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Geometry A: “Reasons” Bank
***Definitions, Postulates, and Theorems are all used as justifications (or reasons) when completing a 2-column proof. The following sheet is a
quick visual aid to assist you in completing proofs.
Directions: Use the glossary or your notes to define each term and create a visual aid for each definition. The first definition is done for you!
Do not complete the visual aid section!!! We will do this together.
Chapter 2 Definitions:
Definitions (from Glossary/Notes)
Shorthand (for use in proofs)
Congruent Segments:
≅ segs. ↔ measures are =
Congruent Angles:
≅ ∠𝑠 ↔ measures are =
Midpoint:
Midpoint ↔ 2 ≅ segments
Visual Aid (come up with a visual description of each
definition)
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Angle Bisector:
∠ bisector ↔ 2 ≅ ∠𝑠
Straight Angle:
Straight ∠ ↔ measure is 180°
Right Angle:
rt. ∠ ↔ measure is 90°
Linear Pair:
lin. pair ↔ opp. rays make a line
Complementary Angles:
comp ∠𝑠 ↔ 2 ∠measures add up to 90°
Supplementary Angles:
supp ∠𝑠 ↔ 2 ∠ measures add up to 180°
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Definitions (from Glossary/Notes)
Shorthand (for use in proofs)
Perpendicular Lines/Segments
⊥ lines/segments ↔ lines/segments
intersect at 90° ∠s
Perpendicular Bisector
⊥ bisector ↔ line intersects a segment at
the segs. midpoint
Altitude of a Triangle
altitude ↔ 2 rt. ∠𝑠
Isosceles Triangle
Isos. Δ ↔ 2 ≅ sides
Visual Aid (come up with a visual description of each
definition)
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Directions: Use your 2.5 notes to state the two Postulates below. Use the visuals included in the 2.5 Notes
Chapter 2 Postulates:
Postulate (from Notes)
Shorthand (for use in proofs)
Visual Aid (come up with a visual description of
each postulate)
Segment Addition Postulate
Seg. Add Post.
Angle Addition Postulate
∠ Add Post.
Directions: Use your 2.5 Notes to write down the following important properties.
8 Properties of Equality:
3 Properties of Congruence:
Add. Prop =
Subtr. Prop =
Mult. Prop =
Divis. Prop =
Subst. Prop =
Transitive Prop =
Refl. Prop =
Sym. Prop =
Transitive Prop. ≅
Sym. Prop ≅
Reflex. Prop ≅
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Chapter 2 and 3: Postulates/Theorems
Postulate/Theorem (from Notes)
Shorthand (for use in proofs)
Linear Pair Theorem:
Lin. Pair Thm
Vertical Angles Theorem:
Vert. ∠𝑠 Thm
Right Angle Congruence Theorem:
𝑟𝑡. ∠ ≅ Thm
Corresponding Angles Postualte/ Converse of
Corresponding Angles Postulate
𝑙𝑖𝑛𝑒𝑠 ∥ ↔ 𝑐𝑜𝑟𝑟. ∠𝑠 ≅
Alternate Interior Angles Theorem/ Converse
of Alternate Interior Angles Theorem
Alternate Exterior Angles Theorem/ Converse
of Alternate Exterior Angles Theorem
Same Side Interior Angles Theorem/
Converse of Same Side Interior Angles Thm
Visual Aid (come up with a visual description
of each postulate)
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