# Geometry

I will be adding a printable with this. For now enjoy these topics and sub topics for Geometry, which is suggested for 9th grade but you can switch it up.

Algebra review

Ratios and proportions

Scale drawings: word problems

Properties of exponents

Write variable expressions

Solve linear equations

Solve linear inequalities

Solve systems of linear equations

Solve a quadratic equation by factoring

Points, lines, line segments, and planes

Lines, line segments, and rays

Properties of planes, lines, and points

Describe intersections in a plane

Lengths of segments on number lines

Midpoints

Congruent line segments

Perpendicular Bisector Theorem

Midpoint formula: find the midpoint

Midpoint formula: find the endpoint

Distance formula

Distance to the origin in three dimensions

Construct the midpoint or perpendicular bisector of a segment

Angles

Angle vocabulary

Angle measures

Identify complementary, supplementary, vertical, adjacent, and congruent angles

Find measures of complementary, supplementary, vertical, and adjacent angles

Angle bisectors

Construct an angle bisector

Construct a congruent angle

Proofs involving angles

Parallel and perpendicular lines

Identify parallel, intersecting, and skew lines and planes

Construct a perpendicular line

Transversals: name angle pairs

Transversals of parallel lines: find angle measures

Construct parallel lines

Proofs involving parallel lines

Lines in the coordinate plane

Coordinate plane review

Slopes of lines

Graph a linear equation

Equations of lines

Slopes of parallel and perpendicular lines

Equations of parallel and perpendicular lines

Find the distance between a point and a line

Find the distance between two parallel lines

Introduction to triangles

Classify triangles

Triangle Angle-Sum Theorem

Exterior Angle Theorem

Exterior Angle Inequality

Two-dimensional figures

Polygon vocabulary

Interior angles of polygons

Exterior angles of polygons

Review: interior and exterior angles of polygons

Construct an equilateral triangle or regular hexagon

Construct a square

Three-dimensional figures

Parts of three-dimensional figures

Three-dimensional figure vocabulary

Nets and drawings of three-dimensional figures

Cross-sections of three-dimensional figures

Solids of revolution

Logic

Identify hypotheses and conclusions

Counterexamples

Conditionals

Negations

Converses, inverses, and contrapositives

Biconditionals

Truth tables

Truth values

Introduction to congruent figures

Congruence statements and corresponding parts

Solve problems involving corresponding parts

Identify congruent figures

Congruent triangles

SSS and SAS Theorems

Proving triangles congruent by SSS and SAS

ASA and AAS Theorems

Proving triangles congruent by ASA and AAS

SSS, SAS, ASA, and AAS Theorems

SSS Theorem in the coordinate plane

Proving triangles congruent by SSS, SAS, ASA, and AAS

Proofs involving corresponding parts of congruent triangles

Congruency in isosceles and equilateral triangles

Proofs involving isosceles triangles

Hypotenuse-Leg Theorem

Transformations

Classify congruence transformations

Translations: graph the image

Translations: find the coordinates

Translations: write the rule

Reflections: graph the image

Reflections: find the coordinates

Rotations: graph the image

Rotations: find the coordinates

Compositions of congruence transformations: graph the image

Transformations that carry a polygon onto itself

Congruence transformations: mixed review

Dilations: graph the image

Dilations: find the coordinates

Dilations: scale factor and classification

Dilations and parallel lines

Triangles

Midsegments of triangles

Triangles and bisectors

Identify medians, altitudes, angle bisectors, and perpendicular bisectors

Angle-side relationships in triangles

Triangle Inequality Theorem

Construct the circumcenter or incenter of a triangle

Construct the centroid or orthocenter of a triangle

Proofs involving triangles

Identify trapezoids

Properties of parallelograms

Proving a quadrilateral is a parallelogram

Properties of rhombuses

Properties of squares and rectangles

Properties of trapezoids

Properties of kites

Symmetry

Line symmetry

Rotational symmetry

Draw lines of symmetry

Count lines of symmetry

Similarity

Similarity ratios

Similarity statements

Identify similar figures

Side lengths and angle measures in similar figures

Similar triangles and indirect measurement

