Presentation on theme: "Chapter 1: Tools of Geometry"— Presentation transcript:
1Chapter 1: Tools of Geometry Lesson 1: Points, Lines and Planes
2Definitions 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 linePlane- flat surface made from points that has no depth and extends in all directions infinitelyCoplanar- points or lines on the same planeSpace- boundless, 3-D set of all points that contains lines and planes
3Chapter 1 FoldableStep 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 creaseStep 3- Cut the folded flaps along the crease so that there are now 4 flaps
4Upper 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.
5Copy the notes into the foldable, then draw and label your own examples based on the information in the chart.NameModelDrawnNamed ByFactsWords/SymbolsExamplesPointAs a dotA capitol letterA point has neither size nor shapepoint PLineWith an arrowhead at both endsTwo letters representing points on the line- or the script letterThere is exactly 1 line through any two pointsline nline ABline BAPlaneAs a shaded, slanted, 4-sided figureA capital script letter or by any three letters of non-collinear pointsThere is exactly 1 plane through any three non-collinear pointsplane Splane XYZplane XZYplane ZXYplane ZYXplane YXZplane YZXPnBAXYZS
6A. 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.
7A. 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.
15Find a if AB = 4a + 10, BC = 3a – 5, and AC = 19.
16Chapter 1: Tools of Geometry Lesson 3: Distance and Midpoint
17DefinitionsMidpoint- the point on a segment that divides the segment into two congruent segmentsSegment bisector- any line, segment or plane that intersects a segment at its midpoint
18Distance and MidpointDistance Formula- used to find the length of a segment.ex: Find the distance betweenA (5,1) and B (-3, -3).*on a number line- subtract the endpoint valuesMidpoint Formula- used to find the point half way down a segmentex: Find the midpoint of JK ifJ(-1,2) and K(6, 1)* on a number line- add the endpoint values and divide by 2
19Use the number line to find the midpoint and the measure of AX.
20Find the midpoint and distance between E(–4, 1) and F(3, –1).
24Find LM. Assume that the figure is not drawn to scale.
25Find the value of x and ST if T is between S and U, ST = 7x, SU = 45, and TU = 5x – 3.
26Find the value of n and WX if W is between X and Y, WX = 6n – 10, XY = 17, and WY = 3n.
27Chapter 1: Tools of Geometry Lesson 4: Angle Measure
28Definitions 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 endpointSides of an angle- raysVertex- the common endpoint of the rays of an angleAngle Bisector- a ray or line that divides an angle into two congruent angles
29Naming and Classifying Angles -B is the vertex-ray BA and ray BC are the sides( BA and BC )-Angle names:ABC, CBAB,-Angle bisector : makes 2 congruent anglesNameMeasureModelRight Angle90Acute AngleLess than 90(0 < x < 90)Obtuse AngleBetween 90 and 180(90 < x < 180)4BC
30A. Name all angles that have B as a vertex. B. Name the sides of 5.C.
31A. 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.
32Chapter 1: Tools of Geometry Lesson 5: Angle Relationships
33DefinitionsAdjacent angles: two angles that lie in the same plane, have a common vertex and a common side, but no common interior pointsVertical angles: two nonadjacent angles formed by two intersecting linesLinear pair: a pair of adjacent angles with non-common sides that are opposite raysComplementary angles: two angles with measures that add up to 90Supplementary angles: two angels with measures that add up to 180Perpendicular ( ): lines, segments or rays that form right angles