Understanding Angle-Angle Similarity
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Beginner
Start here! Easy to understand
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Beginner Explanation
The AA (Angle-Angle) Similarity states that if two triangles have two pairs of corresponding angles that are congruent, then the triangles are similar.
Practice Problems
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1
Quick Quiz
Single Choice Quiz
Beginner
Given triangles ABE and DCE that share vertex E (with triangle ABE formed by vertices A–E–B in clockwise order and triangle DCE formed by vertices D–C–E in clockwise order), and given that $\angle A \cong \angle D$ (angle at vertex A in triangle ABE corresponds to angle at vertex D in triangle DCE) and $\angle E \cong \angle B$ (angle at vertex E in triangle ABE corresponds to angle at vertex B in triangle DCE), are the triangles ABE and DCE similar?
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2
Real-World Problem
Question Exercise
Intermediate
The Leaning Tower of Pisa
A group of students want to measure the height of the Leaning Tower of Pisa, but they can't measure it directly. They decide to use a metre stick and the principles of AA Similarity. If a 1m stick casts a shadow of 2m at the same time the tower casts a shadow of 90m, can you find the height of the tower?
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3
Thinking Challenge
Thinking Exercise
Intermediate
Think About This
Triangle ABC and triangle DEF are such that $\angle A \cong \angle D$ and $\angle B \cong \angle E$, establishing the correspondence A↔D, B↔E, and C↔F. If AB = 5cm, AC = 3cm, and DF = 10cm, find the length of DE.
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4
Challenge Quiz
Single Choice Quiz
Advanced
In triangle PQR, $\angle P = 40^\circ$ and $\angle Q = 60^\circ$. In another triangle STU, $\angle S = 40^\circ$ and $\angle T = 60^\circ$. Are the triangles PQR and STU similar?
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