Podcast
Questions and Answers
The __________ to the hypotenuse of a right triangle forms two triangles similar to it and to each other.
The __________ to the hypotenuse of a right triangle forms two triangles similar to it and to each other.
altitude
The altitude to the hypotenuse of a right triangle is the _____________ _________ between the segments into which it divides the hypotenuse.
The altitude to the hypotenuse of a right triangle is the _____________ _________ between the segments into which it divides the hypotenuse.
geometric mean
Each leg of a right triangle is the geometric mean between the hypotenuse and its _____________ onto the hypotenuse.
Each leg of a right triangle is the geometric mean between the hypotenuse and its _____________ onto the hypotenuse.
projection
What is the Pythagorean Theorem?
What is the Pythagorean Theorem?
What does the Isosceles Right Triangle Theorem state?
What does the Isosceles Right Triangle Theorem state?
Each diagonal of a square is ______ times the length of one side.
Each diagonal of a square is ______ times the length of one side.
What does the 30-60-90 Right Triangle Theorem state?
What does the 30-60-90 Right Triangle Theorem state?
Two non vertical lines are parallel iff___________________
Two non vertical lines are parallel iff___________________
Two non vertical lines are perpendicular iff ____________.
Two non vertical lines are perpendicular iff ____________.
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Study Notes
Right Triangle Properties
- The altitude to the hypotenuse of a right triangle creates two triangles that are similar to the original triangle and to each other.
- The altitude divides the hypotenuse into segments where each segment's length represents the geometric mean of the two segments.
Leg and Hypotenuse Relationships
- Each leg of a right triangle acts as the geometric mean between the hypotenuse and the projection of that leg onto the hypotenuse.
Pythagorean Theorem
- The relationship expressed by the Pythagorean Theorem states that in a right triangle, the square of the hypotenuse equals the sum of the squares of the two legs (a² + b² = c²).
Isosceles Right Triangle Theorem
- In an isosceles right triangle, the hypotenuse's length is √2 times the length of each leg.
Square Diagonal Relationship
- Each diagonal of a square is √2 times the length of one of its sides.
30-60-90 Right Triangle Theorem
- In a 30-60 right triangle, the hypotenuse is double the length of the shorter leg, while the longer leg measures √3 times the length of the shorter leg.
Parallel Lines
- Two non-vertical lines are parallel if their slopes are equal, indicating that they run in the same direction without intersecting.
Perpendicular Lines
- Two non-vertical lines are considered perpendicular if the product of their slopes equals -1, indicating they intersect at a right angle.
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