Pre-AP Geometry Unit 2 Note Packet Week 10 PDF

## Unit 2 Tools & Techniques of Geometric Measurement Note Packet ### What is Angle "BAD"? A diagram showing an angle with a question mark inside. The angle is labeled "BAD," with points "A" at the top, "B" at the bottom left, and "C" at the bottom right. The bottom point is labeled "D" and is positioned to the right of "C." **FOR ME ALL ANGLES ARE BAD** ### Key Concepts: 1. Measurement in Geometry 2. Parallel & Perpendicular Lines 3. Measurement in Right Triangles (Trigonometry) ### Enduring Understandings: - A formal mathematical argument establishes new truths by logically combining previously known facts. - Measuring features of geometric figures is the process of assigning numeric values to attributes of the figures, which allows the attributes to be compared. - Pairs of lines in a plane that never intersect or that intersect at right angles have special geometric and algebraic properties. - Right triangles are simple geometric shapes in which we can relate the measures of acute angles to ratios of their side lengths. ## Tentative Time Frame: (Check with digital file & Canvas for updates & changes) | Week | Date | Topics | |------|------|---------------------------| | 10 | Oct 14-18 | 2.1 Measuring Segments & Angles & Defining Congruence | | 11 | Oct 21-25 | 2.2 Finding Segment Measures using Segment Addition Postulate 2.3 Measuring Distance in the Coordinate Plane (Distance Formula) | | 12 | Oct 28-Nov 1 | 2.3 Measuring Distance in the Coordinate Plane (Distance Formula) Day 2 | | 13 | Nov 4-8 | 2.4 Parallel & Perpendicular Lines in the Coordinate Plane (2 days) Learning Checkpoint 2.1 & Vocabulary Quiz | | 14 | Nov 11-15 | Assessment 2.1-2.4 Review/Practice Activity | | 15 | Nov 18-22 | 2.1A Partitioning a Segment & Bisecting a Segment 2.2AB Transversals 2.5 Triangle Sum Theorem | | 16 | Dec 2-6 | Thanksgiving Break: November 25-29 Trig Ratios: SOH CAH TOA Finding Missing sides in Right Triangles Trig Ratios: SOH CAH TOA Finding Missing angles in Right Triangles Angles of Elevation and Depression | | 17 | Dec 9-13 | Applications of Trig Ratios/Group Quiz Final Review | | 18 | Dec 16-20 | All SEMESTER 1 Work due by DECEMBER 15 SEMESTER 1 FINAL EXAMS | ## Unit 2 DICTIONARY: GEOMETRY BASICS | Points, Lines, & Planes | Definition | Example or Visual | |-------------------------|----------------------------------------------------------------------------------------|-------------------| | POINT | A point is a location with no size or shape. | A• B • C | | LINE | A line is made up of points with no thickness or width. | X------Y | | LINE SEGMENT | A measurable part of a line Consisting of two endpoints. | R-------S | | RAY | A line that extends Indefinitely in one direction. | →F E | | PLANE | A plane is a flat surface made up of points and extends indefinitely in all directions. | [Diagram of a plane] | | COLLINEAR | Points that lie on the same Line. *Non-collinear: points that do not lie on the same line.* | L•M•N | | COPLANAR | Points that lie on the same plane. *Non-coplanar: points that do not lie on the same plane.* | [Diagram of a plane]| | CONGRUENT SEGMENTS | If two segments have the same length, then they are Congruent. | [Diagram showing congruent line segments]| ## Segment Addition Postulate - If A, B, and C are collinear points and B is between A and C, then AB + BC = AC. ## Distance Formula - The formula used to find the distance between two points on a coordinate plane. $d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ ## Midpoint Formula - The formula used to find the midpoint between two endpoints. $M = ( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})$ ## Segment Bisector - A segment, line, or plane that intersects a segment at its midpoint. ## Perpendicular Bisector - A line, segment, or ray perpendicular to a segment at its midpoint. ## Parallel Lines - Two lines that never intersect. ## Angle - The intersection of two rays at an endpoint. ## Vertex - The common endpoint of an angle (where the sides intersect) ## Right Angle - An angle with a degree measure of 90°. ## Acute Angle - An angle with a degree measure less than 90°. ## Obtuse Angle - An angle with a degree measure greater than 90°. ## Straight Angle - An angle with a degree measure of 180°. ## Congruent Angles - Two angles that have the same measure are Congruent ## Adjacent Angles - Two angles that share a common side and vertex. ## Angle Addition Postulate - If ∠ABD and ∠DBC are adjacent, then ∠ABD + ∠DBC = ∠ABC. ## Angle Bisector - A line or ray that divides an angle into two equal parts. ## Vertical Angles - Two angles directly across from each other on intersecting lines. *Always congruent.