unit 1 lesson 13 proving angle theorems.notebook l13 partially...1)
TRANSCRIPT
Unit 1 Lesson 13 Proving Angle Theorems.notebook
1
Oct 117:23 AM
Do NOW! This is on a worksheet I gave you last week called Practice with Proofs. #1
Always start with the givens.
1) A, B, & C are collinear.
B is btwn A & C. AC=32, AB = 2x
& BC= 4x+2
1) Given
.A B C
2)
2)
Sep 298:58 AM
Definitions/Postulates REVIEW!1. Def of midpoint: a point that divides a segment into 2 congruent segments or 2 equal segments.
2. Def of angle bisector: a segment, ray, or line that divides an angle into 2 congruent angles or 2 angles equal in measure.
3. Angle Addition postulate: (2 versions)If point B is on the interior of <AOC
a) ...then m<AOB + m<BOC = m<AOCb) ...the whole = the sum of its parts
4. Segment Addition postulate:
a) If B is a point between endpoints A and C, then AB + BC = ACb) ...the whole = the sum of its parts
5. def. of Perpendicular Lines: 2 lines that meet to form right angles.
Unit 1 Lesson 13 Proving Angle Theorems.notebook
2
Sep 308:58 AM
Unit 1Lesson 13
Proving Angle Theorems
"If 2 angles are vertical angles, then they are congruent."
A theorem is a statement proved by deductive reasoning.
Remember...
A postulate is a statement that is accepted without proof.
Below is a theorem about vertical angles:
In an if...then statement,
the "if" is the given information
the "then" is what you have to prove.
Lets prove it!
Always start with what you have been given. THIS IS WHAT WE KNOW!!!
Sep 298:58 AM
"If 2 angles are vertical angles, then they are congruent."
Write a story to prove the theorem!
There are many forms of a proof. A paragraph proof is written as sentences in a paragraph. Like a story.
Given: are vertical anglesProve:
what you knowwhat you show (prove)
1
2Add a 3 to the diagram 3
I was given that angle 1 and 2 are vertical angles. I know that <1 & <3 form a linear pair and so do <2 & < 3. Since a linear pair of angles are supplementary, I know that the m<1+m<3=180° and m<2+m<3=180°. If they are both equal to 180°, then I know by the substitution property, that they are both equal to each other. *m<1+m<3 = m<2+m<3* If I subtract the m<3 from both equations, then I get that m<1=m<2. If 2 angles are = in measure, then they are , therefore, <1 <2
Here's my story!!
Unit 1 Lesson 13 Proving Angle Theorems.notebook
3
Oct 107:51 AM
Let's do this in a 2column proof format.
My story was called a paragraph proof.
Statements Reasons1) <1 & <2 are vertical angles 1) Given2) <1 & <3 are supplementary 2) If 2 angles for a linear pair, then
they are supplementary.
Sep 2912:52 PM
used in proofs
Prove this theorem using a 2-column proof.
= implies
Statements Reasons
Now that we've proved this, we can use this rule in a proof!!
Unit 1 Lesson 13 Proving Angle Theorems.notebook
4
Sep 2912:52 PM
used in proofs
used in proofs
used in proofs
Lets prove 1 or more of these theorems. Remember, once a theorem is proved, it is yours to keep.....meaning, you can simply use the theorem in a proof instead of going through all of the steps required in proving the theorem.
* prove this one!
In an if...then statement,
the "if" is the given information
the "then" is what you have to prove.
Sep 2912:52 PM
Prove: All right angles are congruentStatements Reasons
1
2
1) 1)<1 and <2 are
right anglesGiven
2)
Unit 1 Lesson 13 Proving Angle Theorems.notebook
5
Sep 2912:53 PM
<1≅<2<1 & <2 are suppm<1 + m<2 = 180m<1 = m<2m<1 + m<1 = 1802(m<1)= 180m<1 = 90m<2 = 90<1 & <2 are right angles
Statements Reasons
1.2.3.4.5.6.7.8.9.
1.2.3.4.5.6.7.8.9.
Sep 2912:53 PM
GH J
K
Given: GH = JKProve: GJ = HK
Statements Reasons
Unit 1 Lesson 13 Proving Angle Theorems.notebook
6
Sep 291:00 PM
Homework
Unit 1 Lesson 13