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1.1: _________________________________________________ Geometry Date: __________ A __________ is a two-dimensional diagram that you can _______ a three-dimensional figure. A net shows _____ of the surfaces of a figure in one view. Ex 1). Circle the net that you can NOT fold into a cube. Ex 2). Suppose you fold the net into a cube. What color will be opposite each face? a) red: _____________________ b) blue: ____________________ c) green: ____________________ Ex 3). Suppose you fold the net into a cube. Which color is missing from each side? a) b) c) __________________ __________________ __________________ Ex 4). The net below folds into a cube. Which letters will be on the top and front of the cube? Top: _______ Front: ________ Ex 5). What is a net for the cereal box below? Label the net with its dimensions. a) b) Homework: pg. 6 #1, 2, 5 β 10, 17 β 20, 22 β 25, 27, 28, contract & supplies check on Monday 1.2 Day 1: __________________________________________ Geometry Date: _________ A ______________ indicates a location and has no size. It is represented by a ______ and is named using a _________________ letter. Ex: A ____________ is represented by a straight path that extends in two opposite directions ____________ end and has no thickness. A line contains ________________ many points. A line is named by any two points on the line or by a single lower case letter. Ex: A ______________ is represented by a flat _______________ that extends without end and has no thickness. A plane contains infinitely many _____________. A plane is name by a capital letter or by at least ____________ points in the plane that ________ ________ all lie on the same line. Ex: _________________ ____________: Points that lie on the same line _________________ ____________/____________: Points and lines that lie in the same plane. Ex 1). a) What are two other ways to name β‘π΄π΅: ____________________ b) What are two ways to name plane Q? ____________________ c) What are the names of three collinear points? ________________ d) What are the names of four coplanar points? _________________ A _________________ is part of a line that consists of two ________________ and all points between them. A segment is named by its two endpoints. Ex: A _________ is part of a line that consists of one ______________ and all the points of the line on one side of the endpoint. A ray extends in ______ _________________. A ray is named by its endpoint and another point on the ray. The ____________ of the points indicates the rayβs _________________. Ex: __________________ ________ are two rays that share the _________ endpoint and form a line. Opposite rays are named by their shared endpoint and any other point on each ray. Ex: Ex 2). a) What are the names of the segments in the figure? _________________________ b) What are the names of the rays in the figure? _____________________________ c) Which of the rays in part (b) are opposite rays? ________________________ β‘ , π π Μ Μ Μ Μ Ex 3). Draw three noncollinear points R, S, and T. Then draw π π, ππ Ex 4). Given four points: a) Are lines β‘π΄π΅ πππ β‘π΄πΆ the same? ________ b) Are line segments Μ Μ Μ Μ π΄πΆ πππ Μ Μ Μ Μ π΅π· the same? _________ c) Are rays πΆπ΄ πππ πΆπ΅ the same? ________ Homework: pg. 12 #1 β 17, 20 β 24(e) 1.2 Day 2: ___________________________________________ Geometry Date: __________ A _________________ or ____________ is an accepted statement of fact. Postulate 1-1: Through any ______ points there is exactly ______ _______. Postulate 1-2: If two distinct lines intersect, then they intersect in ______________ ______ _________. Postulate 1-3: If two distinct planes intersect, then they intersect in ______________ _______ _______. Ex 1). Each surface represents part of a plane. What is the intersection of plane AEH and plane EGH? _________ Ex 2). Each surface of the box represents part of a plane. a) What is the intersectio of plane RNQ and plane JMN? _____________ b) Which plane contains points J, M, and L? ______________ c) Which plane contains points L, P, and Q? ______________ d) Which plane contains points M, J, and P? Shade below. _______________ e) Which plane contains points J, K, and Q? Shade below. ______________ f) What other point is in the same plane as points N, P, and Q? ____________ g) What other point is in the same plane as points J, M, and Q? ___________ h) What lines contain two of the four points: J, K, L, and M? _______________ _______________________________________________ j) What is the intersection of the plane JMP and plane PQL? _______________ Ex 3). a) Name four points: _________________________________ b) Name two lines: ___________________________________ c) Name two planes: _________________________________ d) Name the intersection of the two planes: __________________ Homework: pg. 17 # 1 β 26 1.3: _________________________________________________ Geometry Date: __________ Recap: ο· Postulate/Axiom is an accepted _____________ ο· Through any two points, there is exactly one _______________ ο· If lines intersect, they always intersect at a ________________ ο· If planes intersect, they always intersect at a ________________ Postulate 1-5: ______________________________________ Every point on a line can be paired with a real number, called a _____________________________. β‘ at the right. The _____________________ Consider, π΄π΅ between A and B is the absolute value of their coordinates. Ex: Ex 1). Find the measure of each segment. a). What is CD? b). What is BD? Postulate 1-6: ______________________________________________ If three points A, B, and C are ______________________ and B is between A and C, then _____________________________. Ex 2). If LN = 32, what are LM and MN? If two segments have the same length, then the segments are _____________ (____) ______________. Ex 3). Are Μ Μ Μ Μ π΄π· πππ Μ Μ Μ Μ π΅πΈ congruent? The ________________ of a segment is a point that divides the segment into two _________________ segments. A ________, _________, _______, or other _______________ that intersects a segment at its midpoint is said to _________________ the segment. That point, line, ray, or segment is called a ________________ ___________________. Μ Μ Μ Μ . What is RS, ST, and RT? Ex 4). S is the midpoint of π π Homework: pg. 24 #1 β 5, 8 β 24(e), 34 1.4: _____________________________________________ Geometry Definition An _____________ is formed by two ________ with the same endpoint. The rays are the __________ of the angle. The endpoint is the of the angle. Date: __________ ANGLE How to Name it Diagram You can name an angle by: ο· Its vertex, ___________ ο· A point on each ray and the vertex, _____________________ ο· A number, __________ The ____________ of an angle is the region containing all of the points _______________ the two sides of the angle. The _____________ of an angle is the region containing all of the points __________ of the angle. Ex 1). What are three other names for ? _________________ _________________ Postulate 1-7: _______________________________________ Consider ______ and a point A on one side of ______. Every ray of the form ______ can be paired one to one with a real number from _____________. Classifying Angles _________________ Ex 2). Find the measure of each angle and classify: a). <LKN: _________________________________ b). <NKM: _________________________________ c). <JKN: __________________________________ Angles with the same measure are _______________ __________. This means that if ______________, then ________________. You can also say that if ___________________, then ______________________. Ex 3). Use the diagram, which angle is congruent to: a). <YAD: ______________ b). <WBM: ______________ c). <ADE: ______________ Postulate 1-8: __________________________________________________ If point B is in the interior of ___________, then _________________________________________ Ex 4). If m<ABC = 175, what are m<ABD and m<DBC? Homework: pg. 32 #1 β 22, 28 β 30, 37 β 40 1.5: __________________________________________ Geometry Types of Angles Definition Example ______________ __________ are two coplanar angles with a common _____, a common ________, and no common interior points. _______________ ________ are two angles whose sides are opposite rays. ______________ __________ are two angles whose measures have a _______ of _______. Each angle is called the ______________ of the other. _______________ _________ are two angles whose measures have a _______ of ________. Each angle is called the ______________ of the other. Ex 1). Use the diagram. Is each statement true? Explain. a). <PAL and <LAM are adjacent angles: ___________________________ ____________________________________________________________________ b). <PAO and <NAM are vertical angles: ____________________________ ____________________________________________________________________ c). <PAO and <NAO are supplementary: ____________________________ Date: _________ There are some relationships you can assume to be true from an unmarked diagram and some you cannot. You CAN assume the following: You CANNOT assume the following: 1. ______________________________________ 