Download Final Exam Review

Final Exam Review
Chapters 1 - 4
The Midpoint Formula
The coordinates of the midpoint of a segment are the…
 x1  x2 y1  y2 
'


2 
 2
The Distance Formula
( x2  x1 )  ( y2  y1 )
2
2
Classifying Angles by their Measures
Acute Angle
Obtuse Angle
Less than 90 degrees
Greater than 90 degrees
Right Angle
Straight Angle
90 degrees
180 degrees
More Angle Pairs
Linear Pair
2 adjacent angles whose noncommon sides are on
the same line.
Add up to 180 degrees
Vertical Angles
2 nonadjacent angles whose sides are formed by 2
intersecting lines. (Like scissors)
These are congruent
Polygons
Properties:
-Plane figure (flat)
-Closed
-Straight sides
-Doesn’t cross itself
*A circle is not a polygon*
Convex – All corners point out
Concave – A corner “caves” in
Classifying Polygons by Sides
# of
sides
Type of polygon
# of
sides
Type of polygon
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
7
Heptagon
n
n-gon
Conditional Statements
A statement where one part relies on the
other (if-then)
Hypothesis – the if part
Conclusion – the then part
If the team loses the game,
then they will be out of the playoffs.
Rewrite If-Thens
• Converse – Switch the hypothesis and
conclusion
• Inverse – Negate the hypothesis and the
conclusion
• Contrapositive – Write the converse, then
negate the hypothesis and conclusion
Pairs of Lines
• Perpendicular – 2 lines that intersect to
form right angles
• Parallel – 2 lines that don’t intersect and
are coplanar. Always the same distance
apart.
• Skew –2 lines that don’t intersect and are
not coplanar. (Run in different directions.)
Slope
rise y2  y1
m

run x2  x1
Slopes of Parallel/Perpendicular
Lines
• Slopes of Parallel Lines – Same slope
• Slopes of Perpendicular Lines – Negative
Reciprocals (Flipped and one negative
one positive)
Slope-Intercept Form
y = mx + b
Where m = slope
And b = y-intercept
Classifying Triangles by Sides
Scalene Triangle
No congruent
sides
Isosceles
Triangle
Equilateral
Triangle
3 congruent sides
2 congruent sides
Classifying Triangles by Angles
Acute Triangle
Obtuse Triangle
All acute angles
1 obtuse angle
Right Triangle
Equiangular Triangle
1 right angle
All congruent angles
Showing Triangles are Congruent
•
•
•
•
•
SSS
SAS
ASA
AAS
HL
NO!!! ASS, SSA, AAA
Equilateral and Isosceles Triangles
• If a triangle is equilateral, then it is equiangular.
• If a triangle is equiangular, then it is equilateral.
• If two sides of a triangle are congruent
(isosceles), then the angles opposite them are
congruent.
• If two angles of a triangle are congruent, then
the sides opposite them are congruent
(isosceles).