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Angles and Sides of
a Triangle
How They Are Related 
The Relationship
• In a triangle, the longest side is across from
the largest angle.
• This also means that the shortest side is
across from the smallest angle.
An Example
• Angle A is the largest, so side BC
is the longest
• Angle C is the smallest, so side
AB is the shortest.
• An inequality to represent the
side lengths from largest to
smallest would be BC > AC > AB.
• An inequality to represent the
side lengths from smallest to
largest would be AB < AC < BC.
You can also classify a
triangle based on what
you know about its sides
and angles.
Let a, b, and c be the side lengths of a
triangle, where c is the longest side.
• If a^2 + b^2 = c^2, then your triangle is
right.
• If a^2 + b^2 > c^2, then your triangle is
acute.
• If a^2 + b^2 < c^2 then your triangle is
obtuse.
Classify each triangle as being
acute, obtuse, or right.
• Triangle with sides of 8 mm, 8
mm, and 10 mm
• 8^2 + 8^2 = 64 + 64 = 128
• 10^2 = 100
• Since 128 > 100, this is an
ACUTE triangle.
• Triangle with sides of 2 ft, 5 ft,
and 12 ft
• 2^2 + 5^2 = 4 + 25 = 29
• 12^2 = 144
• Since 29 < 144, this is an
OBTUSE triangle.

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Angles and sides of a triangle

  • 1. Angles and Sides of a Triangle How They Are Related 
  • 2. The Relationship • In a triangle, the longest side is across from the largest angle. • This also means that the shortest side is across from the smallest angle.
  • 3. An Example • Angle A is the largest, so side BC is the longest • Angle C is the smallest, so side AB is the shortest. • An inequality to represent the side lengths from largest to smallest would be BC > AC > AB. • An inequality to represent the side lengths from smallest to largest would be AB < AC < BC.
  • 4. You can also classify a triangle based on what you know about its sides and angles.
  • 5. Let a, b, and c be the side lengths of a triangle, where c is the longest side. • If a^2 + b^2 = c^2, then your triangle is right. • If a^2 + b^2 > c^2, then your triangle is acute. • If a^2 + b^2 < c^2 then your triangle is obtuse.
  • 6. Classify each triangle as being acute, obtuse, or right. • Triangle with sides of 8 mm, 8 mm, and 10 mm • 8^2 + 8^2 = 64 + 64 = 128 • 10^2 = 100 • Since 128 > 100, this is an ACUTE triangle. • Triangle with sides of 2 ft, 5 ft, and 12 ft • 2^2 + 5^2 = 4 + 25 = 29 • 12^2 = 144 • Since 29 < 144, this is an OBTUSE triangle.