GEOMETRY Chapter 1: Foundations for Geometry Name: Teacher: Pd:
Table of Contents Lesson 1.1: SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Pgs: 1-4 Lesson 1.2: SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. Pgs: 5-10 Lesson 1.3: SWBAT: Name, classify and calculate the measure of angles. Pgs: 11-14 Full Period Quiz Lessons: 1.1-1.3 Lesson 1.4: SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles. Pgs: 15-19 Lesson 1.6: SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of a line segment. Pgs: 20-23 Full Period Quiz Lessons: 1.4 and 1.6 Practice Test: Pgs: 24-25
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Warm Up: Complete the chart in pencil. Chapter 1 1 Terms Labels Diagrams Plane A lowercase letter or two points on the line. Point Line line l A capital letter point P A script capital letter or 3 points not on a line. plane R or plane ABC Term Definition Label/Name Diagram, names a location and has no size. It is represented by a dot., is a straight path that has no thickness and extends forever., is a flat surface that has no thickness and extends forever. Points that lie on the same line are collinear. K, L, and M are collinear. K, L, and N are noncollinear. Points that lie on the same plane are coplanar. Otherwise they are noncoplanar. 1
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Example 1: Naming Points, Lines, and Planes A. Name four coplanar points. B. Name three lines. Directions: Complete the chart below in pencil. Terms Labels Diagrams Ray A capital letter, C and D Endpoint It s endpoint and any other point on the ray Opposite Rays Segment The common endpoint and any other point on each ray The two endpoints Term Definition Labels/Name Diagram is the part of a line consisting of two points, and all points between them. is a point at one end of a segment or the starting point of a ray is a part of a line that starts at an endpoint and extends forever in one direction are two rays that have a common endpoint and form a line. 2
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Example 2: Draw and label each of the following. A. a segment with endpoints M and N. B. opposite rays with a common endpoint T. A postulate, or axiom, is a statement that is accepted as true without proof. Postulates about points, lines, and planes help describe geometric properties. Example 3: Name a plane that contains three noncollinear points. Use a dashed line to show the hidden parts of any figure that you are drawing. A dashed line will indicate the part of the figure that is not seen. Example 4: Sketch a figure that shows each of the following. A. Two lines intersecting in exactly one point. B. Two planes intersecting in one line. 3
SWBAT: Identify, name, and draw points, lines, segments, rays, and planes. Homework: pg 9 Numbers 1-21 Homework: Page 9, #'s 1-21 4
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. Warm Up Chapter 1 2 Notes: 5
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. Example 1: Finding the Length of a Segment Find each length. Practice: Finding the Length of a Segment Find each length. In order for you to say that a point B is between two points A and C, all three points must lie on the same line, and AB + BC = AC. 6
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. Example 2: Using the Segment Addition Postulate M is between N and O. Find NO. Practice: Using the Segment Addition Postulate E is between D and F. Find DF. The midpoint M of AB is the point that bisects, or divides, the segment into two congruent segments. If M is the midpoint of AB, then AM = MB. So if AB = 6, then AM = 3 and MB = 3. 7
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. Example 3: Using Midpoints to Find Lengths Practice: Challenge: 8
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. 9
SWBAT: Use the length and midpoint of a segment to calculate the missing lengths. Homework: Page 17, #'s 3, 4, 6, 7, 9, 10, 15, 17, 18 10
SWBAT: Name, classify and calculate the measure of angles. Warm Up Chapter 1 3 U is the midpoint of TV, TU = 3x + 4, and UV = 5x - 2. Find TU, UV, and TV. Example 1: Naming Angles An is a figure formed by two rays, or sides, with a common endpoint called the (plural: vertices). You can name an angle several ways: by its vertex, by a point on each ray and the vertex, or by a number. Practice: Naming Angles 1. A surveyor recorded the angles formed by a transit (point A) and three distant points, B, C, and D. Name three of the angles. 2. Write the different ways you can name the angles in the diagram. 11
SWBAT: Name, classify and calculate the measure of angles. Directions: Match the terms with its correct image in pencil. Congruent angles are angles that have the same measure. In the diagram, m ABC = m DEF, so you can write ABC DEF. This is read as angle ABC is congruent to angle DEF. Arc marks are used to show that the two angles are congruent. 12
SWBAT: Name, classify and calculate the measure of angles. Example 2: Using the Angle Addition Postulate Practice: Using the Angle Addition Postulate Example 3: Finding the Measure of an Angle KM bisects JKL, m JKM = (4x + 6), and m MKL = (7x 12). Find m JKM. Practice: Find the measure of each angle. 13
SWBAT: Name, classify and calculate the measure of angles. QS bisects PQR, m PQS = (5y 1), and m PQR = (8y + 12). Find m PQS. Holt: pages 24-27 #'s 9-10, 17-18, 29-31,& 41-43 Homework 14
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles. Warm Up: Pairs of Angles Adjacent angles: Linear pair: a) a) b) b) Use the diagram below for questions 1 and 2. 1. Identify angles those are only adjacent. 2. Identify angles that are not adjacent. 15
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles. Use the diagram below for question 3. 3. Identify angles that are adjacent and form a linear pair. Complementary angles: Supplementary angles: 16
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles. Practice Problems Ex. 4: Finding the measures of complements and supplements a) complement of F b) complement of E c) supplement of F d) supplement of G Ex 5. An angle is 10 more than 3 times the measure of its complement. Find the measure of the complement. Ex 6. An angle s measure is 12 more than ½ the measure of its supplement. Find the measure of the angle. Ex 7. Write an equation to find the measure of angle x. 17
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles. 8) If the m ABC = (4x 10) o, and m CBD = (2x + 40) o then what is x, m ABC and m CBD? A C x = o m ABC = o m CBD = o B D Vertical angles: Ex 9: In the accompanying diagram, line a intersects line b. What is the value of x? Ex10: AB and CD intersect at E. If m AEC 5x 20 and m BED x 50, find, in degrees, m CEB. 18
SWBAT identify adjacent, vertical, complementary, supplementary and calculate the measures of pairs of angles. Homework: For homework help go to: http://my.hrw.com, username: square2, password: e7p4v and select pg 32. Do # s 14-22, 24, and 26-31. 19
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of a line segment. Warm Up Chapter 1 6 1. Find CD. 2. 3. Find the missing side length. Example 1: a. b. 20
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of a line segment. Practice: a. b. c. Example 2: Finding the Coordinates of an endpoint when given a midpoint. Practice: Finding the Coordinates of an endpoint when given a midpoint. a. b. 21
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of a line segment. Example 3: a. b. Practice: a. b. c. d. 22
SWBAT: apply the formulas for midpoint and distance in conjunction with the Pythagorean Theorem to find the length of a line segment. Homework 23
Name Geometry Chapter 1 Date Practice Test WORKSPACE
intersect, 15. In the accompanying figure, two lines intersect, m<1 = (4x 20), and m<3 = (2x 40). Find the number of degress in m<2.