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Honors Geometry
Day 1 – Basic Definitions 1.1 and 1.2
Term
Collinear
points
Definition
Points that lie on the same line
Coplanar
Points that lie in the same plane
Segment
Part of a line consisting of two
points and all points between
them
Ray
Part of a line that starts at an
endpoint and extends forever in
one direction
Two rays that have a common
endpoint and form a line.
Opposite
Rays
Skew
Labeling
2 non-coplanar lines that are not
parallel and never intersect.
1
Picture
ALWAYS, SOMETIMES, NEVER
1) Two points lie in exactly one line.
Circle the letter(s) that apply:
8) Three different points:
a) always determine a plane
b) can be collinear
c) can be non-collinear
d) always lie in at least one plane
2) Three points lie in exactly one line.
3) Three collinear points lie in exactly one plane.
4) Two intersecting planes intersect in a segment.
9) A plane is determined by:
a) a line and a point
b) two intersecting lines
c) any three points
d) a line and a point not on the line
5) Three points determine a plane.
6) Two intersecting lines determine a plane.
7) Two non-intersecting lines determine a plane.
10) Three points are _____________ coplanar. (A/S/N)
2
Segment Bisector: A segment, line, or ray that intersects a segment at its midpoint.
H
MS at point D. What are conclusions one may make?
HL and KT intersect at the midpoint of HL .
Line a bisects
T
True or False.
1. KM = MT
2.
3.
4.
5.
M
KT is a bisector of LH .
MT bisects LH .
HL is a bisector of KT .
M is the midpoint of KT .
K
L
1a) If SR = 15 and RI = 22, find SI.
1b) If SR = 5 and SI = 18, find RI.
1c) If SI = 60, SR = 2x – 8 , RI = 3x – 12 , find x and then find SR and RI.
1d) If SR = x2 + 7, RI = 4x – 5 , and SI = 34, find x.
Example 1 -In the figure below, B is the midpoint of
with an equation, and find x and AC.
. AB = 2x + 12 and BC = 5x + 10. Draw the example, come up
Example 2- In the figure, RS = 2x – 4, ST = 3x + 7, and RT = 43. Draw the example, come up with an equation, and find
x, RS, and ST.
Example 3 -In the figure below, C is the midpoint of
equation, and find x and AC.
. AC= 5x-6 and CB = 2x. Draw the example, come up with an
Example 4 -In the figure, RS = 3x – 12, and ST = 2x – 8, and RT = 60. Draw the example, come up with an equation,
and find x, RS, and ST.
Example 5 G is the midpoint of
x and EG.
. EG = 3y, and GF = 36 – y. Draw the example, come up with an equation, and find
3
1.4 and 1.5 – Angles and Angle Bisectors
Angle: the union of 2 non-collinear rays with a common endpoint
Vertex:
B
1
A

Sides:
Interior of an angle:
Exterior of an angle:
Name this angle in 4 different ways:

C
Name three of the angles.
Measure: of an angle is usually given in degrees.
Protractor Postulate: Given line AB and a point O on AB, all
rays that can be drawn from O can be put into a one-to-one
correspondence with the real numbers from 0 to 180.
AcuteObtuseRight-
Straight-
Perpendicular –
Example - Use the diagram to find the measure of each angle. Then classify each as acute, right, or
obtuse.
a) <BOA
b) <DOB
c) < EOC
d) <EOB
e) <AOD
Congruent Angles: angles that have the same measure.
Angle Bisector: a ray that divides an angle into two congruent angles.
Example 1 - Draw a picture. If CD bisects  ACB,
Then _______  _______.
Example 2 –Draw a picture and solve. m<DEG = 115 and m<DEF = 48. Find m<FEG.
Example 3- Draw a picture for the following and write an equation to solve for x. RQ bisects  PRS. If
m  PRQ = x + 40 and m  QRS = 3x – 2, solve for x,
4
Example 4 - Write an equation to solve for x.
x = _____________
m BAD = 122, x = _______
Example 5 - Draw a picture for the following problem. E is on the interior of <SRP. mSRP = 157
m  ERP = 98
Find mPRS = _________and
m SRE = _________
Example 6- Draw a picture for the following and write an equation to solve for x. If SU bisects <RST, and
m<RSU = 2x - 11, and m<RST = 3x+23, find
x = ___________
m<TSU = ______________ m<RST = ________________
Example 7 - Draw a picture for the following and write an equation to solve for x. <DEF is a right angle.
m<DEG = (3x + 8) ° and m<GEF = (6x – 17) °. Find the m<DEG.
Write the equation for #s 9-13. Then solve.
5
Pairs of Angles
*Two angles are ________________ if their sides form two pairs of opposite rays.
2
1
Examples:
3
4
vertical angles are always ______________
*Two angles are ________________ if they have a common side, a common vertex, and no common
interior points.
2
1
3
Examples:
*Two angles are ____________________ if the sum of their measures is 90.
Each angle is a complement of the other.
A
35
55
C
Examples:
B
*Two angles are ____________________ if the sum of their measures is 180.
Each angle is a supplement of the other.
Examples:
D
E
Linear Pair: _____________angles whose non-common sides form a _________
linear pair is always _____________and ________________
m<1 + m<2 = ________
1
2
Use this figure for 1 - 6
1. Name all angles shown.

