Download Geometry: 1-1 Day 1 Points, Lines and Planes

Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-1 Day 1 Points, Lines and Planes
What are the Undefined Terms?
The Undefined Terms are:
What is a Point?
How is a point named?
Example:
What is a Line?
A line is named two ways. What are the two ways?
Give an example of each:
What is a Plane?
There are two ways to name a line. What are the two ways?
Give an example of each.
Define Collinear:
1 Mrs. Hefty Geometry: Chpt. 1 notes Define Noncollinear:
Define intersection:
Exercises
1. Draw and Label a point, line and plane.
Refer to the figure.
2. Name the intersection of plane N and line AE.
3. Name the intersection of BC and DC.
4. Does DC intersect AE? Explain.
Refer to the figure.
5. Name the three line segments that intersect at point A.
6. Name the line of intersection of planes GAB and FEH.
7. Do planes GFE and HBC intersect? Explain.
8. Are G, D and B coplanar?
9. Are F, H, and A coplanar?
10. Are F, H and B coplanar?
2 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-1 Day 2 Points, Lines and Planes
Describe what you see in as many ways as you can.
1.
2.
Draw and label the figure for each relationship
3. Plane N contains line b.
4. Planes R and S intersect at line MN.
3 Mrs. Hefty Geometry: Chpt. 1 notes 5. A, B, and C do not intersect.
4 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-2
Linear Measure
What is the difference between a line and a line segment?
Define congruent:
What is the congruent symbol?
How are congruent segments labeled in a figure?
Discovering Segment Addition Postulate using Sketchpad
1. Construct a line segment
2. Using the select tool, select the line and measure the line segment by going to
measure, length. Move this measurement beside the line segment
3. Place a point on the line
4. Measure the two smaller line segments you have created by selecting the two
point. Go to measure, distance. Move these measurements beside the line
segments they represent.
5. Find the sum of the two smaller segments by going to measure, calculate. Do not
type the lengths of the segments here but click on the segment length in
sketchpad with an addition sign between them.
6. Grab the point that is between the other points with the select tool. Move it
around. What do you notice about the numbers?
Lesson 1-2
Segment Addition Postulate
5 Mrs. Hefty Geometry: Chpt. 1 notes Exercises
1. Find the value of x and KL if K is between J and L.
JK = 2x, KL = x + 2, and JL = 5x – 10
2. Find the value of x and JL if K is between J and L.
JK=x2 – 13x, KL= 2x , and JL= 60.
6 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-3
Distance and Midpoint
Use the number line to find the distance of AB
Use the coordinate plane to find
the distance of KL K (-2, 10), L(-4, 3)
There are two ways.
1. Make a right triangle
2. Use the distance formula. Use this when you do not have a
coordinate plane.
Without a coordinate plane find the distance of EF E(-12, 2), F(-9, 6)
Define Midpoint:
7 Mrs. Hefty Geometry: Chpt. 1 notes Use the number line to find the coordinate of the midpoint of each
segment. CE Find the coordinates of the midpoint
of EF where E (-2, 6), F (-9, 3)
Find the coordinates of the missing
endpoint if E is the midpoint of DF
where D(-3, -8), E(1, -2)
8 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-4 (day 1) Angle Measure
Use your book to complete the following
Define Ray:
How is a ray named? Give an example
Define Opposite Ray:
Draw a picture of opposite rays and name the two rays.
Define angle:
Draw an angle and then identify it’s parts.
Angles are measure in units called ______________
Name the ways to classify the angles, define them and draw a picture.
Exercises
Refer to the figure at the right.
1. Name the vertex of ∠4.
2. Name the sides of ∠BDC.
3. Write another name for ∠DBC.
9 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-4 (day 2) Angle Measure
Complete the sketch in geometer’s sketchpad.
Angle Addition Postulate Sketch
1. Draw an angle
2. Measure each angle my selecting the three points in order that you
would say them if you were naming it. Go to measure, angle. Drag the
measurement by the angle.
3. Draw a ray that is on the interior of the angle by using the line
segment tool.
4. Measure the two angles that are created. Remember to select the
points in order that you would use when naming it. Place the
measurement by the angles.
5. Add the two smaller angles together by going to measure, calculate.
Click on one of the measures, click the add symbol on the calculator,
click on the other measure. Click okay.
