IN THIS UNIT
IN THIS UNIT......
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.
BFF02 I can explain the Parallel Postulate: through a point not on a given line there is exactly one parallel 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)
BFF05 I can correctly name points, segments, rays, lines and planes (using letters and symbols).
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.
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.
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.
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. SHOW WORK.
BFF 09 I can state then apply the Midpoint Formula to find the midpoint of a segment on a number line.
BFF 10 I can state three valid conclusions given that C is the midpoint of segment AB. (Consider both congruence and equality).
BFF 11 Given a segment, I can sketch a bisector correctly showing congruent parts.
*Construction Based Skills*
BFF 50 I can construct a circle
BFF 51 I can construct two segments of equal length (aka congruent)
BFF 52 I can construct a segment that is the sum or difference of two other segments (using Segment Addition Postulate)
BFF 53 I can construct a perpendicular bisector of a given segment
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.
BFF02 I can explain the Parallel Postulate: through a point not on a given line there is exactly one parallel 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)
BFF05 I can correctly name points, segments, rays, lines and planes (using letters and symbols).
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.
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.
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.
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. SHOW WORK.
BFF 09 I can state then apply the Midpoint Formula to find the midpoint of a segment on a number line.
BFF 10 I can state three valid conclusions given that C is the midpoint of segment AB. (Consider both congruence and equality).
BFF 11 Given a segment, I can sketch a bisector correctly showing congruent parts.
*Construction Based Skills*
BFF 50 I can construct a circle
BFF 51 I can construct two segments of equal length (aka congruent)
BFF 52 I can construct a segment that is the sum or difference of two other segments (using Segment Addition Postulate)
BFF 53 I can construct a perpendicular bisector of a given segment
BFF 01
Collinear-2 or more points are collinear if and only if a line can be drawn to contain them.
Example: Points P, Q, and R are collinear, but points X, Y, and Z are NOT collinear.
Example: Points P, Q, and R are collinear, but points X, Y, and Z are NOT collinear.
Coplanar-2 or more points are coplanar if and only if a plane can be drawn to contain them.
Example:
Example:
Parallel-2 or more lines are parallel if and only if they a) never intersect and b) are coplanar
Example: The first 2 lines are not parallel because if you continue their lines, they will intersect. The 2nd pair is parallel, however, because they will never intersect, no matter how long the lines go on for.
Example: The first 2 lines are not parallel because if you continue their lines, they will intersect. The 2nd pair is parallel, however, because they will never intersect, no matter how long the lines go on for.
Intersecting-2 or more objects are intersecting if and only if they share at least 1 point.
Example: These lines are intersecting because they share at least 1 point.
Example: These lines are intersecting because they share at least 1 point.
Skew-2 or more lines are skew if and only if they a) are non-coplanar and b) never intersect
Example: As you can see by the diagram, the two lines do not lie on the same plane, and if you extended them, they would not intersect.
Example: As you can see by the diagram, the two lines do not lie on the same plane, and if you extended them, they would not intersect.
BFF-02
The basic definition for the parallel postulate is that in a plane, through any point not on a given line only one new line can be drawn that is parallel to the original one.
This video below does a good job explaining more about the origins and definition of the parallel postulate, |
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BFF 03
Not everything in geometry is black and white, or true or false. That's why we use the terms: always, sometimes, and never. Examples are situations for which both the condition and the claim about the condition are true.
Counterexamples are situations where the condition is true, but the claim about the condition is NOT true.
If a situation has ONLY examples, then it is ALWAYS TRUE.
If a situation has BOTH examples and counterexamples, it is SOMETIMES TRUE.
If a situation has only counterexamples, and no examples can be found, it is NEVER TRUE.
Here is a helpful Quizlet for extra practice on the using the terms always, sometimes, and never in real examples.
Counterexamples are situations where the condition is true, but the claim about the condition is NOT true.
If a situation has ONLY examples, then it is ALWAYS TRUE.
If a situation has BOTH examples and counterexamples, it is SOMETIMES TRUE.
If a situation has only counterexamples, and no examples can be found, it is NEVER TRUE.
Here is a helpful Quizlet for extra practice on the using the terms always, sometimes, and never in real examples.
BFF 04
bff 05
This notes explain how to name points, segments, rays, lines, and planes.
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BFF 06
Ruler Postulate: We can measure the distance between A and B by taking the absolute value of the difference between their coordinates on a number line
Formula: AB=|a-b|
Example: As you can see the quantity of A on the number line is -9 and the quantity of B is -7. If you plug that into the formula AB=|-9--7|, you would get -2, therefore the distance between them is -2 units.
Formula: AB=|a-b|
Example: As you can see the quantity of A on the number line is -9 and the quantity of B is -7. If you plug that into the formula AB=|-9--7|, you would get -2, therefore the distance between them is -2 units.
BFF 07
The Segment Addition Postulate states that if B is collinear with and between A and C, then AB + BC = AC.
Here is an example below.
Here is an example below.
BFF 08
It is important to know the difference between congruence and equality when expressing things in geometry. This table shows when to notate something as congruent and when to notate something as equal and how to express that.
BFF 08.5h1
This document below explains step by step how to derive the Segment Overlap Theorem.
AND BFF 08.5H2
Formula: If AB=CD, then AC=BD
(can also be written as) If AC=BD, then AB=CD
(can also be written as) If AC=BD, then AB=CD
BFF 09
Midpoint Formula: m=(a+b)/2
To see an example of this, look below.
To see an example of this, look below.
BFF 10
Given that C is the midpoint of segment AB, state 3 valid conclusions.
BFF 11
Given a segment, sketch a bisector.
Here is a video below explaining the process |
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*Construction Based skills* Bff 50-53
The video below explains how to do constructions for all of these skills.
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Extras for this unit
Extra help with challenging topics discussed