G
2. Name 1 in 2 other ways.

D
3. Name all angles which have side EF .
4. Name a point in the interior of GEF.
5. Name a point in the exterior of 2.
6. Name 2 pairs of adjacent angles.
6
H
1
2

E
3

F
State whether the numbered angles shown in 9 – 16 are adjacent or not. If NOT, explain.
7.
8.
2
1
1
D
2
B
1
2
11.
A
10. ABC, ABD
9.
C
12
12.
1
13.
2
14.
1
2
1
2
Verifying Angle Relationships-Label the diagram below so that m∠BGC=33 and m∠DGE=57
1. ∠FGA ≅ __________2. m∠CGD = _________
5. ∠EGC and ______________are supplementary
3. ∠BGF and _________ are supplementary
4. m∠AGF = _________
6. m∠AGB = __________
F
A

7. m∠AGC = ________
8. m∠BGD= _________
9a. Are ∠AGF and ∠CGD supplementary?________why/why not?
B
G

E

D

C
b. Are they a linear pair?________why/why not?

Solve the following for the indicated variable. Set up an equation using the angle relationships
1.
2.
3x – 5
6x – 23
2x – 16
x + 16
3.
4.
x
3x – 8
50
2y – 17
x
2x – 36
More Angles
1. The supplement of a right angle is a ____________angle.
2. The supplement of an obtuse angle is a _____________angle.
3. The supplement of an acute angle is a ______________angle.
7
3x – y
4. Vertical angles are ____________.
5. ________________lines form right angles.
6. Congruent supplementary angles each have a measure of ___________.
7. Congruent complementary angles each have a measure of __________.
8. The angles in a linear pair are ___________________and_____________________.
9. m<1 = 40. What is the measure of its complement? _________Its supplement? ________
10. m<2 = 120. What is the measure of its complement? _________ Its supplement?_________
11. m<A = x. What is the measure of its complement? __________Its supplement? __________
Complete with Always, Sometimes, or Never
1. __________ Two <’s that are supplementary ___________form a linear pair.
2. __________ Two <’s that form a linear pair are ____supplementary.
3. __________Two congruent angles are _________right.
4. __________Two right angles are ___________congruent.
5. __________ Two angles that are vertical are _________adjacent.
6. __________ Two angles that are non-adjacent are _________vertical.
7. __________ Two angles that form a linear pair are ___________congruent.
8. __________Two angles that form a right angle are ______complementary.
9. __________Two angles that form a right angle are ______ supplementary.
10. _________ Two angles that are supplementary are _______ congruent.
11. __________ Vertical angles ________ have a common vertex.
12. ___________ Two right angles are _________ complementary.
13. __________ Right angles are __________ vertical angles.
14. __________ Angles A, B, and C are __________ supplementary.
15. __________ Vertical angles __________ have a common supplement.
Given: ∠1 is a right angle, m∠5=30, and ∠2 ≅ ∠3. Find the following
1
2
3
4
m∠1=______ m∠2=_____
7
●
6
5
m∠3=_____
m∠4=_____
m∠3 + m∠2 +m∠1 = ___________
8
m∠6=_____
m∠7=_____
EOA is
a.
b.
c.
d.
e.
f.
Acute
Right
Obtuse
Linear Pair
Congruent
Vertical
________
EOA and DOB are
________
COB is
_________
EOA and AOB are
__________
EOD and AOB are
__________
DOC is
__________
DOC and <AOC
g.
h.
i.
Complementary
Supplementary
Adjacent
_________
DOC and COB are
__________
COB and BOA are
___________
Incorporating Algebra into Geometry
I. Define variables and write an equation for each problem, then solve and circle final answers.
1. Two angles are complementary and one’s measure is twice the measure of the other. Find the measures of the two angles.
2. Two angles are complementary and the measure of one angle is 36 less than the other. Find the measures of the two angles.
3. The supplement of an angle exceeds five times the measure of the angle by 6. Find the measures of the supplementary angles.
4. The supplement of an angle exceeds five times the measure of the complement of the angle by 10. Find the measure of the angle.
5. An angle is six less than two times the measure of its complement. Find the measure of the angle.
6. The measure of a supplement of an angle is 15 more than 2 times the complement. Find the measures of the angle, the
complement, and the supplement.
1.6 Distance and Midpoint
Distance Formula:
Midpoint Formula:
3.) Y is the midpoint of
a) coord. Of X is –8
coord. Of Z is 6
coord. Of Y = ____
XZ .
Find the coordinate of the 3rd point for each example.
b) coord. of X is 11
coord. of Y is 15
coord. of Z = _____
c) coord. of Y is -8
coord. of Z is -19
coord. of X = _____
4) Find the midpoint of AG if A(4, -7) and G(-9, 4). ______________
5) Find B if M (1, 11) is the midpoint of BT and T(7,-14) _________________________
6) Use the Distance Formula to find the distance between K(-7, -4) and L(-2, 0).
7)
_______________
Find the length of F(9, 5) and G(–2, 2). _____________________________
In 9 – 14, the numbers given are the coordinates of two points. Fin the distance between the points.
9. -8 and 4
10. -13 and -14
11. 0 and 7.5
12. 12 and 37
13. -5.6 and 7.4
14. a and b
9