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This text explores the concept of altitude in right triangles, highlighting how an altitude drawn from the right angle forms two additional right triangles that are similar to the original triangle. It discusses the Angle-Angle (AA) Similarity Theorem, demonstrating that while these triangles share a right angle, their acute angles can differ, leading to the conclusion that not all right triangles are similar. This foundational concept is essential for deeper understanding of triangle properties in geometry.
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A B C This is altitude . Notice altitude drawn from A. H
A C B H A A H H B C What do you notice when this altitude is drawn?
A C B H A A H H B C We have 2 Right Triangles new
A C A H C Not only are the 2 triangles right triangles but they are both similar right triangles. A B m BAC= m AHC= 90° m ACB= m HCA ∆ ACB~ ∆ HCA AA Similarity Theorem
A = = C A H B Not only are the 2 triangles right triangles but they are both similar right triangles. A B m BAC= m BHA= 90° m ABC= m ABH ∆ ABC~ ∆ HBA AA Similarity Theorem
A C B H Theorem 21 states that an altitude drawn from the right angle of a right triangle forms 2 more right triangles similar to the first. QUESTION: Are ALL right triangles similar to each other?
QUESTION: Are ALL right triangles similar to each other? ANSWER: No because their acute angles are not necessarily the same.
