Derek Owens Geometry Chapter 11 Flashcards
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Questions and Answers

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.

geometric mean

Each leg of a right triangle is the geometric mean between the hypotenuse and its _____________ onto the hypotenuse.

projection

What is the Pythagorean Theorem?

<p>In a right triangle, the square of the hypotenuse is equal to the sum of the squares of the legs.</p> Signup and view all the answers

What does the Isosceles Right Triangle Theorem state?

<p>In an isosceles right triangle, the hypotenuse is √2 times the length of a leg.</p> Signup and view all the answers

Each diagonal of a square is ______ times the length of one side.

<p>√2</p> Signup and view all the answers

What does the 30-60-90 Right Triangle Theorem state?

<p>In a 30-60 right triangle, the hypotenuse is twice the shorter leg and the longer leg is √3 times the shorter leg.</p> Signup and view all the answers

Two non vertical lines are parallel iff___________________

<p>Their slopes are equal</p> Signup and view all the answers

Two non vertical lines are perpendicular iff ____________.

<p>The product of their slopes is -1</p> Signup and view all the answers

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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Test your knowledge of Geometry Chapter 11 with these flashcards! Focus on key concepts related to right triangles and their properties, including the altitude and geometric mean. Perfect for students looking to reinforce their understanding of essential geometric principles.

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