Notes #3: Sections1.5
Definition of Segment Bisector
WriteIf a segment, ray, or line is a bisector to a segment, then they intersect at the segment’s ______.
“bisect”: / Draw / Use
1.) bisects . What can you conclude based on the Definition of Segment Bisector?
2.) Using the definition of midpoint, what can you conclude next?
Segment Addition Postulate
WriteIf B is between collinear points A and C, then
______+ ______= ______
“in between”: / Draw / Use
3.) If RS = 5 and ST = 9, find RT
4.) If RS = 7 – x, ST = 3x – 5, and
RT = 10, write an equation and solve for x.
5.) Name a situation in which we would use an equal sign (=) and a situation in which we would use a congruent sign () to state geometric relationships.
Write an equation and solve:
6.) Use the picture on the right. Given: E is the midpoint of .
DE = 3x – 5, EF = 5x – 9. Solve for x, DE, and EF.
7.) GE = y + 3, EH = 2y – 4, GH = 6y – 10. Solve for y, GE, EH, and GH. Using this information,
is E the midpoint of ?
8.) N is between collinear points A and B. If AB = 25, AN = 2x – 6, and NB = x + 7, find AN
9.) M is the midpoint of , RM = 5x + 9 and TM = 8x – 36. Find RT.
10.) F is in between collinear points E and G. If EG = 75 and EF = 28, what is FG?
11.) F is in between collinear points E and G. If EG = 49, EF = 2x + 3, and FG = 4x – 2, find x & FG.
Examples: Justify each statement with a definition or postulate.
12.) If , then . / 13.) If H is the midpoint of , then14.) If line m is the segment bisector of and intersects at point D, then D is the midpoint of . / 15.) If VX = RS, then .
16.) If A is between P and R, then
PA + AR = PR.
Algebra Practice: Solve each equation. Write your answers as reduced fractions, if necessary.
17. 18. 19.
20. 21.
Notes #4: Sections 1.6-1.7
More defined terms…
Angles:
Describe / Draw and Name / Vertex:Sides:
Acute anglesRight anglesObtuse angles
Straight anglesCongruent anglesAdjacent angles
Vertical anglesComplementary anglesSupplementary angles
State another name for the given angle. If the picture is drawn to scale, is the given angle acute, right, obtuse, or straight,?
1.) 2.)
3.) 4.)
Using the figure at the right, answer each of the following questions.
5.) Name two supplementary angles.6.) Name two vertical angles.
7.) Name two complementary angles.
8.) Name two congruent angles.
Angle Addition Postulate
WritePART 1:
If A lies in the interior of , then
______+ ______= ______
PART 2:
If A lies in the interior of straight angle , then
______+ ______= ______ / Use
9.) If = 72°, solve for y, , and .
10.) Solve for m.
Perpendicular Lines
Describe / Draw and NameDefinition of Perpendicular Bisector:
Describe / Draw and Name / Use11.) If is the perpendicular bisector of at T, then _____ is the midpoint of ______, , and ______is a right angle.
Definition of Angle Bisector
WriteIf bisects , then
______= ______
______ ______ / Draw / Use
12.) bisects . Solve for a and .
Practice: Write an equation & find the indicated value(s).
13. bisects
14. Find the value of x in the diagram below if and .
15. bisects
16. is the perpendicular bisector of . If , CH = 3y + 2, and CM = y + 8, find the value of x and y.
Examples: Justify each statement with a definition, postulate, or theorem
17.) If R is between F and M, then FR + MR = FM / 18.) If is a segment bisector of and intersects at H, then H is the midpoint of .19.) Given the picture at the right,
/ 20.) If are supplementary, then
21.) If bisects , then / 22.) If , then BD = MN.
Algebra Practice:Solve each equation. Write your answers as reduced fractions, if necessary.
Steps: 1.) Find the LCM of all of the denominators
2.) Multiply all terms in the equation by this numbers (denominators should cancel!)
3.) Solve new equation
23. 24.
25. 26.
Notes #5—Sections 1.7, 1.8, & Quiz Review
Complete the statement AND name the reason (definition, postulate, or theorem) you used:
1.) /2.)
3.)If bisects , then X is the ______of .
4.)
5.) If XC = XD, then ____________/ 6.) m + ______= m
7.)
Parts to the Coordinate Plane: Label Quadrant I (QI), QII, QIII, QIV, x-axis, and y-axis
Plot and label the following points:
A(7, -3)B(-6, -1)C(0, 8)
D(-4, 0)E(5, 2)
Midpoint FormulaThe midpoint of a segment connecting two points, and is:
(average the x’s, average the y’s)
Use the midpoint formula to find the midpoint of the segment with the given endpoints.
(Hint: first label your points as and
8.) (0, 2) and (6, 4) 9.) (-2, 6) and (4, 3)
10.) (a, 3) and (3a + 2, -1)
The midpoint M and one endpoint, A, of segment is given below. Find the coordinates of the second endpoint, B.
11.) M(4, -6) and A(2, -3)12.) M(1, 3) and A(8, 9)
13.) M(-1, 5) and A(1, 4)
Algebra Practice: Evaluate each expression.
14.) 15.)
16.) 17.)
Quiz Review:
Given the figure at the right, name the following:
18. two segments on Figure A
19. two rays on Figure A
20. two opposite rays on Figure A
21. two parallel segments on Figure B
22. two skew lines on Figure B
23. two parallel planes on Figure B
Figure B
What is the intersection of the following…
24. two distinct lines 25. two non-parallel planes26. a line & a plane that are not parallel
27. Given collinear points B & C and point F between them, find the value of x, BF, and CF if .
For #28-29, find the value of x.
28. B is the midpoint of and AC=9629.
For #30-31, use the figure at the right to find the value of the variable.
30.
31.
For #32-33, set up equations & solve for the indicated values.
32. is a bisector of , , find the value of x.
33. is a perpendicular bisector of in the figure on the right.
Find the values of x & y if CH = 3x + 4, HA = 4x – 9, and .
Chapter 1 Quiz Review Sheet
Sections 1.3-1.8
Complete each problem on this worksheet. Show all of your work!
1. The length of is 45 and B lies between collinear points A and C. If AB = x + 8 and BC = 3x – 3, find the value of x.
2. C is the midpoint of . If EC = 2x +10 and CF = 5x – 11, find EF.
3. is the perpendicular bisector of . If , PX = 6y – 8 and QX = 4y + 20, find the values of x and y.
4. is the bisector of . Name two congruent angles.
5. Find possible values of .
For questions 6-8, use the figure at the right.
6. Name three non-collinear points.
7. Name a pair of parallel planes.
8. Name three segments that intersect at D.
For questions 9-12, complete each statement with always, sometimes, or never to make a true statement.
9. A line and a point are ______coplanar.10. Two segments are _____ coplanar.
11. Skew lines are _____ coplanar12. Two points are _____ collinear.
13. Find x.
14. Name a pair of each of the following.
A.) complementary angles. B.) supplementary angles
C.)vertical anglesD.) adjacent angles
15. Refer to the picture on the right. If ,
find the value of y.
For 16-17, find the value of each expression. Leave your answer as a reduced fraction, if necessary.
16. 17.
For #18-20, fill in the blank.
18. If M is the midpoint of then, by the Definition of Midpoint
19. If is the bisector of then by the Definition of Angle Bisector
20. If is a straight angle and R is any point not on , then by the Angle Addition Postulate.
For #21-25, justify each statement with a definition, postulate, or theorem.
21.) If D is the midpoint of , .
22.) If , then is the bisector of .
23.)
24.) BD + DC = BC.
25.)
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