| Segment Addition Postulate is one of those concepts that is obvious, and yet can confuse students by it simplicity. The idea makes sense to them, and they can do it automatically, but to actually write out the theorem or set up equations using it can still trip them up for a while. I decided to bother with a quick guided inquiry lesson to really cement the idea into student brains. So out came the straws again! They pretty much only make an appearance outside the cupboard for math and margaritas... (two of my favorite things! I guess straw days are good days!). |
I prepped this by cutting a bunch of straws all in the same place. That way, I could just swap out colored sets so that each table had this:
For something this quick, I like to keep it as a full-class guided inquiry. Just say "Without measuring, I can tell you you may assume that both of these new "straws" are the same length. Now what if I told you that the yellow and blue pieces are also the same length? What could you conclude about the green and pink pieces. Why?"
Give some time. Allow them to discuss with a partner. Yes, it's obvious, but require each pair to come up with a very clear explanation of WHY.
Then, have them write it out (just in a notebook or on scrap paper for something like this). It only takes a minute, and does not require a formal worksheet. When students think they have a great explanation, allow them to share it out loud with the class.
This is a great opportunity to zero in on properties and vocabulary. I'm a big stickler on this. It is so crucial that students do not write that the pink piece is "equal to" the green one. I also do not allow explanations that say "the yellow piece plus the pink piece." Students must say that "the length of the yellow piece plus the length of the pink..."
I always feel like I cannot possibly over-reinforce the fact that measurements can be equal, whereas segments are congruent. Otherwise, when we lead into proof writing, I see angles being added instead of angle MEASURES being added.
I like to show this slide to clarify that over and over! (Check out proof writing in more detail here.)
Once they really tweak and perfect the explanations, develop an official postulate together and clarify that now they can use this new "Segment Addition Postulate" to justify steps.
The key to the guided inquiry process is that the students have noticed the properties that are at play here, and they explore it enough to write their own postulate. It's hard to hold back, but don't be tempted to feed the postulate to them. They'll get there eventually as you slowly help them revise their "explanations."
Next phase: Tell a story!
I like to tell the students stories about real-life projects, so for this one I chose to use a bench that my husband and I just built. Feel free to steal my story (I stretched the facts to make the math situation work anyway, but I willingly admit it). And project or display my bench pictures as your sample if you want!
"We were assembling this lovely bench at my parents' house, 3 hours away, because that's where all the good tools were. So it was sitting there on the garage floor covered in wet paint until our next road trip to go pick it up. I wanted to put it in my daughter's room when we brought it back home. I was getting all the furniture moved around in her room, and making space for it. I was wondering if I could fit it under the window, when suddenly I realized I had forgotten to measure it! We did not follow any particular plan to know the exact dimensions! However, I had taken a photo of our hard work, and I knew that we had used 2x4s for the legs. (Explain that 2x4s are actually only 3.5 inches wide.) I remembered cutting the bottom front faces to 14 inches each. Can I figure out how long the whole bench is?"
Of course, they will be able to handle this math. They could have answered the problem in 4th grade. Make sure to then lead into variables and replace each 3.5 with an x, and each 14 with a y. Then show the next picture, and ask them to write an equation that's more complicated. Try taking out different missing pieces of information. Ask them if they knew the full length, how could they find one piece? This will lead into sample problems. Have students set up an equation for only AD, then for AE, etc.
Wrap it up by going back to the straws. Now, give them measurements for each segment (as expressions with variables!) and ask them to write an expression representing the length of all 4 of the pieces lined up as one long segment.
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FAQs
The segment addition postulate states that if we are given two points on a line segment, A and C, a third point B lies on the line segment AC if and only if the distances between the points meet the requirements of the equation AB + BC = AC.
What is the postulate of addition? ›
Addition Postulate If equal quantities are added to equal quantities, the sums are equal. Transitive Property If a = b and b = c, then a = c.
How to solve segment addition problems? ›
Step 1: Identify the collinear points and note down the given lengths of the line segments. Here, C lies between A and B. Step 2: Write the segment addition formula with respect to the given collinear points. Step 3: Substitute the values and simplify.
