Download Unit 25 PPF 501 503 Lesson Notes

PPF 501 & PPF 503 LESSON _NOTES CRS SKILL PPF 501 PPF 503 Period____________ Name_________________________________________ LEVEL Level 1 – ALL students must attain mastery at this level DESCRIPTION PPF 301 Exhibit some knowledge of he angle associated with parallel lines PPF 401 Find the measure of an angle using properties of parallel lines PPF 402 Exhibit knowledge of basic angle properties and special sums of angle measures Level 2 – MOST students will PPF 501 Use several angle properties to find an attain mastery of the focus skill in unknown angle measures isolation. PPF 503 Use properties of isosceles triangles Level 3 – SOME students will attain mastery of focus skill with other skills Level 4 – SOME students will attain mastery of focus topics covered in a more abstract way Level 5 – FEW students will PPF 601 Draw conclusions based on a set of attain mastery of the extension conditions skill. VOCABULARY Point, Line, Ray, Segment, Angle, Plane, Acute Angle, Obtuse Angle, Straight Angle, Right Angle, Vertical Angles, Complementary Angles, Supplementary Angles, Linear Pair, Transversal, Corresponding Angles, Alternate Interior Angles, Alternate Exterior Angles, Consecutive Interior, Isosceles triangle REQUIRED SKILL TO MASTER Parallel Lines 1, Complementary and supplementary angles, Equation practice with vertical lines Additional Practice on KHAN Equations practice with congruent lines, Equation practice with angle addition, Finding angle measures 1, Finding angle measures 2, Angles of a polygon Push: Line and angle proofs Level 1 1. Name each angle in 3 different ways, and tell whether each angle is acute, obtuse, right, or straight. 1 2. Match the following terms with their picture and with their symbol Name Picture Symbol Point Line Ray Segment Plane Angle Picture Choices Symbol Choices 
1. NP A. 2. NP B. 3. ∠NPQ C. D. 4. PQR or ℜ 
5. NP or q E. 6. N F. 2 3. Use the diagram to the right to find the measure of each angel. a. m∠ORE=____________ b. m∠ORN=____________ c. m∠REA=____________ d. m∠N=____________ N e. m∠GEA=____________ 4. Measure each angle with a protractor. Recort your measurments to the right (extend lines if needed) 5. Find the value of x in each of the following. a. b. c. 3 Term
Vertical Angles
Rule
If angles are vertical, then they are
________________.
Linear Pair
If angles are a linear pair, then
Complementary
Angles
_____________________
If two angle are complementary then
the sum of their measures is _______
Supplementary
Angles
If two angle are supplementary then
the sum of their measures is _______
Picture
4
1
2
3
1
2
Bisector
Angles of a
Triangle
The sum of the measures of a triangle
equals __________.
The sum of the
angle of any
polygon
The sum of the angles of any polygon
can be found using the following
formula_____________________
Whole equals
the sum of the
parts
Transversal
A line that intersects _____
_______________________
t
g
h
4 Parallel lines
cut by a
transversal
If two parallel lines are cut by a
transversal then________________
___________________________
___________________________
Consecutive
Angels of a
Parallelogram
Consecutive angles of a parallelogram
are__________
3
1
_______________________
4
2
Opposite
angles of a
parallelogram
Opposite angles of a parallelogram
are _______________________
3
1
_______________________
4
2
Corresponding
Angles
If two parallel lines are intersected by
t
g
a transversal, then _______
__________________________
h
__________________________
Alternate
Interior Angles
If two parallel lines are intersected by
t
g
a transversal, then _______
h
__________________________
__________________________
Alternate
Exterior Angles
If two parallel lines are intersected by
w
a transversal, then _______
r
__________________________
y
__________________________
Consecutive
Interior Angles
If two parallel lines are intersected by
w
a transversal, then _______
__________________________
__________________________
r
y
5 6. Find the missing angle measure in each figure below. 7. If the measure of ∠1 = 70° and line p is parallel to q, find the measures of the other angles in the diagram. ∠2 =_______ ∠3 =_______ ∠4 =_______ ∠5 =_______ ∠6 =_______ ∠7 =_______ ∠8 =_______ 8. Find the value of x and y in the figure below. 6 
9. In the figure below BD is the angle bisector of ∠CBA. Find the m∠CBD and m∠CBA. Level 2 10. In the picture below lines j and k are parallel. Solve for x and find the measure of the each angle. X = __________________ j
m∠1 = ______________ ∠1=(8x+60)°
m∠2 = ______________ ∠2=(2x+120)°
∠3
k
m∠3 = ____________ 11. Given m∠ADC = 135°, find x, m∠BDC, and m∠ADB. X=__________ m∠BDC=__________ m∠ABD=__________ 12. Solve for x using the angle relationship. 7 13. Find the measure of each angle below. 14. Given that line l and m are parallel, find the unknown angle measures: 15. Find the measure of ∠1 in each figure below. 16. In the figure below find the m∠AEB. m∠CED, and m∠EDC m∠AEB=__________ m∠CED=__________ m∠EDC=__________ C
m∠ECD = 9 2°
A
m∠EAB = 7 9°
B m∠ABE = 5 5°
E
D
8 17. If m∠ACD=17°, find m∠BDA, and m∠ABD. B
m∠BDA=__________ m∠ABD=__________ A
18. Find m∠BCE in the figure to the right. m∠ABC = 155°
B
A
19. Given m∠ABC = 116°, find x, m∠DBC, and m∠DBA. m∠DBC=__________ m∠DBA=__________ D
C
C
m∠CED = 5 1°
E
D
9 20. Find the measure of ∠A in the isosceles triangles below. 21. Find the value of x in each of the following. 10 Level 3 22. Find the measure of ∠V in each figure. 23. Find the m∠LNO in the figure below. P
m∠KPO = 5 6°
L
K
O
M
N
24. Find the value of x and y in the figure below. 11 Level 4 25. In the figure below L1 and L2 are parallel, T1 and T2 are also parallel. If m∠a =105°, find the measure of the all other angles. 26. How many sides does a regular polygon have if one of its interior angles measures 144°? 27. If a regular polygon has 8 sides, how many degrees are there in any one of its angles? 12 Level 5 28. Find the measure of each missing angle indicated below. m∠a=__________ m∠b=__________ m∠c=__________ m∠d=__________ m∠e=__________ m∠f=__________ m∠g=__________ m∠h=__________ m∠k=__________ m∠m=__________ m∠p=__________ m∠r=__________ m∠s=__________ 29. Find the measure of each of the following: m∠1=___________________ m∠2=___________________ m∠3=___________________ m∠4=___________________ m∠5=___________________ m∠6=___________________ m∠7=___________________ m∠8=___________________ m∠9=___________________ 13