Geo Grid Slides Geo Prep Power
Arkansas EOC Mastery: Part 1 — Congruence, Similarity, and Proofs
AR Standard: G.CO
AR Standard: G.SRT
The EOC Landscape
What to expect in Arkansas
Item Types
Multiple choice, multiple select, and technology-enhanced items (drag-and-drop proofs).
High Stakes Topics
Congruence and Similarity transformations are "Major Clusters" on the AR exam.
Pro-Tip:
"Arkansas Geometry exams love diagrams. Never trust your eyes—only trust the markings (ticks, arcs, and boxes)."
Congruence vs. Similarity
Congruence ≅
Rigid Motions: Reflection, Rotation, Translation
Same Size, Same Shape
Ratios are exactly 1:1
A
Similarity ~
Dilation (with Scale Factor k)
Same Shape, Different Size
Ratios are proportional
Cracking the Proof Code
Two-Column Logic for AR Success
KEY REASONS
• CPCTC
• Vertical ∠s
• Alt. Interior ∠s
• Reflexive Prop.
Think: "If... Then..."
Most EOC proof items are partially filled. Your job is to find the "Missing Link."
The CPCTC Trap
Remember: You can ONLY use CPCTC after you have proved the triangles are congruent.
Standard Proof Flow
1
Identify Given info & Mark Diagram
2
Find "Freebies" (Vertical ∠s, etc.)
3
Choose Postulate (SSS, SAS, AAS, ASA, HL)
4
Conclusion Statement
The Coordinate Toolkit
Distance Formula
\(d = \sqrt{(x_2-x_1)^2 + (y_2-y_1)^2}\)
Use for: Proving Congruence of segments or side lengths.
Slope Formula
\(m = \frac{y_2 - y_1}{x_2 - x_1}\)
Use for: Proving Parallel (m₁ = m₂) or Perpendicular (m₁ · m₂ = -1).
Midpoint Formula
\((\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\)
Use for: Proving Bisectors or finding centers of shapes.
Arkansas Edge: Partitioning Segments
Don't forget questions that ask for point P that divides segment AB in ratio a:b. Start at A and add a fraction of the "run" and "rise".
Sample Item #1 AR G.SRT.B.5
In △ABC, segment DE || segment BC. If AD = 4, DB = 6, and AE = 5, what is the length of segment EC?
A B C D E
A
3.5
B
7.5
C
8.0
D
10.0
Solution: Item #1
Strategy: Side-Splitter Theorem
\(\frac{AD}{DB} = \frac{AE}{EC} \rightarrow \frac{4}{6} = \frac{5}{x}\)
4x = 30 → x = 7.5
Choice B is Correct!
The Paragraph Proof Shift
On the EOC, you may be asked to complete a paragraph proof by selecting phrases from a drop-down menu.
Transition Words are Key:
• "Given that..."
• "Therefore..."
• "Consequently..."
• "By definition of..."
• "Since... it follows that..."
Drafting a Paragraph Proof
"It is given that segment AB ≅ segment CD and segment AB || segment CD. By the Alternate Interior Angles Theorem, ∠BAC ≅ ∠DCA. Since segment AC is a shared side, segment AC ≅ segment AC by the Reflexive Property. Thus, △ABC ≅ △CDA by SAS."
SAS Congruence Found!
EOC Readiness Check
Formula Sheet
Know which formulas are provided and which you must memorize (like Slope!).
Visual Check
Always look for hidden shared sides (Reflexive) and hidden angles (Vertical).
Pacing
Congruence/Similarity is often 20-25% of the total points. Prioritize it!
Marking
If using scratch paper, redraw the diagram and label with all known facts.
Arkansas Strong!
Proof Pilot Worksheet Proof Pilot Worksheet
Arkansas Geometry EOC Prep: Part 1
Student Name:
Date:
01 // Congruence & Similarity
Consider the two triangles shown below. Which sequence of transformations maps △ABC onto △DEF to prove they are congruent?
A (-4,-1) B (1,-1) C (1,4) D E F
A. A reflection across the y-axis followed by a translation 1 unit left.
B. A reflection across the x-axis followed by a rotation of 90° clockwise.
C. A translation 2 units right followed by a dilation with scale factor 1.
D. A rotation of 180° about the origin followed by a translation 3 units down.
In the figure below, ∠LMN ≅ ∠PQR and ∠MLN ≅ ∠QPR. Which statement must be true to prove that △LMN ~ △PQR?
L M N P Q R
A. Side LN ≅ Side PR
B. The ratio LM/PQ = MN/QR
C. No further info is needed (AA similarity).
D. △LMN must be a right triangle.
02 // Geometric Proofs
Complete the two-column proof below:
Given: segment AB || segment DE; C is the midpoint of segment AE.