What is the segment congruence postulate? ›
If two collinear segments adjacent to a common segment are congruent, then the overlapping segments formed are congruent. If two angles adjacent to a common angle are congruent, then the overlapping angles formed are congruent.
What is the AB BC AC theorem? ›
If there are three colinear points A, B, and C, and B is between A and C, then AB+BC=AC. If there are three points, then there is at least one plane through all three points. If there is a line, then there are at least two points on that line.
What is segment addition postulate? ›
The segment addition postulate is used to determine whether a point lies on a line segment. The segment addition postulate states that a point lies on a line segment if and only if the sum of the distances from the point to each endpoint of the line segment equals the length of the line segment itself.
What are the 4 postulates of geometry? ›
POSTULATES
- To draw a straight line from any point to any point.
- To produce a finite straight line continuously in a straight line.
- To describe a circle with any center and distance.
- That all right angles are equal to one another.
One postulate in math is that two points create a line. Another postulate is that a circle is created when a radius is extended from a center point. All right angles measure 90 degrees is another postulate.
What is the segment addition property of congruence? ›
Segment Addition Postulate: If A, B, and C are collinear, then point B is between A and C if and only if AB + BC = AC. Properties of Segment Congruence: • Reflexive Property of Congruence: AB = AB • Symmetric Property of Congruence: . If AB = CD, then CD = AB.
What is the formula of segment? ›
Here is a list of area of segment formula class 10: Area of a Segment in Radians = A = (½) × r2 (θ – Sin θ) Area of a Segment in Degrees = A = (½) × r2 × [(π/180) θ – sin θ]
For example, if ∠AOB and ∠BOC are adjacent angles on a common vertex O sharing OB as the common arm, then according to the angle addition postulate, we have ∠AOB + ∠BOC = ∠AOC.
What are the 4 congruence postulates? ›
Conditions for Congruence of Triangles:
SSS (Side-Side-Side) SAS (Side-Angle-Side) ASA (Angle-Side-Angle) AAS (Angle-Angle-Side)
What is the segment midpoint postulate? ›
Midpoint Postulate: Any line segment will have exactly one midpoint. Do not assume a point is the midpoint if there are no tick marks showing the segments are congruent!
How to prove AB BC AC? ›
According to the segment addition postulate, if a line segment has endpoints A and C, and a third point B, then only if the equation AB + BC = AC is true does the third point B lie on the line segment AC. To further comprehend this postulate, look at the illustration provided below.
What allows you to write ab, bc, ac? ›
Answer and Explanation:
The commutative property is a property that states that numbers can basically be swapped without changing the answer. It is very important to note that this property is only valid for addition and multiplication. If, AC = AB + BC, then AB + BC = AC by the commutative property.
What proof is ab bc ac? ›
CONSTRUCTION: CX perpendicular to AB. The definition, postulate, or theorem that you would use to prove that AB + BC = AC is the Segment Addition Postulate. This postulate states that if B is between A and C, then AB + BC = AC.
What are the postulates in math? ›
A statement, also known as an axiom, which is taken to be true without proof. Postulates are the basic structure from which lemmas and theorems are derived.
What does postulate 4 mean? ›
This postulate says that an angle at the foot of one perpendicular, such as angle ACD, equals an angle at the foot of any other perpendicular, such as angle EGH.
What are postulates of algebra? ›
Operational postulates use mathematical operations as a reference. Among them are the addition postulate (if x = x , then x + 5 = x + 5 ), the subtraction postulate (if y = y , then y − 2 = y − 2 ), the multiplication postulate (if x = x , then 2 ∗ x = 2 ∗ x ), and the division postulate (if y = y , then y 4 = y 4 ).
What is the 5 postulate? ›
5. If two lines are drawn which intersect a third in such a way that the sum of the inner angles on one side is less than two Right Angles, then the two lines inevitably must intersect each other on that side if extended far enough. This postulate is equivalent to what is known as the Parallel Postulate.
