Bell Work 1) Sketch a ray with an initial point at B going through A

Slides:



Advertisements
Similar presentations
Chapter 1 Basics of Geometry
Advertisements

Defined Terms and Postulates April 3, Defined terms Yesterday, we talked about undefined terms. Today, we will focus on defined terms (which are.
Warm Up Find the values of y by substituting x = 2, 3, y = 3x-1 2. y = 4(x+3) 3. y = 8(x+4) + x(8+x)
Geometry Review Test Chapter 2.
1.3 Segments and Their Measures
Focus Graph and label the following points on a coordinate grid.
Use Segments and Congruence
1.3 What you should learn Why you should learn it
California State Standards 1. Understand and Use undefined terms, axioms, theorems, and inductive and deductive reasoning 15. Use the Pythagorean Theorem.
Measure and classify Angles
1.4 Angles and Their Measures
Section 1-4: Measuring Segments and Angles
Geometry Ch 1.1 Notes Conjecture – is an unproven statement that is based on observation Inductive Reasoning – is a process used to make conjectures by.
Tools of Geometry Chapter 1 Vocabulary Mrs. Robinson.
Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC.
1-2: Measuring & Constructing Segments. RULER POSTULATE  The points on a line can be put into a one-to-one correspondence with the real numbers.  Those.
Chapter 1 Basics of Geometry.
GEOMETRY Chapter 1. CONTENTS Naming Figures Naming Figures Describing Figures Describing Figures Distance on a number line Distance on a number line Distance.
Angles and Their Measures
Points, Lines, and Planes Sections 1.1 & 1.2. Definition: Point A point has no dimension. It is represented by a dot. A point is symbolized using an upper-case.
1-3 and 1-4 Measuring Segments and Angles. Postulate 1-5 Ruler Postulate The point of a line can be put into a one- to-one correspondence with the real.
DO NOW. Ruler Postulate The distance between any two points on the number line is the absolute value of the difference of their positions. AB = |a –
Some Basic Figures Points, Lines, Planes, and Angles.
PLANES, LINES AND POINTS A B A A B C A B C m A.
Mind on Math Complete the “Work Together” in your note packet with your partner.
Geometry 1 Unit 1: Basics of Geometry
1.3 Segments and Their Measures Learning Targets: I can use segment postulates. I can use the Distance Formula to measure distances.
Section 1-4 Angles and their Measures. Angle Formed by two rays with a common endpoint –T–The rays are the sides of the angle –T–The common endpoint is.
1.6 Angles and Their Measures
Angles and Their Measures
1.4 Measure and Classify Angles. Definitions Angle – consists of two different rays with the same endpoint. B C vertex The rays are the sides of the angle.
Answers to homework (page 11 in packet) problems
Lesson: Segments and Rays 1 Geometry Segments and Rays.
Chapter 1 Essentials of Geometry. 1.1 Identifying Points, Lines, and Planes Geometry: Study of land or Earth measurements Study of a set of points Includes.
1.3 Segments and Their Measures
Lesson 1-1 Point, Line, Plane Modified by Lisa Palen.
1.4 Angles and Their Measures. Objectives: Use angle postulates Classify angles as acute, right, obtuse, or straight.
1-2: Measuring & Constructing Segments. RULER POSTULATE  The points on a line can be put into a one-to-one correspondence with the real numbers.  Those.
1.3 Segments, Rays, and Distance. Segment – Is the part of a line consisting of two endpoints & all the points between them. –Notation: 2 capital letters.
Goal 1: Use segments postulates Goal 2: Use the distance Formula to measure distances. CAS 1,15,17.
Chapter 1-2 (Segments and Congruence)
Basics of Geometry Chapter Points, Lines, and Planes Three undefined terms in Geometry: Point: No size, no shape, only LOCATION.  Named by a single.
Lesson 1-4 Angles (page 17) Essential Question How are the relationships of geometric figures used in real life situations?
Warm - up Draw the following and create your own intersection –Line AB and line t intersecting –Plane Q and line XY intersecting –Plane K and plane M intersecting.
1-4: Measuring Angles. Parts of an Angle Formed by the union of two rays with the same endpoint. Called sides of the angle Called the vertex of the angle.
Points, Lines, and Planes. Even though there is no formal definition for these terms, there is general agreement of their meaning: A point is a dimensionless.
Chapter 1: Basics of Geometry
Defined Terms and Postulates
Basics of Geometry Chapter 1.
GEOMETRY Chapter 1.
1.3 Segments and Their Measures
Measuring and Constructing Line Segments
Points, Lines, and Planes
Section 1.2 – Use Segments and Congruence
Let’s Get It Started Find the next two terms and describe the sequence in words: 5, 25, 125, 625, , 1, 4, 9, 16, 25, , 3,125 and 15,625.
1.3 Segments & Their Measures
Segments and Their Measures
1.4 Angles and Their Measures
Let’s Get It Started Find the next two terms and describe the sequence in words: 5, 25, 125, 625, , 1, 4, 9, 16, 25, , 3,125 and 15,625.
Chapter 1 Exploring Geometry: Points, Lines, and Angles in the Plane
1.4 Angles and Their Measures
1-2 Vocabulary coordinate distance length construction between
Section 1.3 Segments and Their Measures
Chapter 1 Section 2 Measuring and Constructing Segments
Chapter 1 Basics of Geometry.
Chapter 1 Basics of Geometry.
1.3 Segments & Their Measures
1.3 Segments and Their Measures
Understanding Points, 1-1 Lines, and Planes Warm Up
Presentation transcript:

