PIB Geometry

2-2:
from Algebra and
Two-Column Proofs!
Conditional:
If 2 coplanar lines are parallel, then they do not
intersect.
T/F?
Converse:
Biconditional:
of Algebra
Use p. 37-38 to help you identify the algebraic property.
1. If 5π‘₯– 3 = 27, then 5π‘₯ = 30.
2. If 𝑧 = 7 and 𝑦 = 7, then 𝑧 = 𝑦.
3. 10(π‘₯ + 7) = 10π‘₯ + 70.
4. If 18π‘₯ = 36, then π‘₯ = 2.
5. If 𝑦 = 3π‘₯ + 7 and π‘₯ = 2, then 𝑦 = 3(2) + 7.
6. 𝑃𝑄 β‰… 𝑃𝑄.
Addition Property of Equality
Adding the same number to
both sides of an equation
keeps the equation true.
Add. Prop. of =
If 𝒂 = 𝒃,
then 𝒂 + 𝒄 = 𝒃 + 𝒄
Multiplication Property of Equality
Multiplying the same number by
both sides of an equation
keeps the equation true.
Mult. Prop. of =
If 𝒂 = 𝒃,
then 𝒂 · 𝒄 = 𝒃 · 𝒄
Reflexive Property of Equality
Relf. Prop. of =
Any value (number)
is equal to itself.
𝒂=𝒂
Symmetric Property of Equality
Sym. Prop. of =
The two sides of an equation
can be written in either order.
If 𝒂 = 𝒃,
then 𝒃 = 𝒂
Transitive Property of Equality
Two values that are
both equal to a third value
must be equal to each other.
Trans. Prop. of =
If 𝒂 = 𝒃, and 𝒃 = 𝒄
then 𝒂 = 𝒄
Substitution Property of Equality
Any value
can be replaced (substituted)
by any value equal to it.
Subs. Prop. of =
If 𝒂 = 𝒃, then 𝒃 can replace
𝒂 in any expression
Distributive Property
Dist. Prop.
A number that multiplies a sum
can multiply each term in the sum.
𝒂 𝒃+𝒄 =𝒂·π’ƒ+𝒂·π’„
Reflexive Property of Congruence
Any geometric figure
that can be measured
is congruent to itself.
Refl. Prop. of β‰…
βˆ π’‚ β‰… βˆ π’‚
𝑨𝑩 β‰… 𝑨𝑩
Symmetric Property of Congruence
The two sides of a
congruence statement
can be written in either order.
Sym. Prop. of β‰…
If βˆ π’‚ β‰… βˆ π’ƒ, then βˆ π’ƒ β‰… βˆ π’‚
If 𝑨𝑩 β‰… π‘ͺ𝑫, then π‘ͺ𝑫 β‰… 𝑨𝑩
Transitive Property of Congruence
Two geometric figures that are
both congruent to a third figure
must be congruent to each other.
Trans. Prop. of β‰…
If βˆ π’‚ β‰… βˆ π’ƒ, and βˆ π’ƒ β‰… βˆ π’„,
then βˆ π’‚ β‰… βˆ π’„
2-Column Proofs
Step-by-step logic
Justify each step
Statements
Reasons
Algebra Examples
Given: π‘Ž 𝑏 + 𝑐 = 𝑑 + π‘Žπ‘, 𝑏 = 1
Statements
Prove: π‘Ž = 𝑑 .
Reasons
Algebra Examples
Given: π‘Ž = 𝑏 + 𝑐, 𝑐 < 0
Statements
Prove: π‘Ž < 𝑏
Reasons
Geometry Time!
Given: π‘šβˆ 1 = π‘šβˆ 3, m∠2 = π‘šβˆ 4
Statements
Prove: π‘šβˆ π΄π΅πΆ = π‘šβˆ π·πΈπΉ
Reasons
𝐴
1
𝐡
2
𝐢
𝐹
4
3
𝐷
𝐸
Geometry Time!
Given: π‘…π‘ˆ = 𝐼𝑇, 𝑅𝑁 = 𝑆𝑇
Reasons
𝑅
𝑆
π‘ˆ
β‹…
β‹…
Statements
Prove: π‘ˆπ‘ = 𝑆𝐼
𝑁
𝐼
𝑇
p. 41: 1-13 odd
You should be copying all diagrams on
homework assignments