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**Chapter 1: Tools of Geometry**

Lesson 1: Points, Lines and Planes

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**Definitions Point- represents a location**

Line- made up of points and has no thickness or width, extends infinitely at both ends (cannot be measured) Collinear- points on the same line Plane- flat surface made from points that has no depth and extends in all directions infinitely Coplanar- points or lines on the same plane Space- boundless, 3-D set of all points that contains lines and planes

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Chapter 1 Foldable Step 1- fold the construction paper in half both by width and length (hamburger and hotdog) Step 2- Unfold the paper and hold width wise, fold in the ends until they meet at the center crease Step 3- Cut the folded flaps along the crease so that there are now 4 flaps

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**Upper Left flap- Lesson 1.1 Points, Lines and Planes**

Label the outside of the flap with the lesson number and title. Inside the flap create a grid with 7 columns and 4 rows.

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Copy the notes into the foldable, then draw and label your own examples based on the information in the chart. Name Model Drawn Named By Facts Words/ Symbols Examples Point As a dot A capitol letter A point has neither size nor shape point P Line With an arrowhead at both ends Two letters representing points on the line- or the script letter There is exactly 1 line through any two points line n line AB line BA Plane As a shaded, slanted, 4-sided figure A capital script letter or by any three letters of non-collinear points There is exactly 1 plane through any three non-collinear points plane S plane XYZ plane XZY plane ZXY plane ZYX plane YXZ plane YZX P n B A X Y Z S

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**A. Use the figure to name a line containing point K.**

B. Use the figure to name a plane containing point L. C. Use the figure to name the plane two different ways.

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**A. Name the geometric shape modeled by a 10 12 patio.**

B. Name the geometric shape modeled by a water glass on a table. C. Name the geometric shape modeled by a colored dot on a map used to mark the location of a city. D. Name the geometric shape modeled by the ceiling of your classroom.

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**A. How many planes appear in this figure?**

B. Name three points that are collinear. C. Are points A, B, C, and D coplanar? Explain.

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**Chapter 1: Tools of Geometry**

1.2 Linear Measure

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Definitions Line segment- part of a line that has two endpoints and can be measured(named by the letters marking the endpoints) Congruent- same shape and size (segments that have the same measure)

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A. Find LM. B. Find XZ.

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**C. Find x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.**

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Find SE.

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**Find a if AB = 4a + 10, BC = 3a – 5, and AC = 19.**

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**Chapter 1: Tools of Geometry**

Lesson 3: Distance and Midpoint

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Definitions Midpoint- the point on a segment that divides the segment into two congruent segments Segment bisector- any line, segment or plane that intersects a segment at its midpoint

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Distance and Midpoint Distance Formula- used to find the length of a segment. ex: Find the distance between A (5,1) and B (-3, -3). *on a number line- subtract the endpoint values Midpoint Formula- used to find the point half way down a segment ex: Find the midpoint of JK if J(-1,2) and K(6, 1) * on a number line- add the endpoint values and divide by 2

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**Use the number line to find the midpoint and the measure of AX.**

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**Find the midpoint and distance between E(–4, 1) and F(3, –1).**

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**Find the distance and midpoint of AM**

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**Find the coordinates of R if N (8, –3) is the midpoint of RS and S has coordinates (–1, 5).**

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**Find LM. Assume that the figure is not drawn to scale.**

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**Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.**

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**Find the value of n and WX if W is between X and Y, WX = 6n – 10, XY = 17, and WY = 3n.**

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**Chapter 1: Tools of Geometry**

Lesson 4: Angle Measure

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**Definitions Degree- the unit of measurement for an angle**

Ray- a part of a line which has one endpoint and one end that extends infinitely (name with the endpoint first and then any other point on the ray) Opposite rays- two rays that share an endpoint and extend in opposite directions (together they make a line) Angle- formed by two non-collinear rays that have a common endpoint Sides of an angle- rays Vertex- the common endpoint of the rays of an angle Angle Bisector- a ray or line that divides an angle into two congruent angles

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**Naming and Classifying Angles**

-B is the vertex -ray BA and ray BC are the sides( BA and BC ) -Angle names: ABC, CBA B, -Angle bisector : makes 2 congruent angles Name Measure Model Right Angle 90 Acute Angle Less than 90 (0 < x < 90) Obtuse Angle Between 90 and 180 (90 < x < 180) 4 B C

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**A. Name all angles that have B as a vertex.**

B. Name the sides of 5. C.

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**A. Measure TYV and classify it as right, acute, or obtuse.**

B. Ray YT bisects angle SYU. Angle TYS = 2x-24, angle UYT = x+16. Find x and the measure of angle SYU.

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**Chapter 1: Tools of Geometry**

Lesson 5: Angle Relationships

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Definitions Adjacent angles: two angles that lie in the same plane, have a common vertex and a common side, but no common interior points Vertical angles: two nonadjacent angles formed by two intersecting lines Linear pair: a pair of adjacent angles with non-common sides that are opposite rays Complementary angles: two angles with measures that add up to 90 Supplementary angles: two angels with measures that add up to 180 Perpendicular ( ): lines, segments or rays that form right angles

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**Angle Relationship examples**

Adjacent angles Vertical angles Linear pair Complementary angles Supplementary angles Perpendicular lines D M A O C B L N E D B A 72 18 C R U S V 40 140 T

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**A. Name two adjacent angles whose sum is less than 90.**

B. Name two acute vertical angles.

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Find the measures of two supplementary angles if the measure of one angle is 6 less than five times the measure of the other angle.

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**A. Name an angle supplementary to BEC.**

B. Name a linear pair whose vertex is E. C. Name two acute vertical angles.

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Find the measures of two complementary angles if one angle measures six degrees less than five times the measure of the other.

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**The supplement of A measures 140 degrees**

The supplement of A measures 140 degrees. What is the measure of the complement of A?

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**ALGEBRA Find x and y so that KO and HM are perpendicular.**

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