NEW: Theorems about perpendicular lines

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10 Οκτ 2013 (πριν από 4 χρόνια και 28 μέρες)

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Notes 3.3


Warmup!




Name 3 segments that satisfy the condition.


1)

GF || _______ ________ ________



2)

AD

___
___
_

________ _________



3)

Lines skew with BF ________ ________ ___
______



NEW:
Theorems about perpendicular lines


1)

ALL RIGHT ANGLES ARE CONGRUENT







2)

IF 2 LINES ARE PERPENDICULAR, THEN THEY INTERSECT TO
FORM 4 RIGHT ANGLES



3)

IF 2 LINES INTERSECT TO FORM ADJACENT CONGRUENT
ANGLES, THEN THE LINES ARE PERPENDICULAR








4)

IF 2 SIDES OF ADJACENT ACUTE ANGLES ARE
PERPENDICULAR, THEN THE ANGLES ARE COMPLEMENARY.





Examples:

1)

In the diagram, a

b. Decide whether enough information is given to conclude
that the statement is true. Explain your reas
oning.


a)

<1
<2


b)

<2
<6


c)

<7
<8







2)

What do you know about two lines intersecting to form adjacent
congruent angles?







3)

In the diagram, HJ

HL and

m<LHK = 42. Find the value of z.






4)

Determine whether enough information is given to conclude that the
statement is true. Explain.


a)

<1
<
3



b)

<
4

<
5



c)

<4 and <5 are complimentary



d)

<2
<3












3.2 Worksheet

Write the theorem that justifies the statement about the diagram.


1)

<5 and <6 are right angles.




2) j

k











3)

m<9 + m<10 = 90








4)

Write an equation to find the value of x.

Th
en solve.




Determine whether there is enough information to conclude that the statement is true

and
explain why
.

5)

<2
<5


6)

<
6
<7


7)

<1
<5


8)

<
1

<
3

What

can you conclude about <1 and <2 using the given information?


9)







10
)
h

k









11)

Students were asked to set up an equation to find the value of x, given that v

w.
De
scribe and correct any errors.





Find the value of x, given that s

t.

12)





1
3
)






1
4
)














1
5
)









1
6
)














1
7
) In the diagram shown, <1 and <3 are congruent and complementary. Can
you conclude
that BA

BC? Explain.









18) What did you learn today?