Download Fold down a corner of a rectangular sheet of paper. Then fold the

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Transcript 
Chapter 2.5­2.6
Fold down a corner of a rectangular sheet of paper. Then fold the next corner so that the edges touch as in the figure. Measure the angle formed by the fold lines. Repeat with another sheet of paper, folding the corner at a different angle. Explain why the angles formed are congruent.
( Hint: Label the angles and note their relationship.)
1
The definition of perpendicular lines can be used in the 2 ways shown below:
1) If 2
If two lines are perpendicular,
then they form congruent adjacent angles.
n
1 2
l
1.) 2.) 3.) 1.)
angles
angles
2.)
3.)
3
If two lines form congruent adjacent angles, then the lines are perpendicular
n
l
12
1.)
1.)
2.) 2.)
3.)
3.)
4.)
4.)
5.)
5.)
6.)
6.)
4
5
LIST OF WHAT WE CAN USE IN PROVING THEOREMS
• def • def midpt
• def seg bise
• def angle bi
• SAP
• AAP
• + =
• ­ =
• mult =
If perp, then rt angles or 90 angles
If perp, then congruent adj angles
If ext sides perp, then int angles comp
If rt angles, then perp lines
If congruent adj angles, then perp lines
• div = • subst
• ref
• trans =
• trans 6
If the exterior sides of two adjacent acute angles are perpendicular,
then the angles are complementary.
A
1
O
B
2
<1 comp <2
C
7
are the following statements true or false?
a. .
______________
<
b. ÐCGB is a right angle.
______________
c. ÐCGA is a right angle.
______________
<
<
d. mÐDGB = 90°
______________
e. ÐEGC and ÐEGA are complements.
_________
<<
<
f. ÐDGF is complementary to ÐDGA.
_________
<
g. ÐEGA is complementary to ÐDGF
<
__________
8
9
If <1 is a right angle and < BOD is a right angle
name other congruent angles.
10
If the measure of < DAC = 130
, and the measure of < ERC = 130
, find m<CAR and m<CRA
11
If two angles are supplements of congruent angles,
(or of the same angle)
then they are congruent
Given: ∠1 and ∠2 are supp
∠3 and ∠4 are supp
∠2 ≅ ∠4
Prove: ∠1 ≅ ∠3
1) ∠1 and ∠2 are supp
1) Given
∠3 and ∠4 are supp
∠2 ≅ ∠4
2) m<1 + m<2 = 180
m<3 + m<4 = 180
3) m<1 + m<2 = 180 = m<3 + m<4 = 180
4) m<2 = m<4
5) m<1 = m<3
6) <1 ≅ <3
12
If two angles are complements of congruent angles, ( or the same angle ),
then they are congruent
1) <2 comp <3 <3 comp <4
2) m<2 + m<3 = 90
m<3 + m<4 = 90
3) m<2 + m<3 = m<3 + m<4
4) m<3 = m<3
5) m<2 = m<4
6) <2 ≅ <4
13
Given: < 1 Prove: <2
<4
<3
Given: Prove: <3 <3 comp <1
<2
14
Given: <1 <3
Prove: < 2 supp <3
15
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