Category: Geometry



5.5 Properties of Parallelograms

5.5 Properties of Parallelograms powerpoint

5.5 Properties of Parallelograms pdf

 

In this lesson you will

 

● Discover how the angles of a parallelogram are related

● Discover how the sides of a parallelogram are related

● Discover how the diagonals of a parallelogram are related

 

You have explored properties of kites and trapezoids and of the midsegments of triangles and trapezoids.

In this lesson you will explore properties of parallelograms.

 

 

5.5 Properties of Parallelograms Practice WS

5.5 Properties of Parallelograms Exam WS

 

 

READ: PROPERTIES OF PARALLELOGRAMS

5.4 Properties of Midsegments

5.4 Properties of Midsegments powerpoint

5.4 Properties of Midsegments pdf

 

In this lesson you will

 

● Discover properties of the midsegment of a triangle

● Discover properties of the midsegment of a trapezoid

 

 

 

In Chapter 3, you learned that a midsegment of a triangle is a segment connecting the midpoints of two sides.

In this lesson you will investigate properties of midsegments.

 

5.4 Midsegment of a Triangle Homework

5.4 Midsegment of a Trapezoid Homework

 

 

READ: PROPERTIES OF MIDSEGMENTS

5.3 Kites and Trapezoids

5.3 Kites and Trapezoids powerpoint

5.3 Kites and Trapezoids pdf

 

In this lesson you will

 

● Investigate the properties of kites

● Investigate properties of trapezoids and isosceles trapezoids

kite is a quadrilateral with two distinct pairs of congruent consecutive sides.

The angles between congruent sides are called vertex angles. We’ll refer to the other two angles as nonvertex angles.

A kite has one line of reflectional symmetry, just like an isosceles triangle.

 

A trapezoid is a quadrilateral with exactly one pair of parallel sides.

The parallel sides are called bases.

A pair of angles that share a base as a common side are called base angles.  

 

5.3 Kites and Trapezoids Homework

 

READ: KITES & TRAPEZPIDS

 

5.2 Exterior Angle Sum

5.2 Exterior Angle Sum powerpoint

5.2 Exterior Angle Sum pdf

 

In this lesson you will

 

● Find the sum of the measures of one set of exterior angles of a polygon

● Derive two formulas for the measure of each angle of an equiangular polygon

In Lesson 5.1, you discovered a formula for the sum of the measures of

the interior angles of any polygon.

In this lesson, you will find a formula for the sum of the measures of a set of exterior angles.

 

 

To create a set of exterior angles of a polygon, extend each side of the polygon to form one exterior angle at each vertex.

5.1 and 5.2 Worksheet.pdf

 

READ: EXTERIOR ANGLE SUM

5.1 Polygon Sum Conjecture (Interior Angle Sum)

5.1 Polygon Sum Conjecture powerpoint

5.2 Polygon Sum Conjecture pdf

 

In this lesson you will

 

● Discover a formula for finding the sum of the angle measures for any polygon

● Use deductive reasoning to explain why the polygon sum formula works

Triangles come in many different shapes and sizes.

However, as you discovered in Chapter 4, the sum of the angle measures of any triangle is 180°.

In this lesson you will investigate the sum of the angle measures of other polygons.

After you find a pattern, you’ll write a formula that relates the number of sides

of a polygon to the sum of the measures of its angles.

 

5.1 Exercise 12 (HW 1)

 

 

READ: POLYGON SUM CONJECTURE

4.9

4.8

4.7

4.6

4.5

4.4

4.3

4.2

4.1 Triangle Sum Conjecture

3.6 Construction Problems

3.6 Construction Problems powerpoint    tool 1

3.6 Construction Problems pdf

 

In this lesson you will

● Construct polygons given information about some of the sides and angles

 

tool 2

In this chapter you have learned to construct congruent segments and angles, angle and segment bisectors, perpendiculars, perpendicular bisectors, and parallel

lines. Once you know these basic constructions, you can create more advanced geometric figures.

 

 

construction

 

3.6.1 Triangle Constructions WS

3.6.2 Constructions Summary    tool 3

 

 

 

 

 

 

READ: CONSTRUCTION PROBLEMS

3.5 Constructing Parallel Lines

3.5 Constructing Parallel Lines powerpoint

3.5 Constructing Parallel Lines pdf

 

parallel lines

 

In this lesson you will
● Construct parallel lines using patty paper and a straightedge

As you learned in Chapter 1, parallel lines are lines that lie in the same plane and do not intersect. So, any two points on one parallel line will be equidistant from the other line. You can use this idea to construct a line parallel to a given line.

