Triangle Similarity & Angle Review
Triangle Similarity & Angle Review
Part 1: The Angle-Angle (AA) Similarity Criterion
Name:
Date: Period:
Angle-Angle (AA) Similarity Rule: If two angles of one triangle equal two angles of another triangle, the triangles are similar (\(\sim\)). 💡 Reminder: Triangle angles add to 180°. If an angle is missing, subtract the known angles from 180°!
Problem 1 • Guided Practice Show each step of your work below
Triangle \(ABC\) has angles of 45° and 65°. Triangle \(XYZ\) has angles of 45° and 70°. Are they similar by AA?
Step 1: Missing in \(\triangle ABC\)
Add: 45° + 65° = ______°
Subtract: 180° − ______°
3rd angle: ______°
Step 2: Missing in \(\triangle XYZ\)
Add: 45° + 70° = ______°
Subtract: 180° − ______°
3rd angle: ______°
Step 3: Compare & Conclude
YES NO
Why?
Do 2 pairs match?
Problem 2 Calculate & Compare
Are Triangle A and Triangle B similar by AA?
35° 85° ? Triangle A 35° 60° ? Triangle B
Missing angle in A: ________°
Missing angle in B: ________°
Similar? YES NO
Problem 3 Right Triangles
Each triangle has a right angle (90°). Are they similar?
32° ? Triangle C 58° ? Triangle D
Missing angle in C: ________°
Missing angle in D: ________°
Similar? YES NO
Problem 4 • Mistake Detective Explain your mathematical thinking
Marcus says: "Triangle J has angles of 50° and 60°. Triangle K has angles of 60° and 70°. Since only one angle matches (60°), they are definitely NOT similar."
Is Marcus correct? Show your angle work and write your explanation below.
Triangle J: (50°, 60°, ? )
180° − (50° + 60°) =
3rd angle = ______°
Triangle K: (60°, 70°, ? )
180° − (60° + 70°) =
3rd angle = ______°
Marcus is: Correct Incorrect
Explain your reasoning:
Unit: Angles & Triangles (8.G.A.5) Page 1 of 2
Triangle Similarity & Angle Review
Part 2: Exterior Angle Theorem & Parallel Transversals
Name:
Date: Period:
Find Exterior Angle
Add 2 remote inside angles:
\(\text{Ext } \angle = \angle A + \angle B\)
Find Remote Inside
Subtract known from exterior:
\(\text{Inside } \angle = \text{Ext} - \text{Known}\)
Parallel Lines & Transversal
Lines \(p \parallel q\):
Only 2 angle measures exist!
Problem 5 • Find the Exterior Angle
Find exterior angle \(y\) using the remote interior angles.
46° 78° y
Equation: \(y = 46^\circ + 78^\circ\)
Value of \(y\): \(y =\) ______\(^\circ\)
Problem 6 • Find the Remote Inside Angle
The exterior angle is 125°. Find missing angle \(w\).
55° w 125°
Equation: \(w = 125^\circ - 55^\circ\)
Value of \(w\): \(w =\) ______\(^\circ\)
Problem 7 • Parallel Lines Cut by a Transversal Lines \(p \parallel q\)
Parallel lines \(p\) and \(q\) are intersected by transversal line \(t\). Angle 1 measures 115°.
p q t 115° ∠2 ∠3 ∠4 ∠5 ∠6 ∠7 ∠8
a) Vertical Angle:
Across from 115° (\(\angle 3\)).
\(m\angle 3 =\) °
b) Supplementary Angle:
Line with 115° (\(\angle 2\)): \(180-115\).
\(m\angle 2 =\) °
c) Corresponding Angle:
Top-right match (\(\angle 5\)).
\(m\angle 5 =\) °
d) Alternate Interior:
Inside, opposite (\(\angle 3\) & \(\angle 5\)).
Equal? [ ] Yes [ ] No
e) Alternate Exterior:
Outside, opposite (115° & \(\angle 7\)).
\(m\angle 7 =\) °
f) Consecutive Interior:
Inside, same side (\(\angle 3 + \angle 6\)):
Sum \(=\) °
The "Two-Angle Rule" Detective Tracker: (Sort 1–8 into each box)
Obtuse (115°): ∠1, ∠___, ∠___, ∠___
Acute (65°): ∠2, ∠___, ∠___, ∠___
⭐ Extra Credit Challenge Algebra Meets the Exterior Angle Theorem
+5 Points
A triangle has remote interior angles of \(2x^\circ\) and \(50^\circ\), and its exterior angle measures \((4x + 10)^\circ\). Solve for \(x\) and find the exterior angle measure.
1. Set Up Equation:
\(\text{Ext} = \text{Remote}_1 + \text{Remote}_2\)
\(4x + 10 = 2x + 50\)
2. Solve for \(x\):
Subtract \(2x\) and \(10\):
\(x =\)
3. Find Exterior Angle:
Plug \(x\) into \(4x + 10\):
\(\text{Angle} =\) ______\(^\circ\)
Unit: Angles & Triangles (8.G.A.5) Page 2 of 2
Triangle Similarity & Angle Review Answer Key
Triangle Similarity & Angle Review
TEACHER ANSWER KEY
Part 1: The Angle-Angle (AA) Similarity Criterion
Page 1 • Total: 15 Pts
Key Teaching Concept: Students testing below level often look only at the two given angles and conclude triangles are not similar when the numbers don't match initially. Remind them to always find all three angles before deciding!
Problem 1 • Guided Practice Solution 3 Points (1 pt per box)
Triangle \(ABC\) has angles of 45° and 65°. Triangle \(XYZ\) has angles of 45° and 70°. Are they similar by AA?
Step 1: Missing in \(\triangle ABC\)
Add: 45° + 65° = 110°
Subtract: 180° − 110° = 70°
3rd angle: 70°
Step 2: Missing in \(\triangle XYZ\)
Add: 45° + 70° = 115°
Subtract: 180° − 115° = 65°
3rd angle: 65°
Step 3: Compare & Conclude
YES NO
Both triangles have angles: 45°, 65°, 70°.
All 3 angle pairs match!
Problem 2 Solution 3 Points
Are Triangle A and Triangle B similar by AA?
35° 85° 60° Triangle A 35° 60° 85° Triangle B
Missing angle in A: 180 − 120 = 60°
Missing angle in B: 180 − 95 = 85°
Similar? YES (Both have 35°, 60°, 85°)
Problem 3 Solution 3 Points
Each triangle has a right angle (90°). Are they similar?
32° 58° Triangle C 58° 32° Triangle D
Missing angle in C: 90 − 32 = 58°
Missing angle in D: 90 − 58 = 32°
Similar? YES (Both have 90°, 32°, 58°)
Problem 4 • Mistake Detective Solution & Rubric 6 Points (2 pts angles, 1 pt claim, 3 pts explanation)
Marcus says: "Triangle J has angles of 50° and 60°. Triangle K has angles of 60° and 70°. Since only one angle matches (60°), they are definitely NOT similar."
Triangle J: (50°, 60°, ? )
180° − (50° + 60°) = 180° − 110°
3rd angle = 70° → (50°, 60°, 70°)
Triangle K: (60°, 70°, ? )
180° − (60° + 70°) = 180° − 130°
3rd angle = 50° → (50°, 60°, 70°)
Marcus is: Correct INCORRECT
Exemplar Student Response:
"Marcus is incorrect because he forgot to find the missing third angles. Triangle J has angles of 50°, 60°, and 70°, and Triangle K also has angles of 50°, 60°, and 70°. Since all three angle pairs are equal, the two triangles ARE similar by the Angle-Angle criterion."
