Download 2. The measure of one angle of a parallelogram

2. The measure of one angle of a parallelogram is 45. What are
the measures of the other angles?
Given: a parallelogram ABCD with
measuring 45°.
Find: The measures of the other three
angles, B, C, and D.
PROOF:
Statements___________ Reasons____________
1. opp angles of parallelogram
1. ZC measures 45°
equal
2. any two consecutive angles
2. ZD = 180°-45°=1350
of a parallelogram are
supplementary
3. opp angles of parallelogram
3.^6=^0=135°
equal
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1 Answer
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Find: The measures of the four angles.
PROOF:
Statements___________ Reasons____________
1 . opp angles of a
1 . m^ B=m^ D
parallelogram are congruent
given
2.
2. 4x+15=6x-27
3. solve
3. x=21
4. given
4. m^B=4x+1 5=4(21 )+1 5=99
5. opp angles of a
5. m^D=99
parallelogram are congruent
6. consecutive angles of a
6. m^A=1 80-99=81
parallelogram are
supplementary
7. opp angles of a
7. m^C=81
parallelogram are congruent
m^D=6x-27
Given: parallelogram ABCD
3.
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I Answer
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6. In the figure ©AKMJ and ©BMJK are parallelograms. If KJ=KM
then fABC is isosceles.
Given: AKMJ and BMJK are parallelograms
KJ=KM
Prove: |ABC is isosceles
PROOF:
Reasons
Statements
4.
OJAivssOKBm
-——.... ...•.«-...
isosceles
|5. AC*CB
6.
5.
3.
13. OMJK=flKBM
14
•
2.
1.
12. OJMB»aMJK
I Answer
opp angles of a parallelogram
are equal
if two sides of a triangle are
congruent, then the angles
opposite these sides are
congruent
opp angles of a parallelogram
are equal
transitivity (OJAK«OJMB,
OJMB^flMJK, flMJK»flKBM)
if two angles of a triangle are
congruent, then the sides
opposite them are congurent
def of isosceles (a triangle
with two congruent sides is
called isosceles)
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