Prove: △ABC ≅ △EDC
A B C D E
Statements
Reasons
1. segment AB || segment DE; C is midpoint of segment AE
1. Given
2. ∠BAC ≅ ∠DEC
2. (A) __________________________
3. segment AC ≅ segment EC
3. Definition of Midpoint
4. (B) __________________________
4. Vertical Angles Theorem
5. △ABC ≅ △EDC
5. (C) __________________________
Available Options
• Reflexive Prop. • Alternate Interior Angles • SAS • ASA • ∠ACB ≅ ∠ECD • SSS
03 // Coordinate Geometry
Quadrilateral WXYZ has vertices W(0,0), X(3,4), Y(8,4), and Z(5,0) . Prove that WXYZ is a rhombus .
Part A: Side Lengths (Distance Formula)
WX =
XY =
YZ =
ZW =
Part B: Written Justification
Explain how the side lengths above prove that the figure is a rhombus.
Point A is at (2, 3) and point B is at (12, 18). Find the coordinates of point P that partitions segment AB in the ratio 2:3.
P = (
Geo Guide Cheat Sheet Geo Guide Cheat Sheet
Arkansas EOC Essentials: Part 1
Congruence ≅
SSS
3 sides ≅
SAS
Side-Angle-Side
ASA
Angle-Side-Angle
AAS
Angle-Angle-Side
HL
Hyp-Leg (Right △ only)
NOT PROOFS:
AAA, SSA
Similarity ~
AA Similarity
2 angles are ≅
SAS Similarity
Sides proportional, ∠ ≅
SSS Similarity
All 3 sides proportional
The Coordinate Toolkit
Distance (Length)
d = √[(x₂-x₁)² + (y₂-y₁)²]
Slope (Steepness)
m = (y₂ - y₁) / (x₂ - x₁)
Midpoint (Center)
((x₁+x₂)/2, (y₁+y₂)/2)
Parallel: Same Slope (m₁ = m₂)
Perpendicular: Opp. Recip. (m₁ = -1/m₂)
Parallel Line Angles
Alternate Interior ≅
Alternate Exterior ≅
Corresponding ≅
Consec. Interior Supp (180°)
Proof "Freebies"
Reflexive Property
Something equals itself (Shared side/∠).
CPCTC
Corr. Parts of ≅ Δs are ≅.
Section Partition Formula
RATIO A:B on AB
P = (x₁ + [a/(a+b)](x₂-x₁), y₁ + [a/(a+b)](y₂-y₁))
Start at A.
Keep this reference for all Unit 1 Practice // Part of Geometry EOC Prep series
EOC Master Teacher Guide EOC Master Teacher Guide
Geo Prep Power // Part 1: Logic & Geometry
Teacher Resource
Pacing Guide (90 Min Block)
10 MIN
Entry Ticket & Standards
Review the Arkansas G.CO and G.SRT standards. Emphasize that congruence is defined by rigid motions (No dilation!).
30 MIN
Guided Review (Geo Grid Slides)
Use Slide 6-7 to model the Side-Splitter Theorem. Discuss how to "see" vertical angles even when not marked.
40 MIN
Independent Pilot Practice
Students complete the Proof Pilot Worksheet . Circulate and check Problem #5 (Partitioning) as it's a common struggle point.
10 MIN
EOC Strategy Debrief
Highlight the "Rhombus vs. Parallelogram" proof logic. All sides equal = Rhombus.
AR EOC Insight
"Arkansas Item Specs place a heavy emphasis on transformations as the foundation for congruence. Ensure students can identify a rotation vs. reflection on a coordinate plane."
Focus Areas:
• G.CO.B.6 (Congruence)
• G.CO.C.9 (Line Proofs)
• G.SRT.A.2 (Similarity)
• G.GPE.B.4 (Coord Proofs)
Worksheet Answer Key
01 // Congruence & Similarity
#1: Choice A
Reflection across y-axis followed by T(-1, 0).
#2: Choice C
AA Similarity requires only 2 sets of congruent angles.
02 // Geometric Proofs (#3)
Reason (A)
Alt. Interior Angles
Statement (B)
∠ACB ≅ ∠ECD
Reason (C)
ASA or AAS
03 // Coordinate Geometry
#4: Rhombus Proof (Corrected Vertices)
Side lengths for W(0,0), X(3,4), Y(8,4), Z(5,0):Conclusion: All four sides are equal (length 5), which satisfies the definition of a rhombus.
#5: Partitioning Point P = (6, 9)
x = 2 + (2/5)(10) = 6
Common Student Pitfalls
Transformation Order: Students often rotate then reflect, but the EOC may require the opposite order. Remind them to test a single point.
Congruence Criteria: SSA is NOT a proof. Students often mistake it for SAS.
