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Chapter 1 postulates:
Postulate
Postulate 1-1:
Illustration
Through any two points there is exactly one line.
Postulate 1-2:
If two distinct lines intersect, then they intersect in
exactly one point.
Postulate 1-3:
If two distinct planes intersect, then they intersect in
exactly one line.
Postualte 1-4:
Through any three noncollinear points there is
exactly one plane.
Postulate 1-5:
Ruler Postulate
Every point on a line can be paired with a real
number. This makes a one-to-one correspondence
between the points on the line and the real number.
Postulate 1-6
Segment Addition
Postulate
If three points, A, B, and C are collinear, and B is in
between A and C, then
AB + BC = AC
Postulate 1-7:
Protractor Postulate
Consider ⃗⃗⃗⃗⃗
𝑂𝐵 and a point A on one side of ⃗⃗⃗⃗⃗
𝑂𝐵. Every
⃗⃗⃗⃗⃗
ray of the form 𝑂𝐴 can be paired one to one with a
real number from 0 to 180.
Postulate 1-8:
Angle Addition
Postulate
If point B is in the interior of ∠AOC, then
𝑚∠𝐴𝑂𝐵 + 𝑚∠𝐵𝑂𝐶 = 𝑚∠𝐴𝑂𝐶
Postulate 1-9 :
Linear Pair Postulate
If two angles form a linear pair, then they are
supplementary.
Chapter 2: Postulates and Theorems:
Theorem 2-1:
Vertical Angle Theorem.
Vertical angles are congruent
Theorem 2-2:
Congruent Supplement
Theorem
If two angles are supplements of
the same angle (or of congruent
angles) then the two angles are
congruent.
Theorem 2-3:
Congruent Complement
Theorem.
If two angles are complements of
the same angle (or of congruent
angles), then the two angles are
congruent.
Theorem 2-4
All right angles are congruent.
Theorem 2-5
If two angles are congruent and
supplementary, then each is a right
angle.
Geometry:
Section 2.6: Proving Angles Congruent
Goal: Students will understand how to defend claims about angle relationships.
Claim: Vertical Angles are Congruent.
Given ∠1 and ∠3 are vertical angles
Prove: ∠1 ≅ ∠3
Statements
Reasons
Problem 1: Use the vertical angle theorem:
Find the value of x.
Problem 2: Proof Using the vertical angle theorem:
Given: ∠1 ≅ ∠4
Prove: ∠2 ≅ ∠3
Problem 3: Writing a paragraph proof.
Given ∠1 and ∠3 are supplementary
Prove: ∠2 and ∠3 are supplementary
Prove: ∠1 ≅ ∠2
Practice:
1.
2. Find m1 using the given information.
m1 = 5x, m4 = 2x + 90
3.Complete the proofs by filling in the blanks
Given: A  BDA
Prove: x = 5
Statements
Reasons
1)
1) Given
2)
2) Vertical Angles are .
3) A  CDE
3)
4)
4) Definition of Congruence
5) 11x + 20 = 12x + 15
5)
6)
6) Subtraction Property of Equality
7)
7)
4. Given: 5 2
Prove: 8  4
Statements
Reasons
1)
1) Given
2) 2  4
2)
3)
3) Transitive Property of Congruence
4)
4) Vertical Angles are .
5) 8  4
5)
5. Use a two column proof or a paragraph proof to
develop the proof below:
Given: 1 and 2 are complementary
2 and 3 are complementary
BD bisects ABC
Prove: m1 = 45
Be sure to copy each step of the proof in your homework, not just the ones you must
fill in. 6, 7, 8, 12 , 17, 18, 20, 21,22, 25 Challenge: 30 and 31