Angle Master Review Worksheet
SPED Scaffolded Review
Parallel Lines & Angle Pairs
Unit 2 Geometry Exam Preparation & Reference Sheet
Name: ________________
Date: _________
Period: ____________
Goal: 100% Mastery
The "Big / Small" Angle Secret Rule: When lines are parallel (\(l \parallel m\)), there are only TWO angle sizes!
Same Type = EQUAL (\(\cong\)) Different = ADD TO 180°
Visual Map (\(l \parallel m\)) line l line m transversal n 1 2 4 3 8 5 7 6
Acute (2, 4, 5, 7) Obtuse (1, 3, 6, 8)
Angle Pair Reference Guide Relationship when \(l \parallel m\)
<table class="w-full border-collapse"><tbody class="divide-y divide-slate-200"><tr class="bg-amber-50/50"><td class="p-1.5 font-bold text-slate-800 w-36">Corresponding</td><td class="p-1.5 text-slate-600">Same corner position</td><td class="p-1.5 font-bold text-emerald-700 bg-emerald-50 text-center">EQUAL (\(\cong\))</td></tr><tr><td class="p-1.5 font-bold text-slate-800">Alternate Interior</td><td class="p-1.5 text-slate-600">Inside lines, opposite sides</td><td class="p-1.5 font-bold text-emerald-700 bg-emerald-50 text-center">EQUAL (\(\cong\))</td></tr><tr class="bg-amber-50/50"><td class="p-1.5 font-bold text-slate-800">Alternate Exterior</td><td class="p-1.5 text-slate-600">Outside lines, opposite sides</td><td class="p-1.5 font-bold text-emerald-700 bg-emerald-50 text-center">EQUAL (\(\cong\))</td></tr><tr><td class="p-1.5 font-bold text-slate-800">Vertical Angles</td><td class="p-1.5 text-slate-600">Opposite each other in "X"</td><td class="p-1.5 font-bold text-emerald-700 bg-emerald-50 text-center">EQUAL (\(\cong\))</td></tr><tr class="bg-teal-50/50"><td class="p-1.5 font-bold text-slate-800">Same-Side Interior</td><td class="p-1.5 text-slate-600">Inside lines, same side</td><td class="p-1.5 font-bold text-purple-700 bg-purple-50 text-center">SUM = 180°</td></tr><tr><td class="p-1.5 font-bold text-slate-800">Same-Side Exterior</td><td class="p-1.5 text-slate-600">Outside lines, same side</td><td class="p-1.5 font-bold text-purple-700 bg-purple-50 text-center">SUM = 180°</td></tr><tr class="bg-teal-50/50"><td class="p-1.5 font-bold text-slate-800">Linear Pair</td><td class="p-1.5 text-slate-600">Adjacent on a straight line</td><td class="p-1.5 font-bold text-purple-700 bg-purple-50 text-center">SUM = 180°</td></tr></tbody></table>
1
Guided Practice: Identify & Classify Angle Pairs
Use the diagram above. Follow the 2 prompts for each angle pair.
[MODEL] \(\angle 1\) and \(\angle 5\) I Do
Location: Both in Top-Right position of their group.
Name: Corresponding Angles
Relationship: Congruent (\(m\angle 1 = m\angle 5\))
Problem 1: \(\angle 8\) and \(\angle 1\) We Do
Are they inside or outside the lines? _________________
Are they on the same or alternate sides? _______________
Angle Pair Name: ____________________________________
Problem 2: \(\angle 4\) and \(\angle 5\) You Do
Both angles are (circle one): [ Acute | Obtuse ]
Angle Pair Name: ____________________________________
Equation rule: [ Equal (=) | Add to 180° ]
Problem 3: \(\angle 4\) and \(\angle 8\) You Do
Both angles are inside lines on the same side of transversal.
Angle Pair Name: ____________________________________
Equation rule: [ Equal (=) | Add to 180° ]
Exam Check 1: Test Each Statement True or False Analysis
When \(l \parallel m\), evaluate each statement as TRUE or FALSE:
I: \(\angle 1\) & \(\angle 5\) are corresponding
[ ] TRUE [ ] FALSE
II: \(\angle 8\) & \(\angle 1\) are alt. exterior
[ ] TRUE [ ] FALSE
III: \(\angle 6\) & \(\angle 2\) are same-side ext.
