TRIANGLESTRIANGLESCLASSIFICATIONS, CLASSIFICATIONS,

ANGLES AND ANGLES AND MORE!!MORE!!

4/21/23

Name a triangle with its 3 corner points (verticies)

ABC,

or BCA,

or CAB…

A

B C

Classify 2 ways: Classify 2 ways: by its sides by its sides

and its anglesand its angles

Classifying Triangles by Their Classifying Triangles by Their SidesSides

EQUILATERAL – 3 congruent sidesEQUILATERAL – 3 congruent sides

ISOSCELES –two sides congruentISOSCELES –two sides congruent

SCALENE – no sides congruentSCALENE – no sides congruent

EQUILATERAL

ISOSCELES

SCALENE

Works with Angles Matching TOO!

3 matching angles also!

2 matching angles also!

No matching angles!

Classifying Triangles by Their Classifying Triangles by Their AnglesAngles

EQUIANGULAR – all angles are congruentEQUIANGULAR – all angles are congruent

ACUTE – all angles are acuteACUTE – all angles are acute

RIGHT – one right angleRIGHT – one right angle

OBTUSE – one obtuse angleOBTUSE – one obtuse angle

EQUIANGULARACUT

E

RIGHT

OBTUSE

60º

60º

60º60º70º

50º

50º

40º

30º

120º

30º

Can You Classify the Different Can You Classify the Different Triangles in the Picture Below?Triangles in the Picture Below?

ACDACD

Obtuse, Scalene Obtuse, Scalene ABC ABC

Equilateral, EquiangularEquilateral, Equiangular ECD ECD

Right, ScaleneRight, Scalene ACE ACE

Scalene, Right Scalene, Right

So how did you do?So how did you do?

Classify the triangles by their sides:Classify the triangles by their sides:

60°

45°

70°

50°

45°

ACT PracticeACT Practice

A B

C

10

6.3210

Classify ABC

a. scalene

b. isosceles

c. Equilateral

d. right

Interior Angles of Triangles have a Interior Angles of Triangles have a SUM of 180ºSUM of 180º

180º180º

x x

65° 75°y z

20º

65º

10º

ON THE TEST!

65º

10º

20º

49º

67º

3x + 99 = 180

Xz

55y

z

64 + x+40 + 2x-5 = 180

- 99 = -993x = 81

x = 27

2727

55

Change notes to 55

Find x and all of the angles.Find x and all of the angles.

(100 - 2x)º3xº

5xº

Stop for Stop for nownow

Isosceles Isosceles TrianglesTriangles

2 sides2 sides2 angles2 angles

BASE is not always at the bottom!!!!

Isosceles TrianglesIsosceles Triangles

Vertex

WARNING: Triangles may not be drawn the correct size. Trust the numbers and/or hatch marks.

1550°

W ° W°

p.34

60º4x-20w

W=

Altitude of an Isosceles TriangleAltitude of an Isosceles Triangle The BASE and VERTEX angle will be BISECTED.The BASE and VERTEX angle will be BISECTED. If the altitude runs from the vertex angle to the base side, it will If the altitude runs from the vertex angle to the base side, it will

always be perpendicular (90always be perpendicular (90º) to the base.º) to the base.

Ready?Ready?