Unit 4
Special Triangle Segments
Perpendicular Bisector
A segment or line that is perpendicular
to another segment at its midpoint.
Angle Bisector
A segment or ray that cuts an angle
into two congruent pieces.
Median
A segment drawn from a vertex of a tri
Addition
Property
Subtraction
Property
Multiplication
Property
Division
Property
If a = b, then a + c = b + c.
If a = b, then a c = b c.
If a = b, then ac = bc.
If a = b and c 0, then a c = b c.
Reflexive
Property
Symmetric
Property
Transitive
Property
Su
Conditional
A logical statement that has two parts, a
Statement
hypothesis and a conclusion.
A form of conditional statement where the if
If-Then
Form
Converse
part contains the hypothesis and the then part
contains the conclusion.
Formed by switching the
Conjecture
Counterexample
Inductive
Reasoning
Deductive
Reasoning
An unproven statement based on observations.
An example that shows a conjecture is false.
Looking for a pattern to make a conjecture.
Uses facts, definitions, and properties in a
logical or
Systems of Equations Help Sheet
Method 1: Substitution
"2 x + 3y = !15
#
$!4 x + y = !19
Isolate either x or y in one of the equations. HINT:
look for what will be easy!
Step 1:
Solving for y in the s
Name _
Definitions & Drawing
On another sheet of paper, draw and carefully label each of the figures below. Use special marks to
indicate right angles, parallel lines, and congruent segments or angles. Use a
Constructions Activity #4
Bisecting an Angle
Name:
Date:
Use the following steps to construct an angle bisector of C .
1. Place the compass point at C. Draw an arc that intersects bot
Constructions Activity #3
Copying an Angle
Name:
Date:
Use the following steps to construct an angle that is congruent to a given angle, A .
1. Draw a line. Label a point on the lin
Unit 1
Bisectors
Bisector
Something that cuts a segment or
an angle into two congruent pieces.
If a segment, on the coordinate plane, has endpoints (x1, y1) and (x2, y2), then
the midpoint of the segment can be
Unit 1
Segments and Their Measures
Vocabulary:
A rule in geometry that is accepted without proof (also
Postulate
called an axiom).
M EASUREMENT
Congruent'
Measurement: Having'the'same'measure.'
!
A'rule'in'Geometry'that'is
Unit 1
Points, Lines, and Planes
Has no dimension (length, width, etc.).
Point
Line
Segment
Collinear Points: Points on the same line.
Coplanar Points: Points in the same plane.
Extends in one dimension
Theorem
A true statement that follows as a result of
other true statements.
Vertical angles are congruent. (Vertical Angles Theorem)
All right angles are congruent. (Right Angles Theorem)
If two angles are complementary to the same angle (or to
congruent
exactly one
Through any two points there exists _ line.
at least two
A line contains _ points.
If two lines intersect, then their intersection is
exactly one point
_.
Through any three noncollinear points there exists
_.
exactly one plane
at least thr
UNIT 3
LINES AND TRANSVERSALS
VOCABULARY
Coplanar lines that do not
Parallel
Lines
intersect. |
suu suu suuu suu
r
r
r
r
Ex: FG & BC, DH & BF, etc.
Noncoplanar lines that do
Skew
Lines
F
B
not intersect.
suu suu suur suu
r
r
r
Ex: FG & AB, EH & BF, etc.
P
Unit 4
Triangle Inequalities
Triangle Postulates and
Theorems
When you add any two
sides of a triangle, the sum is
greater than the third side.
C
A
AB + BC > AC
BC + AC > AB
B AC + AB > BC
In any triangle, the smallest side is opposite
the smallest angle
Unit 4
Triangles and Angles
Triangle Postulates and
Theorems
The measure of an exterior
angle of a triangle is equal to
the sum of the two interior
angles that are not next to it.
3
2
1
m3 = m1 + m2
Example 1:
Find the value of x. Then find the measure of
Unit 4
Properties of Isosceles and
Equilateral Triangles
Properties of Isosceles and
Equilateral Triangles
If two sides of a triangle are
congruent, then the angles
opposite them are congruent.
Base Angles Theorem
If two angles of a triangle are
congruent
Unit 4
Classifying Triangles
Classification by Sides
Equilateral Triangle
Isosceles Triangle
Leg
Scalene Triangle
Leg
Base
3 Congruent Sides
At least 2 Sides
No Congruent Sides
Classification by Angles
Acute Triangle
Equiangular
Triangle
Right Triangle
Le
Unit 4
Angle Measures in Polygons
Day 2
Vocabulary
Exterior
Angles
The angles adjacent to the
interior angles when the
sides of a polygon are
extended.
# Sides
Name
3
Triangle
4
Quadrilateral
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
Unit 4
Angle Measures in Polygons
Vocabulary
Interior
Angles
The angles inside a polygon.
Polygons
Polygon
Concave
Polygon
Convex
Polygon
A closed figure made up of
3 or more segments
A polygon that contains
one or more interior angles
that is more than 1
UNIT 3
PA R A L L E L A N D P E R P E N D I C U L A R L I N E S O N
T H E C O O R D I N AT E P L A N E
FINDING THE SLOPE OF A LINE
Method 1:
Using Two
Points
Method 2:
SlopeIntercept
Form
Method 3:
Standard
Form
y2 y1
x2 x1
y = mx + b
Slope is # attached
UNIT 3
P R O V I N G L I N E S PA R A L L E L
Congruent
Corresponding angles are _
Corresponding
Angles Postulate
Alternate exterior angles are Congruent
_
Alternate Exterior
Angles Theorem
Congruent
Alternate interior angles are _
Alternate Interior
Angl
Name _
Properties of Parallel Lines Guided Practice
suu suu suu suu uuu
r
rr
rr
2. In the figure, BG | CE, BE | CD, BG bisects
1. Given that m5 = 65 , find the measure
of each numbered angle.
EBA, m8 = 42 , and m
UNIT 3
PA R A L L E L L I N E S A N D T R A N S V E R S A L S
Congruent
Corresponding angles are _
Congruent
Alternate exterior angles are _
Congruent
Alternate interior angles are _
Supplementary
Same-side (consecutive) interior angles are _
Supplementar
M12/4/CHEMI/HP3/ENG/TZ1/XX/M
MARKSCHEME
May 2012
CHEMISTRY
Higher Level
Paper 3
20 pages
2
M12/4/CHEMI/HP3/ENG/TZ1/XX/M
This markscheme is confidential and for the exclusive use of
examiners in this examination session.
It is the property of the Internati