Parts of a Triangle & the Pythagorean Theorem

Parts of a Triangle & the Pythagorean Theorem

Define: Triangle

Define: Triangle

A triangle is a polygon with three sides and three vertices. It is one of the basic shapes in geometry.

Define: Triangle

A triangle with vertices A, B, and C and sides a, b, and c.

Define: Right Triangle

A right triangle or right-angled triangle is a triangle in which one angle is a right angle.

The side opposite the right angle is called the hypotenuse. The sides adjacent to the right angle are called legs.

REPEAT:

Right Triangle

A right triangle or right-angled triangle is a triangle in which one angle is a right angle.

The side opposite the right angle is called the hypotenuse. The sides adjacent to the right angle are called legs.

Right Triangle Fact

The hypotenuse is ALWAYS the longest side in a right triangle.

Multiple Choice

Which is correct:

• The hypotenuse is a and the legs are b and c.

• The hypotenuse is b and the legs are a and c.

• The hypotenuse is c and the legs are a and b.

Multiple Choice

Which is correct:

• The hypotenuse is x and the legs are y and z.

• The hypotenuse is y and the legs are x and z.

• The hypotenuse is z and the legs are x and y.

Multiple Choice

Which is correct:

• The hypotenuse is 12 and the legs are 16 and 20.

• The hypotenuse is 16 and the legs are 12 and 20.

• The hypotenuse is 20 and the legs are 12 and 16.

Multiple Choice

Which is correct:

• The hypotenuse is 40 and the legs are 24 and 32.

• The hypotenuse is 32 and the legs are 24 and 40.

• The hypotenuse is 24 and the legs are 32 and 40.

• There is no hypotenuse because this is not a right triangle.

  
  

  The sides of a triangle are 24, 32, and 40.

Multiple Choice

Which is correct:

• The hypotenuse is 29 and the legs are 44 and 50.

• The hypotenuse is 50 and the legs are 29 and 44.

• The hypotenuse is 44 and the legs are 29 and 50.

• There is no hypotenuse because this is not a right triangle.

  
  

  The sides of a triangle are 29, 44, and 50.

Pythagorean Theorem

was named after the ancient Greek mathematician Pythagoras.

Pythagorean Theorem

is a fundamental relation in Euclidean geometry among the three sides of a right triangle.

It states that the area of the square whose side is the hypotenuse (c) is equal to the sum of the areas of the squares on the other two sides (a and b)

Pythagorean Theorem

or more simply . . .

a² + b² = c²

Fill in the Blanks

Fill in the Blanks

Fill in the Blanks

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Poll

My understanding of the parts of a right triangle is:

• Excellent; I know where the legs and hypotenuse are located.

• Good; I know mostly where the legs and hypotenuse are located and need some extra practice.

• Poor; I don't know where the legs and hypotenuse are located and need extra assistance.

• HUH ! Triangles have legs ??

Poll

My understanding of the Pythagorean Theorem is:

• Excellent; I can find ANY missing side of a right triangle.

• Good; I can solve problems looking for the hypotenuse and need some extra practice finding the other leg.

• Poor; I understand the theorem but struggle with the problems and need extra assistance.

• HUH ! Triangles are named Pythagoras ??

Thank you for your EFFORT today ! ! !

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