Bell Work 1) Sketch a ray with an initial point at B going through A 2) Sketch collinear points A, B, C that are not collinear to D 3) Find the next 3 in the sequence and describe the pattern: -3, 3, 9, 15,… 4)

Outcomes I will be able to: 1)Measure and Calculate segment lengths 2) Calculate Distances using the Distance Formula 3) Use the Angle Postulates 4)Classify Angles as acute, right, obtuse or straight

Agenda 1) Bell Work 2) Outcomes 3) Building Blocks continued 4) Finding Segment Length 5) Using the Distance Formula

Geometric Proof Most things in Geometry must be proven. Theorems – Rules that must be proven However, a few things exist that do not need to be proven. Postulates or Axioms – Rules that are accepted without proof.

Segment Measure Ruler Postulate – Points on a line can be matched one to one with real numbers. The real number that corresponds to a point is the Coordinate. The Distance between two points A and B, written as AB, is the absolute value of the difference between the coordinates of A and B. AB is also called the length of AB. *Note: Absolute values are always positive. This is because absolute values represent the distance from 0. See Page 17 AB =l x₂ - x₁l x₁ x₂

Segment Measure What is the measure of Segment MN? What is the measure of Segment NP? What is the measure of Segment MP? When three points are on one line, you can say that one point is between the other two. Segment Addition Postulate- If a point is between another two, we can find the distance of the larger segment by adding the two smaller segments.

Segment Measure OR… Segment Addition Postulate- If B is between A and C, then AB + BC = AC. And… If AB + BC = AC , then B is between A and C. Label segments AB, BC and AC. A B C

Examples 1. Two friends leave their homes and walk in a straight line towards the other’s house. When they meet, one has walked 578 feet and the other has walked 498 feet. How far apart are the two homes?

Examples 2. A U-haul with a trailer has a total length of 35 feet. If the trailer is 29 feet, how long is the cab?

Examples 3. Suppose J is between H and K. Use the Segment Addition Postulate to solve for x. Then find the length of each segment. HJ = 2x + 4 JK = 3x + 3 KH = 22

Distance Formula Distance Formula – If A (x1, y1) and B (x2, y2) are points in a coordinate plane, then the distance between A and B is… Distance Formula – How can we relate the distance formula to measurement of segments and Pythagorean Theorem?

Length ***Note: If we are finding the length of the segment between points, we denote it by: mAB not AB ***This is so we know we are talking about the measurement and not the segment itself.

Congruent Segments Congruent Segments – Segments that have the same length Lengths are equal Segments are congruent AB = CD AB ≅ CD “The length of AB is equal to the length of CD” “AB is congruent to CD”

Example Plot A(-1, 1) B(-4, 3), C(3, 2) and D(2, -1). Draw line segments AB, AC, and AD. Find the length of each segment. Are any of them congruent? Yes, AB is congruent to AD

Distance Formula With a partner find distance between: 1)A and B 2)D and E 3)A and C 4)E and C 5)B and D ***Be ready to share your answers

Simplifying Radicals When simplifying radicals, sometimes it helps to use a Prime Factoring Tree. Look for factors that are written twice and circle them. When we take the square root, we write only one of the circled numbers. The numbers uncircled, without a pair, remain under the radical, multiplied back together. Square root of 72 2 x 2 x 2 x 3 x 3 = 6√2 Take 10 minutes to work

1.4 Angles and their Measures An Angle consists of two different rays that have the same initial point. The rays are the sides of the angle. The initial point is the vertex.

Measure of an Angle The measure of an ∠A is denoted as m∠A The measure of an angle can be measure with a protractor in degrees. Write it as m∠BAC = 50° Congruent Angles – Angles that have the same measure Note: Measures are equal, and angles are congruent m∠BAC = m∠DEF ∠BAC ≅ ∠DEF Say “is equal to” “is congruent to”

Classify Angles Acute 0° < m∠A <90° DRAW Right m∠A = 90° Obtuse 90° < m∠A < 180° Straight m∠A = 180°

Protractor Postulate Consider a point A on one side of line OB. The rays that form OA can be matched with the real numbers from 0 to 180. The measure of ∠AOB is equal to the absolute value of the difference between the real numbers for OA and OB.

Protractor Postulate Interior point – A point that lies between points that lie on each side of the angle. Exterior points – A point that does not lie on the angle or in its interior. Exterior Interior

Angle Addition Postulate Angle Addition Postulate – If P is in the interior of ∠RST, then m∠RSP + m∠PST = m∠RST R P S T

Examples 1) In the figure on your paper, m∠CDE = 62° and m∠EDF = 18° . Find the measure of ∠CDF. 2) Plot the points and classify the angles with your table partner. 3) Discuss and solve the third example on your paper with your table partner.

Adjacent Angles Adjacent Angles – Are two angles that share a common vertex and side but have no common interior points Complete the drawings described in examples 1 and 2 on your paper.

Exit Quiz Plot the following points on the graph on the exit quiz. S at (-3, -1); T at (-4, 1); M at (1, 1); G at (1, -2); E at (-1, 4); N at (3, -4); and E at (4, 3) Using the distance formula and starting at S, use the following distances to find the word hidden in the letters. The correct order of distances is as follows: You must show all distance formula work in the exit quiz.