 

train

3.5.1 Investigation Constructing Parallel Lines by Folding

3.5.2 Constructing Parallel Lines WS

 

READ: CONSTRUCTING PARALLEL LINES

3.4 Constructing Angle Bisectors

3.4 Constructing Angle Bisectors powerpoint

3.4 Constructing Angle Bisectors pdf

 

In this lesson you will

 

● Construct an angle bisector using patty paper and a straightedge, and using a compass and a straightedge

● Complete the Angle Bisector Conjecture

 

StepsAn angle bisector is a ray that divides an angle into two congruent angles. You can also refer to a segment as an angle bisector if the segment lies on the ray and passes through the angle vertex.

 

 

 

 

 

READ: CONSTRUCTING ANGLE BISECTORS

3.3 Constructing Perpendiculars to a Line

3.3 Constructing Perpendiculars to a line powerpoint

3.3 Constructing Perpendiculars to a line pdf

perpendicular

 

In this lesson you will

 

● Construct the perpendicular to a line from a point not on the line

● Complete the Shortest Distance Conjecture

● Learn about altitudes of triangles

In Lesson 3.2, you learned to construct the perpendicular bisector of a segment. In this lesson you will use what you learned to construct the perpendicular to
a line from a point not on the line.

 

Altitude

 

 

READ: CONSTRUCTING PERPENDICULARS TO A LINE

3.8 The Centroid

3.7 and 3.8  Constructing Points of Concurrency and Centroid powerpoint

3.7 and 3.8 Constructing  Points of Concurrency and Centroid pdf

 

 

 

 

 

 

 

 

 

In this lesson you will

 

● Review how to construct the incenter, circumcenter, and orthocenter of a triangle

● Make conjectures about the properties of the incenter and circumcenter of a triangle

 

 

We will be working on Points of Concurrency Project. See 3.7 for details.

 

READ: THE CENTROID

 

 

 

3.7 Points of Concurrency

3.7 and 3.8 Review Points of Concurrency powerpoint

3.7 and 3.8 Review Points of Concurrency pdf

 

 

 

 

 

 

In this lesson you will

● Review how to construct the incenter, circumcenter, and orthocenter of a triangle

● Make conjectures about the properties of the incenter and circumcenter of a triangle

 

You can use the constructions you learned in this chapter to construct special segments related to triangles.

In this lesson you will construct the angle bisectors and altitudes of a triangle, and the perpendicular bisectors of a triangle’s sides.

After you construct each set of three segments, you will determine whether they are concurrent.

 

3.7.1 Points of Concurrency Project

3.7.2 All 4 Triangles

READ: CONSTRUCTING POINTS OF CONCURRENCY

 

3.2 Constructing Perpendicular Bisectors

3.2 Constructing Perpendicular Bisectors powerpoint

3.2 Constructing Perpendicular Bisectors pdf

 

post office

The island shown at right has two post offices. The postal service  wants to divide the island into two zones so that anyone within each zone is always closer to their own post office

than to the other one.

 

 

What to do?

 

In this lesson you will

 

● Construct the perpendicular bisector of a segment using patty paper and a straightedge, and using a compass and straightedge

● Complete the Perpendicular Bisector Conjecture

● Learn about medians and midsegments of triangles

● Find the answer on the post office question

 

 

READ: CONSTRUCTING PERPENDICULAR BISECTORS

 

3.1 Duplicating Angles and Segments

 

3.1 Duplicating Angles and Segments powerpoint

3.1 Duplicating Angles and Segments pdf

 

In this lesson you will

 

● Learn what it means to create a geometric construction

● Duplicate a segment by using a straightedge and a compass and by using patty paper and a straightedge

Duplicate an angle by using a straightedge and a compass and by using patty paper and a straightedge

 

           

 

 

3.1.1 Investigation Duplicating Angles and Segments

3.1.2 Constructions

3.1.3 Duplicating Angles and Segments WS

 

READ: DUPLICATING ANGLES AND SEGMENTS

2.4 Mathematical Modeling

2.4 Mathematical Modeling powerpoint

2.4 Mathematical Modeling ppt

 

handshakes

 

