TYPES OF TRIANGLESSection 3.6Kory and Katrina Helcoski

CLASSIFYING TRIANGLES BY SIDES

Scalene- a triangle in which no two sides are congruent

AB=7 BC=10 CA=8 AA

B

C

CLASSIFYING TRIANGLES BY SIDES

A

B

C

Isosceles- a triangle in which at least 2 sides are congruent

The legs of an isosceles triangle are congruent

<A and <C are called base angles and <B is called the vertex angle

AB= 10 BC= 10 AC= 5

leg leg

base

CLASSIFYING TRIANGLES BY SIDES

Equilateral- a triangle in which all sides are congruent

An equilateral triangle is also and isosceles triangle.

AB=7 BC=7 CA=7

A

B

CWOW

CLASSIFYING TRIANGLES BY SIDES

Triangle Video (Microsoft PowerPoint was not allowing us to attach the video to it, see other attachment from E-Mail)

CLASSIFYING TRIANGLES BY ANGLES

Equiangular- a triangle in which all angles are acute and congruent

<ABC = 60° <BCA = 60° <CAB = 60°

An equiangular triangle is also an equilateral triangle and vice versa.

A

B

C

CLASSIFYING TRIANGLES BY ANGLES

Acute triangle- a triangle in which all angles are acute.

<ABC=50° <BCA=70° <CAB=60° C

A

B

C

CLASSIFYING TRIANGLES BY ANGLES

A

BC

Right Triangle- a triangle in which one of the angles is a right angle

hypotenuse > either leg

Pythagorean Theorem- leg² + leg² = hyp²

<ACB is a right angle (90°)

hypotenuseleg

leg

CLASSIFYING TRIANGLES BY ANGLES

Obtuse Triangle- a triangle in which one of the sides is an obtuse angle

<ABC= 40° <ACB=110° <BAC=30°

A

BC

SAMPLE PROBLEMS

Given: <BCD=80°

Prove:ΔABC is obtuse

Proof: <BCD= 80° and <ACD is a straight angle, which is 180°, so <ACB is 100° by subtraction. Since ΔABC contains an obtuse angle it is an obtuse triangle.

A

B

C D80

SAMPLE PROBLEMSA

B

C1 2

D E

1. 1. given 2. <1 <2 2. given

3. F is the mdpt of 3. given

4. 4. mdpts divide segs into 2 segs

5. ΔDAF ΔECF 5. SAS (1,2,4)

6. <DAF <ECF 6. CPCTC

7. ΔABC is isos 7. If 2 angles of the Δ are , the Δ is

isos

CFAF

F

<1 <2F is the mdpt ofProve: ΔABC is isos

AC

EFDF

AC

CFAF

given

100%

PRACTICE PROBLEMS

If ΔABC is equilateral, what are the values of x and y?

A

BC

6x

23

2y

8

PRACTICE PROBLEMS (ANSWER)

x + 6=8x = 2

y =15

823

2y

103

2y

PRACTICE PROBLEMS

Given: ΔABC is an isosceles triangle with base

D is the midpoint of

Prove: <A <C

CACA

A

B

CD

PRACTICE PROBLEMS (ANSWER) Statements Reasons

1.ΔABC is an isosceles 1. Given

Triangle with base

2. D is the midpoint of 2. Given

3. 3. If a point is the midpoint of a segment, then it divides the segment into two congruent segments

4. 4. legs of an isosceles triangle are congruent

5. 5. Reflexive Property

6. ΔABD ΔCBD 6. SSS (3, 4, 5)

7. <A <C 7. CPCTC

CA

CADCDA

DCDA

BDBD

WORKS CITED PAGE

Rhoad, Richard , George Milauskas , and Robert Whipple . "3.6- Types of Triangles ." Geometry for Enjoyment and Challenge. Boston: McDougal Littell, 1991. 142-147. Print.