1. Curriculum (Section 1-4)

At the end of the lesson, the students are expected to:

・find Segment Lengths

・find Angle Measures

2. Teaching Plan and Subject matter

Topic: Measuring Segments and Angles

Techer	Student
a. Routinized Activities
Good morning class!
	Good morning ma’am. It’s  nice to see you today.
How are you today?
	It’s good ma’am.
It is nice to hear. Before we start to learn today, president please lead the prayer.
	Father God thank you for this day for making us safe. Thank you for the strength and for the knowledge you imparted on us every day. Please guide us as well as our family at home. Amen.
Is there any absence today?
	No ma’am
Thank you for secretary. Are you ready to learn new things today?
	Yes ma’am.
Please sit down properly and prepare your book and handout.
b. Review
Today, we are going to learn how to measure segments and angles.
First, we are going to find lengths of segment. I want you to remember the lesson from yesterday about segments. What are segments?
	Segment is the part of a line consisting of two endpoints and all points between them.
That’s right. Here I introduce new postulate to measure the segment. By the way do you remember what postulate is?
	It is an accepted statement of fact.
c. Lesson Proper
Yes, and you can also say it as axiom. Here’s the new postulate called Ruler postulate. I want you to read it together.
	The points of a line can be put into one-to-one correspondence with the real numbers so that the distance between any two points is the absolute value of the difference of the corresponding numbers.
The ruler postulates tell us how to find the distance between two points.
First, we have to match each of the two points to a number. We call these numbers the coordinates of the points.
Then we subtract the coordinates from each other. If the resulting difference is negative, we take the absolute value because distance is always positive. In case you hardly remember what absolute value is, here is the definition. “distance of a number from zero.”
In this case its (-5)-1 equals to what?
	-6
Yes, but we cannot say the distance is -6 so we take absolute value which is expressed |(-5)-1|
Can anyone remember how to solve? From line 1?
	|(-5)-1|=|-6|=6
Right. Here we get 6.
So we can see this process in the following formula. AB=|a-b|
The next is congruent segments. Do you know what congruent means?
	no
It basically means “the same”. Let’s see the case of congruent segments. Please read this together.
	Two segments with the same length.
Here is the example of congruent segments. These two segments are the same 2 cm. Here we can say AB=CD then you can also write it as Segment AB is congruent to Segment CD (). When you express congruent, you need an equal sign and this worm sign which means two figures are equal in size and same in shape.
Do you have any question so far?
	No ma’am
Alright, let’s do example 1. ●   ●   a. Find AB, BC b. Compare AB and BC Let’s do from a. I need two students to write it on the blackboard.
	I do. S1: AB= |-8-(-5)|=|-3|=3 S2: BC=|-5-(-2)|=|-3|=3
Thank you.
Next is b. here you compare AB and BC and tell me what you find.
	They are both the same length.
That’s right. Then how do you write the same length? can you write it on the board?
	AB=BC so
Thank you. Very well done.
We move on to next postulate, segment addition postulate. Can you read it please?
	If three points A,B, and C are collinear and B is between A and C, then AB + BC = AC.
Now we examine the postulate with substitute numbers which you see on example 2.
First, let’s operate this in order. What do we know about Segment EF?
	The length is 4x-20
What about FG?
	2x+30
Right. What about EG?
	100
According to the postulate how can we make an equation? Can someone tell me in alphabet?
	EF+FG=EG
Alright. We know the substitute number of the segment, don’t we? Can you make an equation using the numbers?
	4x-20+2x+30=100
Can anyone from third line want to operate the equation to get x?
	I do. 4x-20+2x+30=100 6x+10=100 6x=90 x=15
Thank you.
After we get the value x, what do we have to answer?
	The length of EF and FG.
That’s right. Can two people write EF and FG here?
	S1: EF=4x-20       =4*15-20       =40 S2: FG=2x+30       =2*15+30       =60
That’s correct. To make sure that your calculating is right, you can add the answer of EF and FG to see it makes 100. In this case is it correct?
	Yes because 40+60=100
Good.
So far, we have been learning the length of segment. This is the last part of segment study which is called midpoint. What is midpoint? Please read it together.
	A midpoint of a segment is a point that divides a segment into two congruent segments.
Thank you. Because midpoint divides the segment into two congruent segments, what can we say about Segment AB and Segment BC?
	Segment AB is congruent to Segment BC.
Right. Let’s do example 3 using midpoint.
Question: B is the midpoint of segment AC. Find AB, BC, and CA
In this picture, because Point B is a midpoint, what do we know about Segment AB and Segment BC?
	Segment AB is congruent to Segment BC. (
Very well.
Since we know the substitute number, can someone make equation using the number?
	2x+1=3x-4
Can someone from Line 1 solve the equation to get x?
	2x+1=3x-4 -x=-5 x=5
Thank you. Now what do we have to answer?
	The length of AB, CB and AC.
Ok, I need three people to come up to the front and write the answer of AC, CB and AB.
	S1: AB=2x+1=2*5+1=11 S2: CB=3x-4=3*5-4=11 S3: AC=2x+1+3x-4=5x-3=5*5-3=22
They are correct.
Now, are you ready to move on to the last topic?
	Yes
Ok, the last topic is called Angle.  Have you heard of the word angle before?
Let’s read what Angle is with your beautiful voice.