 

 

 

 

 

 

 

 

In this lesson you will

 

● Attempt to solve a problem by acting it out

● Create a mathematical model for a problem

● Learn about triangular numbers and the formula for generating them

 

 

READ: MATHEMATICAL MODELING

2.3 Finding the nth Term

2.3 Finding the nth Term powerpoint

2.3 Finding the nth Term pdf

 

2.3 Finding the nth term

 

 

 

 

 

 

 

In this lesson you will

 

● Learn how to write function rules for number sequences with a constant difference

● Write a rule to describe a geometric pattern

● Learn why a rule for a sequence with a constant difference is called a linear function

 

2.3.1 Investigation “Finding the Rule”

2.3.2 Finding the nth Term WS - solutions

 

READ: FINDING NTH TERM

2.2 Deductive Reasoning

2.2 Deductive Reasoning powerpoint

2.2 Deductive Reasoning pdf

 

inductive vs deductive

In this lesson you will

● Learn about deductive reasoning

● Use deductive reasoning to justify the steps in the solution of an equation

● Use a deductive argument to explain why a geometric conjecture is true

 

 

To explain why a conjecture is true, you need to use deductive reasoning. Deductive reasoning is the process of showing that certain statements follow logically from accepted facts.

 

2.2.1 Deductive Reasoning WS

2.2.2 Deductive Reasoning Homework WSlogic

2.2.3 Inductive and Deductive Reasoning WS

 

READ: DEDUCTIVE REASONING

2.1 Inductive Reasoning

2.1 Inductive Reasoning powerpoint

2.1 Inductive Reasoning pdf

 

sherlock holmes

 

In this lesson you will

● Learn how inductive reasoning is used in science and mathematics

● Use inductive reasoning to make conjectures about sequences of numbers and shapes

Inductive reasoning is the process of observing data, recognizing patterns, and making generalizations based on those patterns. You probably use inductive reasoning all the time without realizing it. For example, suppose your history teacher likes to give “surprise” quizzes. You notice that, for the first four chapters of the book, she gave a quiz the day after she covered the third lesson. Based on the pattern in your observations, you might generalize that you will have a quiz after the third lesson of every chapter. A generalization based on inductive reasoning is called a conjecture.

2.1.1 Inductive Reasoning WS  - solutions

2.1.2 Patterns and Inductive Reasoning  WS 

READ: INDUCTIVE REASONING 

1.8 Space Geometry

1.8 Space Geometry powerpoint

1.8 Space Geometry pdf

 

 

 

 

 

 

In this lesson you will

● Learn about the space

● Learn the names of common three-dimensional objects and how to draw them

● Solve problems that require you to visualize objects in space

The work you have done so far has involved objects in a single plane. In this lesson you will need to visualize objects in three dimensions, or space.

In geometry, it is important to be able to recognize three-dimensional objects from two-dimensional drawings, and to create drawings that represent three-dimensional objects.

1.8.1 Sketch Me Now!

1.8.2 More Nets of Solids

1.8.3 Cross Sections

 1.8.4 Space Geometry

READ: SPACE GEOMETRY    CHAPTER 1 TEST REVIEW

 

1.7 Isometric Drawing

1.7 Isometric Drawings powerpoint

1.7 Isometric Drawings pdf

 

 

In this lesson you will

● Learn about the space

● Learn how to do the Isometric Drawing

● Solve problems that require you to visualize objects in space

The work you have done so far has involved objects in a single plane. In this lesson you will need to visualize objects in three dimensions, or space.

In geometry, it is important to be able to recognize three-dimensional objects from two-dimensional drawings, and to create drawings that

represent three-dimensional objects.

 

1.7.1 Isometric Paper WS

1.7.2 More Isometric Cube Shapes WS

 

READ: SPACE GEOMETRY

2.6 Special Angles on Parallel Lines

2.6 Special Angles on Parallel Lines powerpoint

2.6 Special Angles on Paralel Lines pdf

 

highway

 

In this lesson you will

● Make three conjectures about the angles formed when two parallel lines are intersected by a transversal

● Determine whether the converse of each conjecture is true

● Prove one of the conjectures assuming one of the other conjectures is true

 

A line that intersects two or more coplanar lines is called a transversal. There are three types of angle pairs formed when a transversal intersects two lines. In the investigation you will look at the angles formed when a transversal intersects two parallel lines.

transversal

 

2.6.1 Special Angles on Parallel Lines WS

2.6.2 Angles Associated with Parallel Lines WS

 

 

READ: SPECIAL ANGLES ON PARALLEL LINES

2.5 Angle Relationships

2.5 Angle Relationships powerpoint

2.5 Angle Relationships pdf         

 

In this lesson you will

● Make a conjecture about angles that form a linear pair

● Make and prove a conjecture about pairs of vertical angles

● Write the converse of an “if-then” statement and determine whether it is true

In this lesson you will use inductive reasoning to discover some geometric relationships involving angles.