Perimeters of similar figures

Similarity rules for triangles

Similar triangles and similarity transformations

Similarity of circles

Triangle Proportionality Theorem

Similarity and altitudes in right triangles

Areas of similar figures

Prove similarity statements

Prove proportions or angle congruences using similarity

Proofs involving similarity in right triangles

Prove the Pythagorean theorem

Right triangles

Pythagorean theorem

Converse of the Pythagorean theorem

Pythagorean Inequality Theorems

Special right triangles

Trigonometry

Trigonometric ratios: sin, cos, and tan

Trigonometric ratios: csc, sec, and cot

Trigonometric ratios in similar right triangles

Trigonometric functions of complementary angles

Find trigonometric functions of special angles

Find trigonometric functions using a calculator

Inverses of trigonometric functions

Trigonometric ratios: find a side length

Trigonometric ratios: find an angle measure

Solve a right triangle

Law of Sines

Law of Cosines

Solve a triangle

Area of a triangle: sine formula

Area of a triangle: Law of Sines

Area and perimeter

Perimeter

Area of rectangles and squares

Area of parallelograms and triangles

Area of trapezoids

Area and perimeter in the coordinate plane

Area and circumference of circles

Area of compound figures

Area between two shapes

Area and perimeter of similar figures

Perimeter and area: changes in scale

Heron’s formula

Area and perimeter mixed review

Surface area and volume

Introduction to surface area and volume

Surface area of prisms and cylinders

Surface area of pyramids and cones

Surface area of spheres

Volume of prisms and cylinders

Volume of pyramids and cones

Volume of spheres

Introduction to similar solids

Surface area and volume of similar solids

Surface area and volume: changes in scale

Perimeter, area, and volume: changes in scale

Surface area and volume review

Circles

Parts of a circle

Central angles and arc measures

Arc length

Area of sectors

Circle measurements: mixed review

Arcs and chords

Tangent lines

Perimeter of polygons with an inscribed circle

Inscribed angles

Angles in inscribed right triangles

Construct a tangent line to a circle

Construct an equilateral triangle inscribed in a circle

Construct a square inscribed in a circle

Construct a regular hexagon inscribed in a circle

Construct the inscribed or circumscribed circle of a triangle

Circles and parabolas in the coordinate plane

Find the center of a circle

Find the radius or diameter of a circle

Write equations of circles in standard form from graphs

Write equations of circles in standard form using properties

Convert equations of circles from general to standard form

Find properties of circles from equations in general form

Graph circles from equations in standard form

Graph circles from equations in general form

Find the vertex of a parabola

Find the focus or directrix of a parabola

Find the axis of symmetry of a parabola

Write equations of parabolas in vertex form from graphs

Write equations of parabolas in vertex form using properties

Convert equations of parabolas from general to vertex form

Find properties of a parabola from equations in general form

Graph parabolas

Measurement

Convert rates and measurements: customary units

Convert rates and measurements: metric units

Convert square and cubic units of length

Precision

Greatest possible error

Minimum and maximum area and volume

Percent error

Percent error: area and volume

Calculate density, mass, and volume

Probability

Theoretical and experimental probability

Outcomes of compound events

Identify independent and dependent events

Probability of independent and dependent events

Counting principle

Permutations

Permutation and combination notation

Find probabilities using combinations and permutations

Find probabilities using two-way frequency tables

Identify independent events

Find conditional probabilities

Independence and conditional probability

Find conditional probabilities using two-way frequency tables

Geometric probability

Find probabilities using the addition rule

Vectors

Compass directions and vectors

Find the magnitude of a vector

Find the component form of a vector

Find the component form of a vector given its magnitude and direction angle

Graph a resultant vector using the triangle method

Graph a resultant vector using the parallelogram method