6. What do you notice about the sum of those two measures compared to
the original?
Angle Bisector Sketch- Start a new sketch
1. Draw an angle
2. Measure each angle my selecting the three points in order that you
would say them if you were naming it. Go to measure, angle. Drag the
measurement by the angle.
3. Create an angle bisector by selecting the point in order that you would
name the angle, go to construct, angle bisector.
4. Measure the two angles that are created. Remember to select the
points in order that you would use when naming it. Place the
measurement by the angles.
5. What do you notice?
6. What does it mean to bisect an angle?
10 Mrs. Hefty Geometry: Chpt. 1 notes Video lesson 1-4 (day 2) Angle Measure
Angle Addition Postulate:
Angle Bisector:
Congruent angles:
11 Mrs. Hefty Geometry: Chpt. 1 notes Exercises
1. In the figure BA and BC are opposite rays. BF bisects ∠CBE.
If m∠EBF = 6x + 4 and m∠CBF = 7x - 2, find m∠EBF.
2. In the figure BA and BC are opposite rays. BF bisects ∠CBE.
Let m∠1 = m∠2. If m∠ABE = 100 and m∠ABD = 2(r + 5), find r and
m∠DBE
3. In the figure, XP and XT are opposite rays and XQ bisects <PXS.
M<RXQ = 2 x + 7, m<RXP =3x - 11, M<PXS = x + 37. Find m<QXS
12 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-5 (day 1) Angle Relationship
Complete the following Chart using your book
Special Angle Pairs
Adjacent Angles
Definition
Example
Nonexample
Linear Pair
Definition
Example
Nonexample
Vertical Angles
Definition
Example
Nonexample
Define Complementary angles and draw examples
Define Supplementary angles and draw 2 different examples
13 Mrs. Hefty Geometry: Chpt. 1 notes What is the difference between linear pair angles and supplementary
angles?
Define Perpendicular lines
What is the symbol that represents perpendicular?
Draw two lines that are perpendicular. What would you do to the
picture to communicate to others that the lines are perpendicular?
Excercises
Name an angle or angle pair that satisfies each condition.
1. two adjacent angles
2. two acute vertical angles
3. two supplementary adjacent angles
4. an angle supplementary to ∠RTS
For Exercises 5–7, use the figure at the right.
5. Identify two obtuse vertical angles.
6. Identify two acute adjacent angles.
7. Identify an angle supplementary to ∠TNU.
14 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-5 (day 2) Angle Relationship
Vertical angle are two nonadjacent angles that are formed by two
intersecting lines.
Complete the sketch in geometer’s sketchpad
Vertical angles sketch:
1. Using the line segment tool draw two line segments that intersect.
2. Measure all four angles. Remember to click on the point in the order
that you would name the angle. This is not necessarily alphabetically.
Move the measurements to the angle that they represent.
3. Look at the vertical angles. What do you notice about vertical
angles?
4. Using the calculator in sketchpad add two angle that are next to
each other. (if you don’t remember see sketch from 1-4 angle
addition postulate sketch step 5)
Exercises
1. Find the value of y, m∠RPT, and m∠TPW
2. Find the value of x and m∠CBA
15 Mrs. Hefty Geometry: Chpt. 1 notes 3. Find the value of x, then determine if AB
CD
16 Mrs. Hefty Geometry: Chpt. 1 notes Geometry: 1-6 Two-Dimensional Figures
Read pages 56-57 and complete the following
Define Polygon. Draw one and label the parts.
What is the difference between a concaved polygon and a convex
polygon?
Polygons can be classified by the sides. Complete the chart
Number of
sides
3
4
5
6
7
8
9
Polygon Name
Number
of sides
9
10
11
12
13
14
Polygon Name
Lesson Video
Define Equilateral Polygon and draw one.
Define Regular Polygon and draw one.
17 Mrs. Hefty Geometry: Chpt. 1 notes A regular polygon with 3 sides is called_____________________
A regular polygon with four sides is called____________________.
Exercises
Name each polygon by its number of sides. Then classify it as convex or
concave and regular or irregular.
Find the perimeter and area of the following.
Graph the following then find the perimeter and area.
18 Mrs. Hefty Geometry: Chpt. 1 notes 19