CLASSIFYING TRIANGLES BY ANGLES

Classifying Triangles by Angles

• ACUTE

• OBTUSE

• RIGHT

• EQUIANGULAR

ACUTE TRIANGLE

•All interior angles are acute (or have a measure less than 90°)

Interior Angle

Example of Acute Triangle

• Phineas’s head is an acute triangle because all interior angles measure less than 90°. This is easy to remember because Phineas is a ‘cute’ character!

EQUIANGULAR TRIANGLE

•All interior angles are congruent (exactly the same measure)

Interior Angle

•All interior angles ALWAYS measure 60° for an equiangular triangle

Examples of Equiangular Triangles

OBTUSE TRIANGLE

•ONE interior angle is obtuse (or has a measure greater than 90°)

Obtuse Angle

•The other two interior angles of an obtuse triangle ALWAYS are acute (or have a measure less than 90°)

Example of Obtuse Triangle

•Dr. Doofenshmirtz’s head is shaped like an obtuse triangle. This is easy to remember because he is an obtuse character. An obtuse character is one that is slow to learn or lacking insight.

RIGHT TRIANGLE

•ONE interior angle is a right angle (or has a measure equal to 90°)

Right Angle

•The other two angles of a right triangle are ALWAYS acute (have a measure less than 90°)

Example of A Right Triangle

YOU TRY

• ACUTE

• OBTUSE

• RIGHT

• EQUIANGULAR

YOU TRY

• ACUTE

• OBTUSE

• RIGHT

• EQUIANGULAR

YOU TRY

• ACUTE

• OBTUSE

• RIGHT

• EQUIANGULAR

YOU TRY

• ACUTE

• OBTUSE

• RIGHT

• EQUIANGULAR

CLASSIFYING TRIANGLES BY SIDES

Classifying Triangles by Sides

• EQUALATERAL

• ISOSCELES

• SCALENE

EQUILATERAL TRIANGLE

•All sides are congruent (exactly the same length)

•EQUILATERAL TRIANGLES ARE ALWAYS ALSO EQUIANGULAR

Examples of Equilateral Triangles

ISOSCELES TRIANGLE

•Two sides are congruent (exactly the same length)

•The angle between the congruent sides is called the VERTEX ANGLE

VERTEX

Examples of Isosceles Triangles

SCALENE TRIANGLE

•NO sides are congruent

Examples of Scalene Triangles

Classifying Triangles

ACUTE ISOSCELES

Angles are classified first by ANGLE

And then by SIDE

ACUTEISOSCELES

Classifying Triangles

RIGHT SCALENE

Angles are classified first by ANGLE

And then by SIDE

RIGHTSCALENE

Classifying Triangles

OBTUSE SCALENE

Angles are classified first by ANGLE

And then by SIDE

OBTUSE SCALENE

YOU TRY

• RIGHT ISOSCELES

• ACUTE ISOSCELES

• EQUIANGULAR EQUILATERAL

• RIGHT SCALENE

YOU TRY

• ACUTE ISOSCELES

• OBTUSE SCALENE

• RIGHT EQUILATERAL

• EQUIANGULAR SCALENE

YOU TRY

• ACUTE ISOSCELES

• OBTUSE SCALENE

• EQUIANGULAR EQUILATERAL

YOU TRY

• ACUTE SCALENE

• OBTUSE SCALENE

• OBTUSE ISOSCELES

YOU TRYGiven: Triangle ABC is equiangular triangle with side AB=3x-5 and side BC=2x-2. What are the lengths of the 3 sides?

A

B C

Step 1Realize that an equiangular triangle is ALWAYS an equilateral triangle an therefore ALL sides are CONGRUENT.

Step 2AB=BC3x-5=2x-2

Step 3Combine ‘x’ term3x-5=2x-23x-5-2x=2x-2x-21x-5=-2

Step 4Solve for x1x-5+5=-2+51x=3

Step 5Plug x into original equation to find length3x-53(3)-5=4

The End

Homework

Worksheet Page 186: 4-9 ALLWorksheet Page 187: 1-3 ALL

YOU ARE CORRECT!

OH DOOFENSHMIRTZ!TRY AGAIN!