types of triangles
DESCRIPTION
Types of Triangles. Section 3.6 Kory and Katrina Helcoski. Classifying Triangles By Sides. Scalene- a triangle in which no two sides are congruent AB=7 BC=10 CA=8. Classifying Triangles By Sides. Isosceles- a triangle in which at least 2 sides are congruent - PowerPoint PPT PresentationTRANSCRIPT
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.