* ## Complementary Angles - Two angles with measures that sum to 90°. *Do not have to be adjacent.* ## Supplementary Angles - Two angles with measures that sum to 180°. *Do not have to be adjacent.* ## Linear Pair - Adjacent angles that are supplementary. Combined, they form a straight line. ## Naming Points, Lines, and Planes: Practice! ### Practice 1: 1. **Four collinear points:** [H, M, K, N] 2. **A line that contains point M:** [line q] 3. **A line that contains points H and K:** [the intersection of line p and line q] 4. **Another name for line q:** [line MN] 5. **The intersection of lines `p` and `r`:** [point J] ### Practice 2: 1. **A line containing point F:** [line k] 2. **Another name for line k:** [line BE] 3. **A plane containing point A:** [plane M] 4. **An example of three non-collinear points:** [A, E, F] 5. **The intersection of plane M and line k:** [point F] ### Practice 3: 1. **Three coplanar points:** [X, V, Y] 2. **A plane containing point X:** [plane ZVY] 3. **The intersection of plane `R` and plane `ZVY`:** [line Y] 4. **How many planes appear in the figure?** [3] 5. **How many planes contain point W?** [2] ### Practice 4: 1. **The intersection of lines `l` and `m`:** [point D] 2. **Another name for plane Q:** [plane DEG] 3. **Are points D and E collinear or coplanar?** [coplanar] 4. **How many times do planes `P` and `Q` intersect?** [1] ## Homework 1: Points, Lines, and Planes (Optional but Recommended Practice) 1. **How many points appear in the figure?** 2. **How many lines appear in the figure?** 3. **How many planes appear in the figure?** 4. **Name a line containing point V.** 5. **Name the intersection of lines a and b.** 6. **Give another name for line b.** 7. **Name three non-collinear points.** 8. **Give another name for Plane D.** <start_of_image> Diagrams for Homework 1: - Diagram 1: [Diagram showing points, lines, and planes] 2. **How many points appear in the figure?** 3. **How many lines appear in the figure?** 4. **How many planes appear in the figure?** 5. **Name three collinear points.** 6. **Name four non-coplanar points.** 7. **Give another name for line e.** 8. **Name the intersection of PQ and MO.** 9. **Name the intersection of plane K and line c.** 10. **Give another name for plane L.** 11. **Give another name for PQ.** Diagrams for Homework 2: - Diagram 2: [Diagram showing points, lines, and planes] 3. **How many points appear in the figure?** 4. **How many lines appear in the figure?** 5. **How many planes appear in the figure?** 6. **Name three collinear points.** 7. **Name four coplanar points.** 8. **Name the intersection of planes ABC and ABE.** 9. **Name the intersection of planes BCH and DEF.** 10. **Name the intersection of AD and DF.** Diagrams for Homework 3: - Diagram 3: [Diagram showing points, lines, and planes] ## Naming points, Lines, and planes: Practice! ### Practice 1: Use the diagram to the right to name the following: - Four collinear points. - A line that contains point M. - A line that contains points H and K. - Another name for line `q`. - The intersection of lines `p` and `r`. Diagrams for Practice 1: - Diagram 1: [Diagram showing points, lines, and planes] ### Practice 2: Use the diagram to the right to name the following: - A line containing point F. - Another name for line `k`. - A plane containing point A. - An example of three non-collinear points. - The intersection of plane M and line k. Diagrams for Practice 2: - Diagram 2: [Diagram showing points, lines, and planes] ### Practice 3: Use the diagram to the right to name the following: - Three coplanar points. - A