Name: Date:

Chapter 1: Foundations of Geometry

Essential Understandings: The characteristics and properties of 2 and 3 dimensional geometric shapes can be analyzed to develop mathematical arguments about geometric relationships.

Essential Question: How do algebraic concepts relate to geometric concepts? How do patterns and functions help us represent data and solve real-world problems?

Section 1: Understanding Points, Lines & PlanesObjectives of Lesson: Identify, name, and draw points, lines, segments, rays, and planes. Apply basic facts about points, lines, and planes.

Undefined Terms: ______________________________________________________

________________________________________________________________________

Undefined TermsTerm Name Diagram

A point names a location and has no size. It is represented by a dot.A line is a straight path that has no thickness and extends forever.

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A plane is a flat surface that has no thickness and extends forever.

Collinear: ______________________________________________________

______________________________________________________

Coplanar: ______________________________________________________

______________________________________________________

Examples: Using diagram below1) Name four coplanar points.

2) Name three lines.

3) Name two possible planes.

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Segments and RaysDefinition Name Diagram

Segment:

Endpoint:

Ray:

Opposite Rays:

Examples: Draw and label each of the following. 1) A segment with endpoints U and V.

2) Opposite rays with a common endpoint Q.

3) Draw and label a ray with endpoint M that contains N.

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Postulate: ______________________________________________________

______________________________________________________

Postulates: Points, Lines & Planes1-1-1 Through any two points, there is

exactly one line. 1-1-2 Through any three non-collinear

points there is exactly one plane containing them.

1-1-3 If two points lie in a plane, then the line containing those points lies in the plane.

Examples: Use diagram to answer questions. 1) Name a line that passes through two points.

2) Name a plane that contains three non-collinear points.

Postulates: Intersection of Lines and Planes1-1-4 If two lines intersect, then they intersect in exactly one

point. 1-1-5 If two planes intersect, then they intersect in exactly one

line.

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Homework: Page 9-10: # 1-12 & 25-27

Section 2: Measuring and Constructing Segments

Objectives of Lesson: Use length and midpoint of a segment. Construct midpoints and congruent segments.

Coordinate: ______________________________________________________

______________________________________________________

Distance: ______________________________________________________

______________________________________________________

Length: ______________________________________________________

______________________________________________________

Examples: Find the length of each segment.

1) DC

2) EF

3) FC

4) DE

Congruent Segments: ____________________________________________________________________________________________________________

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Construction: ____________________________________________________________________________________________________________

Examples: Construct a Congruent Segment to AB, call it CD.

A B

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Between: ____________________________________________________________________________________________________________

Postulate 1-2-2 (Segment Addition Postulate)

Examples: Use the segment addition postulate to solve the following problems.

1) B is between A and C, AC = 14 and BC = 11.4. Find AB.

2) S is between R and T. Find RT.

3) Y is between X and Z, XZ = 3, and XY = 1 . Find YZ.

4) E is between D and F. Find DF.

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Midpoint: ____________________________________________________________________________________________________________

Bisect: ____________________________________________________

5) The map shows the route for a race. You are 365m from drink station R and 2km from drink station S. The first-aid station is located at the midpoint of the two drink stations. How far are you from the first-aid station? What is the distance to a drink station located at the midpoint between your current location and the first aid station?

6) B is the midpoint of , AB = 5x, and BC = 3x + 4. Find AB,

BC and AC.

Segment Bisector: ______________________________________________________________________________________________________

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Construction of a Segment BisectorSTEPS

1) Draw line segment if not already given2) Put tip on end point and extend leg past midpoint3) Make arc above and below line segment 4) Repeat steps 2 & from other endpoint5) Draw line through intercepted arcs 6) You now know that:

A B

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Homework: Practice B (1.2)

Section 3: Measuring and Construction Angles

Objectives of Lesson: Name and classify angles. Measure and construct angles and angle bisectors.

Angle: ____________________________________________________________________________________________________________

Vertex: ____________________________________________________________________________________________________________

Examples: Name the following angles

Measure: ____________________________________________________________________________________________________________

Degree: ____________________________________________________________________________________________________________

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Using a Protractor

Types of Angles

Examples: Measuring the following angles1) <AOD

2) <COD

3) <BOA

4) <DOB

5) <EOC

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Congruent Angles: ____________________________________________________________________________________________________________

Practice Constructing Congruent Angles

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Postulate 1-3-2 (Angle Addition Postulate)

Examples: Use angle addition postulate to answer the following questions

1) m<ABD = 37° and m<ABC = 84°. Find m<DBC.

2) m<XWZ = 121° and m<XWY = 59°. Find m<YWZ.

Angle Bisector: ____________________________________________________________________________________________________________

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Practice Constructing Angle Bisectors

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Examples: Find the measure of the following angles1) bisects <ABC, m<ABD = (6x + 3)°, and m<DBC = (8x – 7)°.

Find m<ABD.

2) bisects <PQR, m<PQS = (5y – 1)°, and m<PQR = (8y + 12)°. Find m<PQS.

3) bisects <LJM, m<LJK = (-10x + 3)°, and m<KJM = (-x+ 21)°. Find m<LJM.

Section 4: Pairs of Angles

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Homework: Page 24-25: #4-10; #17-22 & #29-32

Objectives of Lesson: Identify adjacent, vertical, complementary, and supplementary angles. Find measures of pairs of angles.

Pair of AnglesAdjacent Angles:

Linear Pair:

Examples: Tell whether adjacent angles or linear pairs1) < 1 and < 2

2) < 2 and < 4

3) < 1 and < 3

4) < 5 and < 6

5) < 7 and < SPU

6) < 7 and < 8

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Complementary Angles: ____________________________________________________________________________________________________________

Supplementary Angles: ____________________________________________________________________________________________________________Examples: Find the measure of each of the following.

1) Complement of <M.

2) Supplement of <N.

3) Complement of <E.

4) Supplement of <F.

5) An angle is 3 less than twice the measure of its complement. Find the measure of its complement.

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6) An angle’s measure is 12° more than ½ the measure of its supplement. Find the measure of the angle.

7) Light passing through a fiber optic cable reflects off the walls in such a way that <1 <2. <1 and <3 are complementary, and <2 and <4 are complementary. If m<1 = 38°, find m<2, m<3, and m<4.

Vertical Angles: ______________________________________________________________________________________________________

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Homework: Page 31-32: # 14-22 & 26-31