Triangle Conditions

Triangle Conditions

Review

• The sum of all angles are 180 degrees

• Triangles are classified according to their side length and angle measure

• The smallest angle will be opposite the shortest side, and vice versa.

• A side is congruent to another side if it has an equal length.

• For a triangle to be formed, the sum of any two sides must be greater than the length of the third side.

• When 3 lengths meet the triangle inequality theorem, then 1 unique triangle will be formed.

Poll

Use the information in the image to predict whether the triangle is unique or not.

• Unique triangle

• Not Unique

Poll

Use the information in the image to predict whether the triangle is unique or not.

• Unique triangle

• Not Unique

Poll

Use the information in the image to predict whether the triangle is unique or not.

• Unique triangle

• Not Unique

Poll

Use the information in the image to predict whether the triangle is unique or not.

• Unique triangle

• Not Unique

Does It Form A Triangle?

Given conditions and what they mean

Three Sides (SSS)

When three sides are given, if the side lengths meet the Triangle Inequality Theorem, then they will form a Unique Triangle.

Two Sides and An Angle (SAS)

When 2 sides and 1 included angle are given, then they will form a unique triangle.

Two Angles and One Side (ASA)

When 2 angles and 1 side are given, if the angles have a sum of less than 180 degrees, then they will form a unique triangle.

Three Angles (AAA)

When 3 angles are given, if the angles meet the angle sum theorem (sum of all angles in a triangle = 180), then they will form more than 1 triangle.

Side Lengths

Use your understanding of the triangle inequality theorem to answer these questions.

Multiple Choice

Triangle with sides of 7, 8, and 9 cm.

• one unique triangle

• more than one unique triangle

• no triangle

Multiple Choice

Triangle with sides of 1.5, 3, and 1.5 cm.

• one unique triangle

• more than one unique triangle

• no triangle

Angle Measures

Use your understanding of the angle sum theorem to answer these questions.

Multiple Choice

Triangle with angles of 55, 45, 75

• one unique triangle

• more than one unique triangle

• no triangle

Multiple Choice

Triangle with angles of 70, 90, 20

• one unique triangle

• more than one unique triangle

• no triangle

Multiple Choice

Two sides of a triangle have lengths of 7 and 15. Which inequalities represent lengths for the third side, x?

• $8<x<22$

• $8<x<15$

• $7<x<15$

• $8<x<7$

Multiple Choice

Which of the following cannot be the angle measures of a triangle?

• 110, 43, 27

• 89, 47, 32

• 95, 32, 53

• 100, 30, 50

Open Ended

Please summarize this lesson.