Download geometry chap 4

Acute triangle: the acute triangles has three acute angles that’s why it is called
acute triangle.
Equiangular triangle: the equiangular triangle has three congruent acute angles.
Right triangle: the right triangle has one angle that makes 90 degrease and
sense we know that this type of angles are called right angles these type of
triangle gets its name from it.
Obtuse triangle: these triangle has one angle of 180 degrease and the 180
degrease angles are called obtuse that’s why the triangle is called obtuse.
Equilateral triangle: these type of triangle has three congruent sides.
Scalene triangle: these triangle has no congruent sides.
Isosceles triangle: at lear 2 congruent sides.
Equiangular
Right
triangle
Equilateral
triangel
Triangle sum theorem: the sum of the angle measures of a triangle is 180.
Parts of a triangle:
Interior: the interior of triangle is the set of all points inside the figure.
Exterior: the exterior on a triangle is totally the opposite of the interior the exterior is the set
of all points outside the figure.
Interior angle: the interior angle of a triangle is formed by two sides of a triangle.
Exterior angle: the exterior angle of a triangle is formed by one side of the triangle and the
extension od an adjacent side.
A
K
45°
C
60° 60°
90°
B
M<ABC +M<ACB +M<CBA=180°
M<ABC +M<ACB=120°
180°-120°=60°
60+60+60=180° D
M
N
m<kMN+m<MNK+m<NKM=180°
m<kMN+m<NKM=135°
180-135=45°
45+45+90=180°
M<DEF+m<EFD+m<FDE=180°
M<DEF+m<EFD=110°
180-110=70°
70+55+55=180°
E
55°
55°
F
The measure of an exterior angle of a triangle is equal to the sum of the measures
of its remote interior angles.
J
7x
H
K
Find m<J
H
M<J +m<H=m<FGH
(6x-1)°
5x+17+6x-1=126
11X+16=126
11X=110
126°
X=10
(6x-1)°
J
F
G
M<J=5x+17=5(10)+17=67°
(5x+17)°
Find m<L
L
M<L+M<K=m<HJL
6x-1+7x=90
13x-1=90
13x=89
X=6.84
m<L=6x-1=6(6.84)-1
40.04
N
(2y+2)°
M
48°
P
Q
find m<m
M<m+m<N=m<NPQ
3y+1+2y+2=48
5y+3=48
5y=45
Y=9
M<m=3y+1=3(9)+1
M<m=28°
Cpctc is a abbreviation for corresponding parts of congruent triangles are congruent
these is proof that you may use. You may use these proof when triangle are on a
coordinate plane. You use the distance formula to find the lengths od the sides of
each triangle. Then, after showing that the triangles are congruent, you can make
conclusions about their corresponding parts.
K
J
reasons
statements
G
H
L
1. JL and HK bisect each
other
2. JG congruent LG and HG
congruent KG
3. <JGH congruent LGK
4. ▲JHG congruent ▲LKG
5. <JHG congruent <LKG
1.
2.
3.
4.
5.
Given
def. of bisect
Vert. <s thm.
SAS
CPCTC
A
B
D
C
1.
2.
3.
4.
5.
AB congruent to DC
<ABC congruent to <DCB
BC congruent to CB
▲ABC congruent ▲DCB
<A congruent <D
1. EG congruent to DF
2. EG II DF
3. <EGD congruent to <FDG
4. GD congruent DG
5. ▲EGD congruent ▲FDG
6. <EDG congruent <FGD
7. ED II GF
1. Given
2. Given
3. reflex. Prop. Of
congruency
4. SAS
5. CPCTC
1.
2.
3.
4.
Given
Given
Alt. int. <s thm.
Reflex. Prop. Of
congruency
5. SAS
6. CPCTC
7. converse of alt. int <s
Thm
SSS: SSS is the abbreviation for side side side and these postulate says that if
three sides of one triangle are congruent to three sides of another triangle, then
the triangles are congruent.
SAS: SAS is the abbreviation for side angle side and these postulate says
that if two sides and the included angle of one triangle are congruent to
two sides and the included angle od another triangle, then the triangles
are congruent.
ASA: ASA is the abbreviation for angle side angle, the postulates says if
two angles and the included side of one triangle are congruent to two
angles and the included side of another triangle, then the triangles are
congruent.
ASS: ASS is the abbreviation for angle angle side and these theorem
says that if two angle and a nonincluded side of one triangle are
congruent to the corresponding angles and nonincluded side od
another triangle, then the triangles are congruent.