CHAPTER ONE TIME TO PUT ON YOUR THINKING CAP!

Please find your assigned seat. Sit QUIETLY and begin to fill out the Student Information Sheet on your desk. PLEASE DO NOT TALK! When you finish, read over the class letter.

Get ready!! P

1-1 Points, Lines, and Planes SPACE – the final frontier

Points A point has no dimension- it is simply a location A Point A

Lines Lineor AB A line extends in one dimension Collinear points are points that lie on the same line.

Planes EXTENDS IN 2 DIMENSIONS AT LEAST 3 NON COLLINEAR POINTS Coplanar points are points that lie on the same plane. Plane M or plane ABC A C M B

Intersections A LINE AND A PLANE

TWO PLANES

III. Problems 1. How many different ways can you name a plane with 3 points?

2. Draw the following: Point A lies on line PQ Planes R and S intersect in line l

S OLUTION Points D, E, F lie on the same line, so they are collinear. There are many correct answers. For instance, points H, E, and G do not lie on the same line. Points D, E, F, and G lie on the same plane, so they are coplanar. Also, D, E, F, and H are coplanar. G H F E D Name three points that are collinear. Name four points that are coplanar. Name three points that are not collinear. 3.

Class work Complete p all

Transparency 2 Click the mouse button or press the Space Bar to display the answers. POD # 1

Transparency 2a

Get ready for 1-2 Complete p

1-2 Linear Measure and Precision What is a line segment? Measure a 2 cm line segment. Measure a 1 8/16 inch line segment.

Measuring Segments  What is a postulate?

The Ruler Postulate  The points on any line can be paired with the real numbers so that given any two points P and Q on the line, P corresponds to zero, and Q corresponds to a positive number.

Segment addition postulate  Suppose R is between P and Q, what is true?

AKA-Betweeness of Points Point m is between points p and q only if p, q, and m are all collinear and PM+MQ = PQ.

Problems: 1. AB = 5.3 AC = 6.7, BC = ? 2.BC = 18.9, AC = 23, AB = ?

Problem 3: Find AC. 4.5 A B C

Problem 4: Find BC. 2 ¾ 15 A B C

Problem 5: Find x and PQ if P is between Q and R. PQ = 4x QR = 5x + 1 PR = 82

Problem 6: Find x and ST if T is between S and U. ST = 7x SU = 45 TU = 5x - 3

Precision Find the precision for each measurement. Explain its meaning ¾ inches millimeters

Precision Depends on the smallest unit available on a measuring tool. – Ex. 3 cm means it is between 2.5 and 3.5 cm. Precision is normally measured to the nearest half unit!

Congruent Segments Segments that have the same measure of length.

Art Quiz Grade Draw anything you want using straight lines. Measure at least 20 lines on the back side using cm. Color!

Class work P all Homework p , 56 even

Get Ready for 1-3 Complete p

1-3 Using formulas I. Rectangles Area: Perimeter: l=8 in, w=6 in A=P=

II. Maximum area The Rouses want to build a veggie garden. They want the garden to have at least an area of 15 sq.yds., but they only have 18 yds of wire. What are all the possible whole number dimensions of the garden?

Maximum area Find the maximum area of a rectangle with a perimeter of 36 feet.

CHALLENGE What is the maximum perimeter of a rectangle whose area is 169 sq m?

III. Problems 1. Find P and A if l-6 and w = If P = 26, and w = 3, find l. 3. If A= 48 and l = 6, find w.

ANOTHER CHALLENGE WHAT IS THE LENGTH OF A RECTANGLE THAT HAS A = 20 AND P = 18?

1-3 Distance I. The Coordinate Plane X-axis Y-axis X-coordinate Y-coordinate Ordered pair Collinear

II. Collinear points 1. Find the coordinates of 3 points, graph the points, name a point not on the line (non-collinear): 6x-2y=12.

2. POINTS (5,7) AND (-1,1) LIE ON THE GRAPH OF Y = X + 2 DETERMINE IF THE POINTS ARE COLLINEAR: (1,-1)(-3,-1)

III. The Pythagorean Theorem  Find the distance from A to D if A = -4 and D = 6 on the # line.  Find the distance between points H(2,3), and K(-3,-1).

 IV. The distance formula  D=  Find JK for J(9,-5), and K(-6,12). That formula has warped my fragile little mind !

CHALLENGE  TRIANGLE ABC HAS VERTICES A(-3,2), B(4,-1) AND C (1,6). NAME THE CONGRUENT SIDES AND STATE THEIR LENGTHS.

V. Midpoints and Segment Congruence Midpoint Formulas Theorem

What is the midpoint of a child’s leg? KIDNEY

VI. Problems 3. Find the midpoint of HJ: H is –5 and J is Find the midpoint of VW if V(3,-6) and w (7,2).

3. The midpoint of RQ is P(4,-1). What are the coordinates of R if Q is (3,-2)? 4. U is the midpoint of XY. If XY= 16x-6 and UY= 4x+9, find x and XY.

