Unit 1: BFF– Building Formative Foundational Skills
BFF01 I can correctly identify relations between and among points lines and planes. Use terms including collinear , coplanar , parallel , intersecting and skew . Points: zero dimension, simply a spot in space Lines: 1 dimension, named by 2 points, made up of infinite amount of points, extends forever in 2 directions. Planes: 2 dimensions, extends forever in 4 directions. Has no width. Collinear: points are collinear if a straight line can be drawn between them (2 points are always collinear, 3+ points are sometimes collinear) Coplanar: points and lines are coplanar if a plane can be drawn, containing all of them (3 points are always coplanar, 4+ points are sometimes coplanar, 2+ lines are sometimes coplanar) parallel: lines are parallel when they are coplanar and do not intersect intersecting: lines are intersecting when they meet at at least one point skew: lines are skew when they are NOT coplanar and do not intersect (need help? visit https://www.khanacademy.org/math/geometry/intro_euclid/e/points_lines_and_planes) BFF02 I can explain the Parallel Postulate: through a point not on a given line there is exactly one parallel line. In other words, if there is a line and point that do not intersect, exactly one line can be drawn through the point and be parallel to the other line. BFF03 I can, using Examples and Counterexamples , answer questions regarding points, lines and planes using “Always”, “Sometimes” or “Never”. BFF04 I can identify the differences among segments , rays , and lines (use the term endpoint ) segments: 2 endpoints (a piece of a line) rays: 1 endpoint (extends forever in one direction lines: zero endpoints (extends forever in 2 directions BFF05 I can correctly name points, segments, rays, lines and planes (using letters and symbols). segments: Name it by naming the two endpoints. Use capital letters and above them, draw a line with an endpoint on each end (a line segment) to show it is a segment rays: Name first the endpoint, then another point on the ray. Put an arrow on top of the two points you names pointing away from the endpoint lines: Name two points on the line, and draw a line with arrows on each end to signify it is a line plane: Name by naming 3 non collinear points that are on the plane. When labeling a plane (different than naming it) use a capital, cursive letter, and put it in a corner (need help? visit https://quizlet.com/13625955/chapter-1-sometimes-always-never-questions-flash-cards/) BFF 06 To find the distance between two points on a number line, I can first state the Ruler Postulate using variables, then use substitution to find the distance between the two points, SHOW WORK. Ruler Postulate: This postulate states that every number on a number line can be paired with a point, and every point with a number. These numbers can be used to calculate the distance between points BFF 07 I can state the Segment Addition Postulate using variables, then use substitution to evaluate the lengths for a given problem. Use correct notation. The Segment Addition Postulate states that if point B is between point A and point C, then the measurement of line segment AB plus the measurement of line segment BC is equal to the measurement of line segment AC. (need help? visit http://www.geom.uiuc.edu/~demo5337/Group3/distanc2.html) BFF 08 I can demonstrate which notations for segments can be used in congruencies and which can be used in equalities . BFF 08.5h1 I can derive the Segment Overlap Theorem from previously known Postulates and the Algebraic Properties of Equality. (need help? visit http://www.tamdistrict.org/cms/lib8/CA01000875/Centricity/Domain/539/Proofs/COMMON%20SEGMENT%20THM.pdf) BFF 08.5h2 I can state the Segment Overlap Theorem (include a sketch of the corresponding diagram) using variables, then apply the theorem to find lengths of segments. BFF 09 I can state then apply the Midpoint Formula to find the midpoint of a segment on a number line. Midpoint formula states how to find the midpoint of a line segment. Given line segment AC, to find the midpoint, you would do A + C divided by two. (This incorporates the ruler postulate, that every point is paired with a number on a number line and it can determine the length of the segment) (need help? visit http://www.purplemath.com/modules/midpoint.htm) BFF 10 I can state three valid conclusions given that C is the midpoint of segment AB. (Consider both congruence and equality). Examples include: --A+B divided by 2 equals C (midpoint formula) --The measure of line segment AC is equal to the measure of line segment CB --line segment AC is congruent to line segment CB BFF 11 Given a segment, I can sketch a bisector correctly showing congruent parts. --Draw a line, ray, or segment, whatever you choose to bisect the segment so it intersects with segment being bisected, close to the center. Draw congruency symbols on either side of the bisector you sketched. (need help? visit http://www.mathsisfun.com/geometry/construct-linebisect.html) Skills below have "50+" numbers, indicating they are Construction Based Skills USE COMPASS BFF 50 I can construct a circle . --To use a compass (a tool used to construct circles), put the sharp part of it (side with no pencil) into a piece of paper. Adjust the size of it to the size you want the radius of your circle to be. Put the side of the compass with the pencil/pen down on the paper and twist it around, making sure to keep the sharp part down on the paper. Continue to circle it until a complete circle is made. BFF 51 I can construct two segments of equal length (aka congruent ). Open your compass the length of the segment. Place one end of the open compass on one endpoint, and draw a mark with the other side. It should cross the other endpoint. If it doesn't, adjust the compass so it does. When it does, using a straight edge, draw another line, longer than the first segment. Place the opened compass on one end of the segment, and draw an arc. Where the arc meets the new line is the length of a segment that copies the first segment. (need help? visit https://www.youtube.com/watch?v=llwX8obAH3U) BFF 52 I can construct a segment that is the sum or difference of two other segments (using Segment Addition Postulate). Using a compass and a straight edge, use the Segment Addition Postulate! Using the same idea from BFF 51. (need help? visit http://www.mathopenref.com/constaddsegments.html) BFF 53 I can construct a perpendicular bisector of a given segment. --To bisect a segment, open your compass so it is just more than half the length of the segment. Draw an arc that wide from each endpoint. Make the arc long enough so the arcs from each side cross. Connect where the arcs cross above and below the segment. The line just drawn bisected the first segment. Remember to draw a symbol to show the congruencies on either side of the bisector and right angle created.(need help? watch this video https://www.youtube.com/watch?v=HmSN34aEE0g) BFF 54 I can construct beautiful and more complicated pictures using a compass. BFF 99 I can solve problems you haven’t seen before, using analysis and synthesis of the information learned so far. |
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