## Geometry

### 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**

### 1.2 Poolroom Math

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.

1.2.2 Poolroom Math Worksheet WS

**READ: POOLROOM MATH**

### 1.3 Defining Angles

1.3 Defining Angles powerpoint

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

1.3.1 Investigation - Defining Angles WS

**READ: WHAT’S A WIDGET?**

### 1.4 Polygons

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.

**READ: POLYGONS**

### 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 **

### 1.6 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.

1.6.3 Using Compas and Identify Parts of the Circles Activity

**READ: ****CIRCLES**

### 1.7 Isometric Drawing

1.7 Isometric Drawings powerpoint

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.

1.7.2 More Isometric Cube Shapes WS

**READ: ****SPACE GEOMETRY**

### 1.8 Space Geometry

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.

**READ: ****SPACE GEOMETRY**** ** **CHAPTER 1 TEST REVIEW**

### 2.1 Inductive Reasoning

2.1 Inductive Reasoning powerpoint

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 **

### 2.2 Deductive Reasoning

2.2 Deductive Reasoning powerpoint

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.

2.2.2 Deductive Reasoning Homework WS

2.2.3 Inductive and Deductive Reasoning WS

**READ: DEDUCTIVE REASONING**

### 2.3 Finding the nth Term

2.3 Finding the nth Term powerpoint

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**

### 2.4 Mathematical Modeling

2.4 Mathematical Modeling powerpoint

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**

### 2.5 Angle Relationships

2.5 Angle Relationships powerpoint

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

2.5.3 Prove Angle Pair Relationships WS

**READ: ANGLE RELATIONSHIPS**

### 2.6 Special Angles on Parallel Lines

2.6 Special Angles on Parallel Lines powerpoint

2.6 Special Angles on Paralel Lines pdf

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.

2.6.1 Special Angles on Parallel Lines WS

2.6.2 Angles Associated with Parallel Lines WS

### 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

3.1.3 Duplicating Angles and Segments WS

### 3.2 Constructing Perpendicular Bisectors

3.2 Constructing Perpendicular Bisectors powerpoint

3.2 Constructing Perpendicular Bisectors pdf

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**

### 3.3 Constructing Perpendiculars to a Line

3.3 Constructing Perpendiculars to a line powerpoint

3.3 Constructing Perpendiculars to a line pdf

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.

### 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

An 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.

### 3.5 Constructing Parallel Lines

3.5 Constructing Parallel Lines powerpoint

3.5 Constructing Parallel Lines pdf

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.

3.5.1 Investigation Constructing Parallel Lines by Folding

3.5.2 Constructing Parallel Lines WS

### 3.6 Construction Problems

3.6 Construction Problems powerpoint

In this lesson you will

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

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.

3.6.1 Triangle Constructions WS

**READ: CONSTRUCTION PROBLEMS**

### 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

**READ: ****CONSTRUCTING POINTS OF CONCURRENCY**

### 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**

### 4.1 Triangle Sum Conjecture

### 4.2

### 4.3

### 4.4

### 4.5

### 4.6

### 4.7

### 4.8

### 4.9

### 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.

**READ: POLYGON SUM CONJECTURE**

### 5.2 Exterior Angle Sum

5.2 Exterior Angle Sum powerpoint

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.

**READ: EXTERIOR ANGLE SUM**

### 5.3 Kites and Trapezoids

5.3 Kites and Trapezoids powerpoint

In this lesson you will

● Investigate the properties of **kites**

● Investigate properties of **trapezoids **and **isosceles trapezoids**

A **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**

### 5.4 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

### 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