5. What is the measure of PR if Q is the midpoint of PR? P Q R x – 3x

VII. Segment bisector Any segment, line, or plane that intersects a segment at its midpoint.

Construction Number 2! Segment Bisector

Classwork P

1-4 Exploring Angles I. Angles Ray- part of a line with one endpoint and goes on and on in one direction... Opposite rays- Opposite directions

Angle-two lines that meet at an endpoint called a vertex. An angle can be named by the three letters that form it or by the letter that is at its vertex.

Sides- initial and terminal- two rays Vertex- point two rays meet at to form angle

Interior- inside the angle Exterior-outside the angle

Degrees- units used to measure angles Measure- from 0 to 360 degrees

Angle bisector- splits the Angle into 2 equal parts

II. Kinds of angles Right angle- measuring exactly 90 degrees Obtuse - has a measure of greater than 90 degrees

Acute -Less than 90 degrees Straight-angle measuring exactly 180 degrees Congruent- equal in measure

III. Postulates Protractor- each angle formed using a straight angle is unique Angle addition-

Problems: 1. a.Name all angles that have B as a vertex. b.Name the sides of  2. c.Write another name for  BCD.

2. Measure each angle named and classify it as right, acute, or obtuse. a.  ABC b.  ABD c.  ABF

3. A trellis is often used to provide a frame for vining plants. Some of the angles formed by the slats of the trellis are congruent angles. In the figure,  ABD   FHG. If m  ABD = 3x + 6 and m  FHG = x + 26, find the actual measurements of  ABD and  FHG.

CHALLENGE BC AND DE INTERSECT AT S. T IS IN THE INTERIOR OF BSD AND ANGLE ESB = 2X – Y, ANGLE BST = X AND TSD = Y. FIND X AND Y SO THAT BC IS PERPENDICULAR TO DE.

Construction number 3 ! Copy an angle!

Classwork P P

Get Ready for 1-5 P

1-5 Angle relationships I. Angles formed by intersecting lines Adjacent Linear Pair 5 6

Vertical angles

Problem 1: Name all types of angles formed

In the stair railing shown,  6 has a measure of 130˚. Find the measures of the other three angles. SOLUTION  6 and  7 are a linear pair. So, the sum of their measures is 180˚. m  6 + m  7 = 180˚ 130˚ + m  7 = 180˚ m  7 = 50˚ Problem 2

Solve for x and y. Then find the angle measure. ( x + 15)˚ ( 3x + 5)˚ ( y + 20)˚ ( 4y – 15)˚ D C B A E SOLUTION Use the fact that the sum of the measures of angles that form a linear pair is 180˚. m  AED + m  DEB = 180° ( 3x + 5)˚ + ( x + 15)˚ = 180° 4x + 20 = 180 4x = 160 x = 40 m  AEC + m  CEB = 180° ( y + 20)˚ + ( 4y – 15)˚ = 180° 5y + 5 = 180 5y = 175 y = 35 Use substitution to find the angle measures ( x = 40, y = 35 ). m  AED = ( 3 x + 15)˚ = ( )˚ m  DEB = ( x + 15)˚ = ( )˚ m  AEC = ( y + 20)˚ = ( )˚ m  CEB = ( 4 y – 15)˚ = (4 35 – 15)˚ = 125˚ = 55˚ = 125˚ So, the angle measures are 125˚, 55˚, 55˚, and 125˚. Because the vertical angles are congruent, the result is reasonable. Problem 3

II. Other pairs of angles Complementary supplementary

III. Perpendicular lines

4. The measure of the supplement of an angle is 60 less than three times the measure of the complement of the angle. Find the measure of the angle.

5. The measure of the complement is 3.5 times smaller that the supplement. Find the measure of the angle.

6. Find x and y so that DG and BE are perpendicular.

7. Determine whether each statement can be assumed from the figure. a.  BFC and  AFG are complementary. b.  DFA and  AFG are a linear pair. c.  DFC and  BFC are complementary.

1-6 Polygons Polygon:

No line containing a side of the polygon contains a point in the interior of the polygon. NOT CONVEX

Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon Decagon Undecagon Dodecagon 13-gon 14-gon The pattern continues # of sides Name Regular Polygon A Polygon that is Both equilateral And equiangular (Remember: If a triangle Is equilateral, then it is Equiangular. This only Works for triangles.)

Perimeter Triangle Square rectangle

Perimeter in the coordinate plane Use the distance formula!

Problem 1 Name each polygon by its number of sides. Then classify it as convex or concave and regular or irregular.

2. A landscape designer is putting black plastic edging around a rectangular flower garden that has length 6.4 meters and width 5.7 meters. The edging is sold in 5-meter lengths. a.Find the perimeter of the garden and determine how much edging the designer should buy.

b.Suppose the length and width of the garden are tripled. What is the effect on the perimeter and how much edging should the designer buy?

3. Find the perimeter of triangle ABC if A(4, 4), B(-4, 2) and C(3, -3).

4. The length of a rectangle is five times the width. The perimeter is 4 yards. Find the length of each side.

Classwork and Homework Complete p – 44 even