### Geometry

**WEBSITES FOR EXTRA HELP**

- Geometry
- Chapter 1- Basics of Geometry
### Chapter 1- Basics of Geometry

Standards:

Know precise definitions of angles, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.1

Make formal geometric constructions with a variety of tools and methods. G-CO.12

Use coordinates to prove simple geometry theorems algebraically. G-GPE.4

Use Coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. G-GPE.7

Use units as a way to understand problems and to guide the solution of multi-step problems: choose and interpret units consistently in formulas; choose and interpret the scale and the origin in graphs and data displays. N-Q.1

- Chapter 2 - Reasonings and Proof
### Chapter 2 - Reasonings and Proof

Standards:

Prove theorems about line and angles. G-CO.9

Prove theorems about triangles. G-CO.10

Prove theorems about parallelograms. G-CO.11

- Chapter 3- Parallel and Perpendicular Lines
### Chapter 3- Parallel and Perpendicular Lines

Standards:

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of points, line, distance along a line, and distance around a circular arc. G-CO.1

Prove theorems about line and angles. G-CO.9

Prove theorems about triangles. G-CO.10

Make formal geometric constructions with a variety of tools and methods. G-CO12

Apply geometric methods to solve design problems. G-MG.3

Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. G-GPE.5

- Chapter 4 - Congruent Triangles
### Chapter 4 - Congruent Triangles

Standards:

Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent. G-CO.7

Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. G-CO.8

Prove theorems about triangles. G-CO.10

Make formal geometric constructions with a variety of tools and methods. G-CO.12

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-SRT.5

- Chapter 5 - Relationships within Triangles
### Chapter 5 - Relationships within Triangles

Chapter Outcomes

Prove theorems about triangles. G-CO.10

Construct and equilateral triangle, a square, and a regular hexagon inscribed in a circle. G-CO.13

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G-C.3

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-SRT5

- Chapter 6 - Quadrilaterals
### Chapter 6 - Quadrilaterals

Standards:

Prove theorems about triangles. G-CO.10

Prove theorems about about parallelograms. G.CO.11

Use coordinates to prove simple geometric theorems algebraically. G-GPE.4

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles; e.g. using the distance formula. G.GPE.7

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometry figures. G-SRT.5

- Chapter 7 - Area
### Chapter 7 - Area

Standards:

Given a geometric figure and a rotation, refection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. G-C.5

Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc. G-CO.1

Construct and equilateral triangle, a square, and a regular hexagon inscribed in a circle. G-CO.13

Use coordinates to compute perimeters of polygons and areas of triangles and rectangles. G-GPE.7

Use geometric shapes, their measures, and their properties to describe objects. G.MG.1

Derive the formula A = 1/2 ab sine@ for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side. G-SRT.9

Use units as a way the understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and origin in graphs and data displays. N-Q.1

Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events. S-CP.1

- Chapter 8 - Similarity
### Chapter 8 - Similarity

Standards:

Create equations and inequalities in one variable and use them to solve problems. A-CED.1

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G.GPE.5

Prove theorems about triangles. G-SRT.4

Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures. G-SRT.5

- Chapter 9 - Right Triangle Trigonometry
### Chapter 9 - Right Triangle Trigonometry

Standards:

Prove theorems about triangles. G-SRT.4

Understand that by similarity, side ratios in right triangles are properties of the angels in the triangle, leading to definitions of trigonometric ratios for acute angles. G-SRT.6

Explain and use the relationship between the sine and cosine of complementary angles. G-SRT.7

Use trigonometric shapes, their measures, and their properties to describe objects. G-SRT.8

Use geometric shapes, their measures, and their properties to describe objects. G-MG.1

Recognize vector quantities as having both magnitude and direction. Represent vector quantities by directed line segments, and use appropriate symbols for vectors and their magnitudes. N-VM.1

Add and subtract vectors. N-VM.4

Add vectors end-to-end, component-wise, and by the parallelogram rule. Understand that the magnitude of a sum of two vectors is typically not the sum of the magnitudes. N-VM.4a

- Chapter 10 - Surface Area and Volume
### Chapter 10 - Surface Area and Volume

Standards:

Give and informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. G-GMD.1

Give and informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures. G-GMD.2

Use volume formulas for cylinders, pyramids, comes and spheres to solve problems. G-GMD.3

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. G-GMD.4

Use geometry shapes, their measures, and their properties to describe objects. G-MG.1

Apply concepts of density based on areas and volume in modeling situations. G-MG.2

Use units as a way to understand problems and to guide the solution of multi-step problems; choose and interpret units consistently in formulas; choose and interpret the scale and origin in graphs and data displays. N-Q.1

- Chapter 12- Transformations
### Chapter 12- Transformations

Standards:

Represent transformations in the plane using, e.g., transparencies and geometry software; describe transformations as functions that take points in the plane as inputs and give other points as outputs. Compare transformations the preserve distance and angle to those that do not. G-CO.2

Given a rectangle, parallelogram, trapezoid, or regular polygon, describe the rotations and reflections that carry it onto itself. G-CO.3

Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments. G-CO.4

Given a geometric figure and a rotation, reflection, or translations, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another. G-CO.5

Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure; give two figures, use the definition of congruence in terms of rigid motions to decide if the are congruent. G-CO.6

- Chapter 11- Circles
### Chapter 11- Circles

Standards: Identify and describe relationships among inscribed angles, radii, and chords. Include the relationship between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; the radius of a circle is perpendicular to the tangent where the radius intersects the circle. G-C.2

Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle. G-C.3

Construct a tangent line from a point outside a given circle to the circle. G-C.4(+)

Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation. G-GPE.1

Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects. G-GMD.4