[ ] TRUE [ ] FALSE
Which statements are true? (a) I only (b) I and II (c) II and III (d) III only My Answer: [ ]
Page 1 of 3 • Geometry Unit 2 Scaffolded Review • Strategy & Foundations
Level 2 & 3: Solving & Proofs
Solving Equations & Proving Lines Parallel
Test Q#2, #3, #6, #7, #8 Prep
3-Step Algebra Decision Protocol:
Step 1: Check Angles Both acute OR both obtuse? \(\rightarrow\) Set Equal (\(A = B\)).
One acute & one obtuse? \(\rightarrow\) \(A + B = 180\).
Step 2: Solve for \(x\) Move variables to one side, isolate \(x\) using inverse operations.
Step 3: Answer Question! Did it ask for \(x\) or an angle measure? Plug \(x\) back in if required!
2
Guided Algebraic Solve
In the diagram, \(p \parallel q\). Given \(m\angle 6 = (5x + 3)^\circ\) and \(m\angle 1 = (11x + 33)^\circ\). Find the value of \(x\), then determine \(m\angle 5\).
p q 1 2 5 6
1. Relationship
\(\angle 1\) and \(\angle 6\) are both obtuse. Alternate exterior angles are:
Congruent (=)
2. Set Up Equation
11x + 33 = 5x + 3...
3. Solve for \(x\)
\(x =\) ______
4. Find \(m\angle 5\)
\(\angle 5\) & \(\angle 6\) form linear pair (180°):
\(m\angle 5 =\) ______°
3
Proving Lines Parallel (The Converse Rules)
Key Rule: Angles MUST connect Line 1 to Line 2! Vertical angles or linear pairs on the same intersection NEVER prove lines are parallel!
Problem 5 (Test #3 Style)
In a diagram, \(m\angle 3 = 27^\circ\) and \(m\angle 5 = 152^\circ\). These are Same-Side Interior angles.
Check the rule: Do they add to \(180^\circ\)?
\(27^\circ + 152^\circ =\) ________°
Are lines \(a\) and \(b\) parallel? [ YES (\(a \parallel b\)) | NO (\(a \nparallel b\)) ]
Problem 6 (Test #10 Style): Non-Proof Identification
Which of the following will NOT prove \(l \parallel m\)?
- • \(\angle 5 \cong \angle 2\) (Alternate Interior Angles)
- • \(\angle 4 + \angle 5 = 180^\circ\) (Consecutive Interior Angles)
- • \(\angle 8 \cong \angle 6\) (Vertical angles on line \(m\))
Explain why: \(\angle 8 \cong \angle 6\) is always true because they are vertical angles, so it (does / does not) prove lines are parallel: _________________
Quick Check (Test #8): If \(\overline{AB} \parallel \overline{CD}\) and \(m\angle 5 = 40^\circ\) (acute), then: All acute angles = 40° All obtuse angles = 180° - 40° = 140°
\(m\angle 4 =\) 140° | \(m\angle 1 =\) 40°
Page 2 of 3 • Geometry Unit 2 Scaffolded Review • Equations & Proofs
Level 4 & 5: Advanced & Open-Ended
Quadratic Equations & Multi-Line Diagrams
Test Q#5, #9, #11, #12-13 Prep
4
Quadratic Angles
In the diagram below, \(\overleftrightarrow{AB} \parallel \overleftrightarrow{CD}\), \(m\angle 1 = (x^2 + 7x)^\circ\) and \(m\angle 5 = (9x + 35)^\circ\). Determine the measure of \(\angle 8\).
Step-by-Step Model
Step 1: Set Up
\(\angle 1\) & \(\angle 5\) are corresponding \(\rightarrow\) EQUAL
x² + 7x = 9x + 35
Step 2: Set to 0
Subtract \(9x\) and \(35\) from both sides:
x² - 2x - 35 = 0
Step 3: Factor
Multiply to \(-35\), add to \(-2\):
(x - 7)(x + 5) = 0
\(x = 7\) (\(x = -5\) gives neg)
Step 4: Find \(m\angle 8\)
Plug \(x = 7\) into \(m\angle 5\):
\(9(7) + 35 = 98^\circ\)
\(\angle 8 = 180 - 98 =\) 82°
5
Right Triangle Angles
In right triangle \(\triangle ABC\) where \(m\angle C = 90^\circ\), \(m\angle A = (x^2 + 5)^\circ\) and \(m\angle B = (20 + 8x)^\circ\). What is the value of \(x\)?
