that two triangles are congruent
3 Proving Triangles are Congruent: SSS and SAS - 7.A.4b, 9.B.4, 9.C.4c Prove that triangles are congruent using the SSS and SAS Congruence Postulates Use congruence postulates in real-life problems, such as bracing a structure Proving Triangles are Congruent: ASA and AAS - 9.B.4, 9.C.4c Prove that triangles are congruent using the ASA Congruence Postulate, and the AAS Congruence Theorem Use congruence postulates and theorems in real-life problems Using Congruent Triangles - 9.B.4, 9.C.4c Use congruent triangles to plan and write proofs Use congruent triangles to prove constructions are valid Isosceles, Equilateral, and Right Triangles - 9.B.4, 9.C.4c Use properties of isosceles and equilateral triangles Use properties of right triangles Triangles and Coordinate Proof - 7.A.4b, 9.B.4, 9.C.4c Place geometric figures in a coordinate plane Write a coordinate proof Properties of Triangles Perpendicular and Bisectors - 9.B.4, 9.C.4c Use properties of perpendicular bisector Use properties of angle bisectors to identify equal distances Bisectors of a Triangle - 9.B.4, 9.C.4c Use properties of perpendicular bisectors of a triangle Use properties of angles bisectors of a triangle Medians and Altitudes of a Triangle - 7.A.4b, 9.B.4 Use properties of medians of a triangle Use properties of altitudes of a triangle Midsegment Theorem - 7.A.4b, 9.B.4, 9.C.4c Identify the midsegments of a triangle Use properties of midsegments of a triangle Inequalities in One Triangle - 9.B.4, 9.C.4c Use triangle measurements to decide which side is longest or which angle is largest Use the Triangle Inequality Indirect Proof and Inequalities in Two Triangles - 9.B.4, 9.C.4c Read and write an indirect proof Use the Hinge Theorem and its converse to compare side lengths and angle measures
4 Quadrilaterals Polygons - 9.B.4, 9.C.4b Identify, name, and describe polygons Use the sum of the measures of the interior angles of a quadrilateral Properties of Parallelograms - 9.B.4, 9.C.4c Use some properties of parallelograms Use properties of parallelograms in real-life situations Proving Quadrilaterals are Parallelograms - 7.A.4b, 9.B.4, 9.C.4c Prove that a quadrilateral is a parallelogram Use coordinate geometry with parallelograms Rhombuses, Rectangles, and Squares - 7.A.4b, 9.B.4, 9.C.4c Use properties of sides and angles of rhombuses, rectangles, and squares Use properties of diagonals of rhombuses, rectangles, and squares Trapezoids and Kites - 7.A.4b, 9.B.4, 9.C.4c Use properties of trapezoids Use properties of kites Special Quadrilaterals - 7.A.4b, 9.B.4, 9.C.4c Identify special quadrilaterals based on limited information Prove that a quadrilateral is a special type of quadrilateral, such as a rhombus or trapezoid Areas of Triangles and Quadrilaterals - 7.A.4b, 9.B.4, 9.C.4c Find the areas of squares, rectangles, parallelograms, trapezoids, kites, rhombuses, and triangles Transformations Rigid Motion in a Plane - 7.A.4b, 9.B.4 Identify the three basic rigid transformations Use transformations in real-life situations Reflections - 9.A.4b, 9.B.4, 9.C.4c Identify and use reflections in a plane Identify relationships between reflections and line symmetry Rotations - 7.B.4, 9.A.4b, 9.B.4, 9.C.4c Identify rotations in a plane Use rotational symmetry in real-life situations Translations and Vectors - 7.A.4b, 8.C.4b, 9.A.4b, 9.B.4 Identify and use translations in a plane Use vectors in real-life situations
5 Glide Reflections and Compositions - 9.A.4b, 9.B.4 Identify glide reflections in a plane Represent transformations as compositions of simpler transformations Frieze Patterns - 9.A.4b, 9.B.4, 9.C.4b Use transformations to classify frieze patterns Use frieze patterns to design border patterns in real-life situations Similarity Ratio and Proportion - 6.D.4, 7.C.4a, 9.B.4 Find and simplify the ratio of two numbers Use proportions to solve real-life problems Problem Solving in Geometry with Proportions - 6.D.4, 7.C.4a, 7.C.4b, 9.B.4 Use properties of proportions Similar Polygons - 6.D.4, 7.C.4a, 9.B.4 Identify similar polygons Use similar polygons to solve real-life problems Similar Triangles - 6.D.4, 7.C.4a, 9.B.4, 9.C.4c Identify similar triangles Use similar triangles in real-life situations Proving Triangles are Similar - 6.D.4, 7.C.4a, 9.B.4, 9.C.4c Use similarity theorems to prove that two triangles are similar Use similar triangles to solve real-life problems Proportions and Similar Triangles - 6.D.4, 7.C.4a, 9.B.4, 9.C.4c Use proportionality theorems to calculate segment lengths Dilations - 6.D.4, 7.A.4a, 7.C.4a, 9.A.4b, 9.B.4 Identify dilations and use properties of dilations to create a real-life perspective drawing Right Triangles and Trigonometry Similar Right Triangles - 6.D.4, 7.C.4a, 9.B.4, 9.C.4c Solve problems involving similar triangles formed by the altitude drawn to the hypotenuse of a right triangle Use geometric mean to solve problems The Pythagorean Theorem - 7.A.4b, 7.C.4a, 9.B.4, 9.C.4c Prove the Pythagorean Theorem Use the Pythagorean Theorem to solve real-life problems
6 The Converse of the Pythagorean Theorem - 9.B.4, 9.C.4c Use the converse of the Pythagorean Theorem to solve problems Use side lengths to classify triangles by their angle measure Special Right Triangles - 7.A.4b, 9.B.4 Find the side lengths of special right triangles Trigonometric Ratios - 6.C.4, 7.A.4b, 7.C.4a, 9.B.4, 9.D.4 Find the sine, cosine, and the tangent of an acute angle Use trigonometric ratios to solve real-life problems Solving Right Triangles - 6.C.4, 9.B.4, 9.D.4 Solve a right triangle Use right triangles to solve real-life problems Vectors - 6.C.4, 7.A.4b, 8.C.4b, 9.D.4 Find the magnitude and the direction of a vector Add vectors Circles Tangents to Circles - 9.B.4, 9.C.4c Identify segments and lines related to circles Use properties of a tangent circle Arcs and Cords - 9.B.4, 9.C.4c Use properties of arcs of circles Use properties of chords of circles Inscribe Angles - 9.B.4, 9.C.4c Use inscribed angles to solve problems Use properties of inscribed polygons Other Angle Relationships in Circles - 9.B.4, 9.C.4c Use angles formed by tangents and chords to solve problems in geometry Use angles formed by lines that intersect a circle to solve problems Segment Lengths in Circles - 9.B.4, 9.C.4c Find the lengths of segments of chords, tangents, and secants Equations of Circles - 9.B.4 Write the equation of a circle Use the equation of a circle and its graph to solve problems Locus - 9.B.4, 9.C.4b Draw the locus of points that satisfy given conditions
7 Area of Polygons and Circles Angle Measures in Polygons - 9.B.4, 9.C.4c Find the measures of interior and exterior angles of polygons Use measures of angles of polygons Areas of Regular Polygons - 7.A.4b, 9.A.4b, 9.B.4, 9.C.4c Find the area of an equilateral triangle Find the area of a regular polygon Perimeters and Area of Similar Figures - 6.D.4, 7.A.4b, 9.B.4 Compare perimeters and areas o similar figures Use perimeters and area s of similar figures to solve real-life problems
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