plane containing point X. - The intersection of plane R and plane ZVY. - How many planes appear in the figure? - How many planes contain point W? Diagrams for Practice 3: - Diagram 3: [Diagram showing points, lines, and planes] ### Practice 4: Use the diagram to the right to name the following: - The intersection of lines `l` and `m`. - Another name for plane Q. - Are points D and E collinear or coplanar? - How many times do planes `P` and `Q` intersect? Diagrams for Practice 4: - Diagram 4: [Diagram showing points, lines, and planes] ## Homework 2: Segment Addition Postulate Use the diagram below to answer questions 1 and 2: 1. If LM = 22 and MN = 15, find LN. 2. If LN = 54 and LM = 31, find MN. ### **This is a 2-page document!** 3. If RT = 36, find the value of x. 4. If DF = 9x-39, find EF. 5. If UW = 6x-35, find UW. 6. If HJ = 7x-27, find the value of x. 7. If BD = 7x – 10, BC = 4x - 29, and CD = 5x – 9, find each value. (x, BC, CD, and BD) 8. If BD = BC, BD = 5x-26, BC = 2x + 1, and AC = 43, find AB. Diagrams for Homework 2: - Diagram 1: [Diagram showing points and segments] - Diagram 2: [Diagram showing points and segments] - Diagram 3: [Diagram showing points and segments] - Diagram 4: [Diagram showing points and segments] 9. If LK = MK, LK = 7x – 10, KN = x + 3, MN = 9x – 11, and KJ = 28, find LJ. 10. If T is the midpoint of SU, find x. 11. If G is the midpoint of FH, find FG. 12. If R is the midpoint of QS, find QS. 13. If B is the midpoint of AC, and AC = 8x – 20, find BC. 14. If EF bisects CD, CG = 5x-1, GD = 7x13, EF = 6x-4, and GF = 13, find EG. 15. If R is the midpoint of QS, RS = 2x – 4, ST = 4x − 1, and RT = 8x – 43, find QS. Diagrams for Homework 2: - Diagram 5: [Diagram showing points and segments] - Diagram 6: [Diagram showing points and segments] - Diagram 7: [Diagram showing points and segments] - Diagram 8: [Diagram showing points and segments] - Diagram 9: [Diagram showing points and segments] - Diagram 10: [Diagram showing points and segments] ## Measuring Segments The distance between two points A and B be written as _AB_ or _AB =_. ## Congruent Segments If _AB_ = _CD_, then the segments are congruent. This is written as _AB_ ≅ _CD_. ## Segment Addition Postulate If A, B, and C, are collinear points and B is between A and C, then _AB_ + _BC_ = _AC_. ## Midpoint of a Segment - The **midpoint** of a segment is a point that divides the segment into two equal parts. - A line, ray, or segment that intersects a segment at its midpoint is said to **bisect** the segment and is called the **segment bisector**. In the diagram to the left, _I_ is the midpoint of _AC_ and _BI_ is a segment bisector of _AC_. ## Examples 1. If PQ = 9 and QR = 28, find PR. 2. If QR = 17 and PR = 21, find PQ. 3. If EG = 71, find the value of x. 4. If TV = 14x-8, find TU. 5. If JL = 5x + 2, find JL. 6. If CE = 7x + 4, find the value of x. Diagrams for Examples: - Diagram 1: [Diagram showing points and segments] - Diagram 2: [Diagram showing points and segments] - Diagram 3: [Diagram showing points and segments] - Diagram 4: [Diagram showing points and segments] - Diagram 5: [Diagram showing points and segments] - Diagram 6: [Diagram showing points and segments] 7. If SK = 13x – 5, KY = 2x + 9, and SY = 36-x, find each value (x, SK, KY, SY). Diagrams for Examples: - Diagram 7: [Diagram showing points and segments] 8. If Q is the midpoint of PR, find the value of x. 9. If H is the midpoint of GI, find GH. 10. If R is the midpoint of QS, find QS. 11. If G is the midpoint of FH and FH = 6y – 2, find y. Diagrams for Examples: - Diagram 8: [Diagram showing points and segments] - Diagram 9: [Diagram showing points and segments] - Diagram 10: [Diagram showing points and segments] - Diagram 11: [Diagram showing points and segments] ## Segment Addition Postulate Maze (Show all work) - **Instructions**: Begin at the "Start Box." Use your solutions to navigate through the maze. Diagrams for Maze: - Diagram 1: [Diagram showing points and segments for maze] - Diagram 2: [Diagram showing points and segments for maze]

Pre-AP Geometry Unit 2 Note Packet Week 10 PDF

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