Angle Alliances Review Worksheet
Geometry Foundations Angle Rules & Justifications
Angle Alliances Review
Parallel Lines • Triangle Exterior Angles • Similar Triangles (AA)
Name:
Date:
Period:
1. Transversal Rules
When two lines are parallel:
• Alt. Interior: EQUAL (Z-shape)
• Corresponding: EQUAL (F-shape)
• Consec. Interior: ADD TO 180°
2. Exterior Angle Rule
Outside angle equals sum of 2 far inside angles:
Outside = Inside + Inside
Example: \( 50^\circ + 60^\circ = 110^\circ \)
3. AA Similarity (Angle-Angle)
If 2 pairs of angles match:
Triangles are SIMILAR (\(\sim\))
Same shape, different size!
WORD BANK Alternate Interior Angles Corresponding Angles Consecutive Interior Angles Exterior Angle Theorem AA Similarity
Part I: Transversals & Parallel Lines Practice
Use the word bank to name each rule
p q t 65° ∠1 = ? Lines \( p \parallel q \) cut by transversal \( t \)
Problem 1. Look at the two marked angles inside the parallel lines on opposite sides of the transversal line.
Step 1: Check the rule These angles form a Z-shape on opposite sides inside. They are:
Circle one: EQUAL (\(\cong\)) ADD TO 180°
Step 2: Justify with the theorem name
Theorem Name:
Step 3: What is the measure of \( \angle 1 \)? Since they are equal, \( m\angle 1 = \)
___°
m n k 120° ∠2 = ? Lines \( m \parallel n \) cut by transversal \( k \)
Problem 2. These two angles are on the same side inside the parallel lines (C-shape).
Step 1: Identify relationship & theorem
Theorem:
Step 2: Consecutive interior angles add up to 180°
Subtract from 180° to find \( \angle 2 \): \( 180^\circ - 120^\circ = \)
Step 3: Final Answer Measure of \( \angle 2 \):
___°
Angle Alliances: Guided Review & Practice Page 1 of 2 Turn over for Exterior Angles & AA Similarity →
Angle Alliances Review
Part II, III & IV: Triangle Angles & Similarity
Student Name:
Part II: Triangle Exterior Angle Theorem
Outside Angle = Inside Angle + Inside Angle
P Q R S 45° 70° ?° Find exterior angle \( \angle QRS \)
Problem 3. Find the measure of outside angle \( \angle QRS \) using the two remote inside angles.
A. Name the theorem:
Theorem:
B. Add the two inside angles:
\( \text{Exterior Angle } (\angle QRS) = 45^\circ + 70^\circ = \)
C. Linear Pair Check: Inside \( \angle PRQ \) and outside \( \angle QRS \) make a straight line (\( 180^\circ \)):
\( 180^\circ - 115^\circ = \) °
Part III: Are These Triangles Similar by AA?
Check if 2 angle pairs match
A B C 50° 65° D E F 50° 65° Compare \( \triangle ABC \) and \( \triangle DEF \)
Problem 4. Determine if \( \triangle ABC \) and \( \triangle DEF \) are similar using the Angle-Angle (AA) rule.
A. Pair 1: Do they share a matching angle?
\( \angle A = 50^\circ \) and \( \angle D = 50^\circ \). Are they equal? [ Circle: YES / NO ]
B. Pair 2: Do they share a second matching angle?
\( \angle B = 65^\circ \) and \( \angle E = 65^\circ \). Are they equal? [ Circle: YES / NO ]
C. Conclusion & Justification: Are the two triangles similar?
[ YES / NO ] by AA Postulate
Mixed Finale
Part IV: The Big Connection (All 3 Topics)
Transversal + Exterior Angle + AA Similarity
G H K P M N 40° 70° ? \( MN \parallel HK \); \( m\angle G = 40^\circ \), \( m\angle GMN = 70^\circ \)
Problem 5. Follow the 3 guided steps to solve the diagram:
Step 1 (Transversal): Find \( m\angle GHK \)
Because \( MN \parallel HK \), \( \angle GHK \) and \( \angle GMN \) are Corresponding Angles (F-shape).
Therefore, \( m\angle GHK = \) ° (they are equal!).
Step 2 (Exterior Angle): Find \( m\angle GKP \)
In \( \triangle GHK \), the two far inside angles are \( 40^\circ \) and \( 70^\circ \). Add them:
\( \text{Exterior } m\angle GKP = 40^\circ + 70^\circ = \) °.
Step 3 (AA Similarity): Are the small & large triangles similar?
Both triangles have a \( 40^\circ \) angle (\( \angle G \)) and both have a \( 70^\circ \) angle.
\( \triangle GMN \sim \triangle GHK \)? [ Circle: YES / NO ] by the AA Postulate.
Angle Alliances: Guided Review & Practice Great Job! Review your angle rules and check your addition. Page 2 of 2
