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CLASSIFYING TRIANGLES BY ANGLES Classifying Triangles by Angles • ACUTE • EQUIANGULAR • OBTUSE • RIGHT ACUTE TRIANGLE Interior Angle •All interior angles are acute (or have a measure less than 90°) 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 Interior Angle •All interior angles are congruent (exactly the same measure) •All interior angles ALWAYS measure 60° for an equiangular triangle Examples of Equiangular Triangles OBTUSE TRIANGLE Obtuse Angle •ONE interior angle is obtuse (or has a measure greater than 90°) •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 Right Angle •ONE interior angle is a right angle (or has a measure equal to 90°) •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 • EQUIANGULAR • OBTUSE • RIGHT YOU TRY • ACUTE • EQUIANGULAR • OBTUSE • RIGHT YOU TRY • ACUTE • EQUIANGULAR • OBTUSE • RIGHT YOU TRY • ACUTE • EQUIANGULAR • OBTUSE • RIGHT 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 VERTEX •Two sides are congruent (exactly the same length) •The angle between the congruent sides is called the VERTEX ANGLE Examples of Isosceles Triangles SCALENE TRIANGLE •NO sides are congruent Examples of Scalene Triangles Classifying Triangles Angles are classified first by ANGLE And then by SIDE ISOSCELES ACUTE ACUTE ISOSCELES Classifying Triangles Angles are classified first by ANGLE And then by SIDE SCALENE RIGHT RIGHT SCALENE Classifying Triangles Angles are classified first by ANGLE And then by SIDE SCALENE OBTUSE OBTUSE SCALENE YOU TRY • RIGHT ISOSCELES • RIGHT SCALENE • ACUTE ISOSCELES • EQUIANGULAR EQUILATERAL YOU TRY • ACUTE ISOSCELES • EQUIANGULAR SCALENE • OBTUSE SCALENE • RIGHT EQUILATERAL YOU TRY • ACUTE ISOSCELES • EQUIANGULAR EQUILATERAL • OBTUSE SCALENE YOU TRY • ACUTE SCALENE • OBTUSE SCALENE • OBTUSE ISOSCELES YOU TRY Given: 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 Step 1 35 Step Step Realize an‘x’ equiangular Step 4x into Step Combine Plug2that original term triangle is ALWAYS an Solve for to x find AB=BC 3x-5=2x-2 equation equilateral triangle an 1x-5+5=-2+5 3x-5=2x-2 therefore 3x-5-2x=2x-2x-2 lengthALL sides are CONGRUENT. 1x=3 1x-5=-2 3x-5 C 3(3)-5=4 The End Homework Worksheet Page 186: 4-9 ALL Worksheet Page 187: 1-3 ALL