Download Section 3.1

Survey
yes no Was this document useful for you?
   Thank you for your participation!

* Your assessment is very important for improving the work of artificial intelligence, which forms the content of this project

page
1
page
2
page
3
page
4
page
5
page
6
page
7
Document related concepts
no text concepts found
Transcript 
1. Under what conditions would the following pairs of figures be congruent?
a)
b)
c)
d)
e)
f)
a)
b)
c)
d)
e)
f)
Two segments
Two lines
Two angles
Two circles
Two squares
Two triangles
§ 3.1
If their measures are the same.
All lines are congruent to one another.
If their measures are the same.
If their radii have the same measure.
If their sides have the same measure.
If their sides have the same measure.
2. Given the figure to the right with CE =
CB and E  B.
E
D
Prove: D  A.
C
Given: CE = CB and E  B
Prove: D  A .
A
B
Statement
Reason
1. CE = CB
Given
2. E  B
Given
3. ACB  DCE .
Vertical Angle Theorem
4. ∆ABC ∆DEC
ASA
 D  A.
CPCTE
C
3. Prove that the base angles of an Isosceles triangle are
congruent.
3. Given: ∆ABC with AC = BC,
Prove: A  B
A
Statement
Reason
1. AC = BC
Given
2. BC = AC
Given
3. AB = AB
Reflexive
4. ∆ABC  ∆BAC
SSS
5. A  B
CPCTE
PAPPAS, CR. 300 ad.
B
4. If two angles of a triangle are congruent, then the sides
opposite them are congruent.
C
4. Given: ∆ABC with A  B,
Prove: AC = BC
Statement
Reason
1. A  B
Given
2. AB = BA
Reflexive
3. B  A
Given
4. ∆ABC  ∆BAC
SAS
5.  AC = BC
CPCTE
A
B
5. Prove that the bisector of the vertex of an isosceles
triangle bisects the base.
C
1 2
5. Given: AC = BC and 1  1
Prove: AM = MB .
Statement
1. AC = BC and  1   2
Reason
2. CM = CM
Reflexive
3. ∆ACM  ∆BCM
SAS
4. AM = MB
CPCTE
QED
Given
A
M
B
C
6. In the figure AC = BC,
A  y and B  x.
D
Prove that ∆CDE is isosceles.
6. Given: MR = KR, MG = KG and M  K
Prove: GR  MK .
Statement
Reason
1. AC = BC
Given
2. A = B
Base Angles
3. A = B = x = y
Given & arithmetic
4. CD = CE
Sides opposite = angles
5. CDE is isosceles
Definition
QED
A
A
x
y E
B
7. Given: M – R – K and MR = KR, MG = KG.
G
Prove: GR  MK
M
Given: M – R – K, MR = KR, MG = KG.
Prove: GR  MK .
Statement
Reason
1. M – R – K, MR = KR, MG =
KG
Given
2. GR = GR
Reflexive
3. ∆MRG ∆KRG
SSS
4. MRG  KRG .
CPCTE
5. MRK is a line
Given
6. MRG  KRG = 90
From 3 & 4
 GR  MK
Definition perpendicular
R
K
Related documents