	An angle is formed by two rays with the same endpoint. The rays are the sides of the angle. The endpoint is the vertex of the angle.
Thank you. There are a lot of angles around us can you find it in the classroom?
	The two intersecting edges of our table.
Right, even when you write an alphabet, like A, the top part s made with angle.
So, angle needs two rays. do you remember ray?
	Yes. Ray is the part of a line consisting of one endpoint and all the points of the line on one side of the endpoint.
It is expressed by an endpoint and an arrow. These be the sides to make the angle, Right here. How can we call these slides?
	We call Ray BT and Ray BQ. ()
Right, and the one endpoint you see here is called Vertex. In this case Point B is the vertex.
Lastly, we want to name this angle right here. We can name this Angle B (∠B) but there are other ways to name the angle. Do you come up with any name?
	Angle 1(∠1), Angle TBQ(∠TBQ), Angle QBT(∠QBT).
Good.
So, as you find some angles around you, you may realize they differ in measure, in other words degree.
We have four classification names for them. Let’s read them out first.
	Acute angle, Right angle, Obtuse angle and Straight angle.
Ok, we go from Acute angle. So, what exactly is acute angle? Acute angle is an angle that is greater than 0 degrees but less than 90 degrees. In this case X represents the angle so X is going to be greater than 0 degree but less than 90 degrees. Since angle is formed by two rays, angle should be more than 0 degrees. This is Acute angle.
Next one is called right angle. Right angle has an angle of exactly 90 degrees. Typically, you’ll see a box right next to the vertex which means this is 90 degrees. Can anyone from line 1 know how to express in equation?
	X=90
That’s good. Are you ok so far? We have two more to go.
	Yes, ma’am
Third one is called obtuse angle. Obtuse means not pointed or sharp. Obtuse angle is relatively large. Its measure is greater than 90 degrees but less than 180. Can anyone express this on the blackboard?
	90<X<180
Thank you. This is Obtuse angle.
Finally, we have straight angle. Straight angle is basically an angle of a straight line. Straight line always has a measure of 180 degrees.
Now, I want you to familiarize with the classification so let’s do one exercise. Name ∠60 , ∠30, ∠A and box angle of the triangle.
	∠60 is Acute angle ∠30 is also Acute angle ∠A is Obtuse angle And box angle is right angle, thus measure is 90 °
Correct.
We are now at the last postulate called Angle Addition Postulate. There are two of them so let’s read from the top together.
	If point B is in the interior of ∠AOC, then m∠AOB+m∠BOC=m∠AOC
Here you see lowercase m right before angle symbol. You write this to indicate the size or degree measure of an angle. Ok?
	Yes.
Let’s read the second one.
	If ∠AOC is a straight angle, then m∠AOB+m∠BOC=180
Thank you. Now we do example 4. Question: if m∠DEG=145, findm∠GEF. Have you got the answer from line 2?
	I do. Its 35.
Could you tell me how you get the answer?
	m∠DEG + m∠GEF=180 145+x=180 X=180-145 X=35°
Well done. If you want to make sure if your calculating is correct, what way do we have?
	I do not know ma’am.
We already know that ∠DEF is a straight angle which is 180 right?
	Yes.
The straight angle never changes from 180. To make sure that your answer is correct, you can examine if addition of known angle 145 and your answer 35 will be 180. Do you understand?
	Yes ma’am.
Ok, for the last lesson I’d like to introduce Congruent angles.
Do you remember what congruent mean?
	Congruent means the same.
Yes. So here we when we say Congruent angles, it means?
	Angles with the same measure.
That’s right. This postulate may confuse you but please listen to me with this figure.
Let’s read the postulate together.
	If m∠1=m∠2, then ∠1≅∠2
Look at this figure, we are going to say this is angle 1 and this is angle 2. If we follow the postulate, m∠1 =m∠2. If so, we can say ∠1 ≅ ∠2. Ok?
	Yes.
You can use the statement interchangeably.
We finish up the lesson with today’s summary ok?
	Ok!
d. Summary
Today what did we learn? Do you remember new words and postulate?
	Ruler postulate
Good. What is it about?
	The points of a line can be put into corresponding real numbers so that we can measure absolute value of the distance.
Exactly.
What other things did we learn?
	Congruent segments
What is congruent segment
	It is two segments with the same length.
Well done. There is segment addition postulate. Do you remember the definition?
	If three points A, B and C are collinear and B is between A and C, then AB + BC= AC.
Good. What else did we learn?
	Midpoint
What is that.
	It divides a segment into two congruent segments.
Yes it does. This was the last postulate for segment. How about angles? How can you form an angle?
	It is formed by two rays with the same endpoint.
Yes, how do you call the rays?
	Sides
How about endpoint?
	Vertex
Great. If I am right, there are 4 names for angle according to each measure. What is the acute angle? If you name the angle X, how do you explain acute angle?
	It is more than 0 and less than 90 degrees.
Good job. How about right angle?
	It is exactly 90 degrees
Obtuse angle?
	X is more than 90 degrees but less than 180.
And the last is straight angle.
	X is exactly 180. So, X=180
Good. We’re almost the end. The angle addition postulate has two statements. If B is interior ∠AOC, then what two angles make m∠AOC?
	m∠AOB+m∠BOC
Right. The other statement is if ∠AOC is a straight angle, what makes 180.
	m∠AOB and m∠BOC
Last postulate is congruent angles. It is?
	Angles with the same measure.
Greta job everybody. That’s all for today.