Triangle Angle Sum
Scaffolded Hint: In a right triangle, the two acute angles add up to \(90^\circ\):
\((x^2 + 5) + (20 + 8x) = 90\)
Combine like terms: \(x^2 + 8x + 25 = 90\) \(\rightarrow\) Subtract 90: \(x^2 + 8x - 65 = 0\)
Factor: \((x + 13)(x - 5) = 0\) \(\rightarrow\) Value of \(x\) (must make angle positive): x = ______
A B C \(\angle A + \angle B = 90^\circ\)
6
Open-Ended Transversal Mastery
Show All Work
In the figure to the right, \(\overleftrightarrow{AB} \parallel \overleftrightarrow{DC}\). The lines intersect at \(O\) with \(\angle DOC\) forming a right angle (\(90^\circ\)). Given \(m\angle OAB = (9x)^\circ\) and \(m\angle CDO = (x^2)^\circ\):
Part A: Find the value of \(x\)
Hint: \(\angle OAB\) and \(\angle CDO\) are Alternate Interior Angles \(\rightarrow\) Set Equal!
\(x =\) _________
Part B: Find \(m\angle DCO\)
Hint: In \(\triangle CDO\), \(m\angle D + m\angle O + m\angle C = 180^\circ\) where \(m\angle O = 90^\circ\).
\(m\angle DCO =\) _________°
A B D C O \(\overleftrightarrow{AB} \parallel \overleftrightarrow{DC}\) with \(\perp\) at \(O\)
Page 3 of 3 • Geometry Unit 2 Scaffolded Review • Quadratics & Applications
Angle Master Answer Key
Teacher Answer Key & SPED Guide
Parallel Lines & Angle Pairs — Solutions
Page 1 Solutions, Modeling Prompts, and SPED Instructional Accommodations
Answer Key
Geometry Unit 2 Review
SPED Instructional Strategy: Color & Shape Anchors
Students with visual processing or working memory difficulties often struggle with the names "alternate interior" vs "consecutive interior." Teach them the "Big Angle / Small Angle" test: all acute angles created by parallel lines are congruent to each other, and all obtuse angles are congruent. An acute + an obtuse angle ALWAYS equals \(180^\circ\).
Visual Reference Map & Classification Key
Acute Angles (All Congruent to Each Other)
\(\mathbf{\angle 2 \cong \angle 4 \cong \angle 5 \cong \angle 7}\)
Every one of these angles has the exact same degree measure!
Obtuse Angles (All Congruent to Each Other)
\(\mathbf{\angle 1 \cong \angle 3 \cong \angle 6 \cong \angle 8}\)
Every one of these angles has the exact same degree measure!
Solutions: Guided Practice & Tier 1 Items
Problem 1: \(\angle 8\) and \(\angle 1\)
• Location: Outside (Exterior)
• Sides: Alternate sides of transversal
• Name: Alternate Exterior Angles
Relationship: EQUAL (\(\cong\))
Problem 2: \(\angle 4\) and \(\angle 5\)
• Both angles are: Acute
• Location: Inside, opposite sides
• Name: Alternate Interior Angles
Relationship: Equal (\(=/\cong\))
Problem 3: \(\angle 4\) and \(\angle 8\)
• Location: Inside lines, same side
• Name: Consecutive (Same-Side) Interior
Relationship: ADD TO 180° (Supplementary)
Notice: \(\angle 4\) is acute and \(\angle 8\) is obtuse!
Exam Check 1 (Test #1 Match)
I: \(\angle 1\) & \(\angle 5\) corresponding \(\rightarrow\) TRUE
II: \(\angle 8\) & \(\angle 1\) alt. exterior \(\rightarrow\) TRUE
III: \(\angle 6\) & \(\angle 2\) same-side ext. \(\rightarrow\) FALSE (\(\angle 6\) is ext, \(\angle 2\) is ext, but they are on alternate sides!)
Correct Option: (b) I and II
SPED Misconception Alert (Test Question #4 Prep):
When a diagram has two parallel lines and two transversals (giving 16 numbered angles), students often get confused by the double intersections. Coach them to so they only see one 8-angle cluster at a time!