 

 

 

 

 

 

2.5.1 Investigation Linear and Vertical Pair of Angles

2.5.2 Angle Relationships WS

2.5.3 Prove Angle Pair Relationships WS

 

 

READ: ANGLE RELATIONSHIPS

1.6 Circles

1.6 Parts of the Circe (Part 1) powerpoint

1.6 Parts of the Circe (Part 1) pdf

1.6 Parts of the Circe (Part 2) powerpoint

1.6 Parts of the Circe (Part 2) pdf

In this lesson you will

●Learn the definition of circle

●Write definitions for chord,diameter,and tangent

●Learn about three types of arcs and how they are measured

A circleis the set of all points in a plane that are a given distance from a given point.The given distance is called the radius and the given point is called the center.

1.6.1 Parts of the Circle WS

1.6.2 Circles WS

 1.6.3 Using Compas and Identify Parts of the Circles Activity

READ: CIRCLES

1.5 Triangles and Quadrilaterals

1.5 Triangles and Special Quadrilaterals powerpoint

1.5 Triangles and Special Quadrilaterals pdf

In this lesson you will

●Learn how to interpret geometric diagrams

●Write definitions for types of triangles

●Write definitions for special types of quadrilaterals

 

When you look at a geometric diagram,you must be careful not to assume too much from it.For example,you should not assume that two segments that appear to be the same length actually are the same length,unless they are marked as congruent.

 

 

 

 

 

1.5.1 Triangles and Special Quadrilaterals WS 

 1.5.2 Quadrilaterals Toolkit WS

 

READ: TRIANGLES                     READ: QUADRILATERALS 

1.4 Polygons

1.4 Polygons powerpoint

1.4 Polygons pdf

In this lesson you will

●Learn the definition of polygon

●Learn the meaning of terms associated with polygons,such as concave,convex,equilateral,equiangular,and regular

●Identify congruent polygons

 

A polygon is a closed figure in a plane,formed by connecting line segments end point to endpoint with each segment intersecting exactly two others.

 

 

 

 

1.4.1 Polygons WS

 

READ: POLYGONS

 

1.3 Defining Angles

1.3 Defining Angles powerpoint

1.3 Defining Angles pdf

In this investigation we will write definitions for some important terms related to angles.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 1.3.1 Investigation - Defining Angles WS

1.3.2 Defining Angles WS

 

READ: WHAT’S A WIDGET?

1.2 Poolroom Math

1. 2 Poolroom Math powerpoint

1.2 Poolroom Math pdf

In this lesson you will

●Learn about angles and how to measure them

●Identify congruent angles and angle bisectors

●Use your knowledge of angles to solve problems involving pool

An angle is two rays with a common endpoint, provided the two rays do not lie on the same line.

 

 

 

 

 

 

 

 

 

 

 

1.2.1 Angle Measuring WS

1.2.2 Poolroom Math Worksheet WS

 

READ: POOLROOM MATH

1.1 Building Blocks of Geometry

 

 

 

 

 

1.1 Building Blocks of Geometry powerpoint

1. 1 Building Blocks of Geometry pdf

1.1. Midpoint of a Segment powerpoint

1.1. Midpoint of a Segment pdf

 

In this lesson you will

●Learn about points, lines,and planesand how to represent them
●Learn definitions of collinear,coplanar,line segment, congruent segments, midpoint,and ray
●Learn geometric notation for lines, line segments, rays,and congruence

Points,lines,and planesare the building blocks of geometry.

Using these threeundefined terms,you can define all other geometric figures and terms.Keep a list of definitions in your notebook.

 

 

 

 1.1.1 Building Blocks in Geometry WS

 

READ: BUILDING BLOCKS OF GEOMETRY