1. ____________________________________ 2. ______________________________________ 2. ____________________________________ 3. ______________________________________ 3. ____________________________________ Ex 2). What can you conclude from the information in the diagram? A _________ ________ is a pair of adjacent angles whose noncommon sides are opposite rays. The angles of a linear pair form a _____________ __________. Postulate 1-9: ___________________________________________________ If two angles form a ______________ _________, then they are _______________________. Ex 3). <ABC and <DBC are a linear pair, m<ABC = 3x + 19, and m<DBC = 7x β 9. What are the measures of <ABC and <DBC? An __________ ____________ is a ray that divides an angle into two congruent angles. Ex 4). πΏπ bisects <JLN. If m<JLM = 42, what is m<JLN? Homework: pg. 40 #1 β 28 1.6: _________________________________________________ Geometry Date: __________ A ___________________ is a ruler with no markings on it. A ______________ is a tool used to draw circles and part of circles called _________. A ___________________ is a geometry figure drawn using a ___________________ and a ________________. *See page 49 for STEPS Ex 1). Construct Μ Μ Μ Μ πΈπΉ so that Μ Μ Μ Μ πΈπΉ β Μ Μ Μ Μ π΄π΅. Ex 2). Construct <C so that <C β <A. ___________________ ___________ are lines that intersect to form right angles. The symbol ______ means βis perpendicular to.β A __________________ ____________ of a segment is a line, segment, or ray that is perpendicular to the segment at its _______________. Ex 3). Construct β‘πΏπ so that β‘πΏπ is the perpendicular bisector of Μ Μ Μ Μ ππ . Ex 4). Construct π·πΈ, the bisector of <D. Homework: pg. 52 #1 β 4, 7 β 11 1.7 Day 1: __________________________________________ Geometry Date: __________ Midpoint Description On a Number Line: Formula Diagram The coordinate of the midpoint is the ___________ or _______ of the coordinates of the endpoints. In the Coordinate Plane The coordinates of the midpoint are the average of the _______________ and the average of the _______________ of the endpoints. Ex 1). Μ Μ Μ Μ ππ¬ has endpoints -3 and 7. What is the coordinate of its midpoint? Ex 2). Μ Μ Μ Μ πΉπΈ has endpoints F(5, -10) and E(3, 6). What is the midpoint of Μ Μ Μ Μ πΉπΈ ? Ex 3). Μ Μ Μ Μ ππ΄ has endpoints S(-4, -2)and A(-7, 1). What is the midpoint of Μ Μ Μ Μ ππ΄? Μ Μ Μ Μ is A(2, -1). One endpoint is L(-3, -5). What are the coordinates of the Ex 4). The midpoint of πΏπ other endpoint? Μ Μ Μ Μ is T(4, -9). Endpoint A has coordinates (-3, -5). What are the coordinates Ex 5). The midpoint of π΄π΅ of B? Homework: pg. 59 #1 β 3, 4 β 24(e) 1.7 Day 2: ___________________________________________ Geometry Date: __________ Distance Formula The distance between two points ____________ and ____________ is: Ex 1). What is the distance between (6, -2) and (-5, 3)? Round to the nearest tenth. Ex 2). What is the distance between (-2, 14) and (3, -1). Round to the nearest tenth. Ex 3). On a zip-line course, you are harnessed to a cable that travels through the treetops. You start at Platform A and zip to each of the other platforms. How far do you travel from Platform B to Platform C? Homework: pg. 62 #1-5, 6-18(e), 28-31 1.8 Day 1: __________________________________________ Geometry Date: __________ The ___________________ P of a polygon is the _______ of the lengths of its sides. Perimeter and Circumference Square Triangle Rectangle Circle Ex 1). To place a fence on the outside of the garden, how much material will you need? Ex 2). What is the circumference of the circle in terms of π? What is the circumference of each circle to the nearest tenth? Ex 3). What is the perimeter of triangle LMN? Ex 4). Graph quadrilateral JKLM with vertices J(-3, -3), K(1, -3), L(1, 4) and M(-3, 1). What is the perimeter of JKLM? Homework: pg. 75 #1, 2, 5 β 13 1.8 Day 2: __________________________________________ Geometry Date: __________ The _________ of a polygon is the number of square units it encloses. Area Square Triangle Rectangle Circle When measuring area, use __________ _______ such as ________, _________, _________ β¦ Always use the _______ unit for both dimensions. Ex 1). You are designing a rectangular flag for your cityβs museum. The flag will be 15 feet wide and 2 yards high. How many square yards of material do you need? Ex 2). The diameter of circle L is 10 cm. What is its area in terms of π. Area Addition Postulate: The area of a region is the ________ of the areas of its __________________ parts. Ex 3). What is the area of the figure below? a) b) c) Homework: pg. 75 #1, 4 β 18(e), 22