Geometry
5-1 Notes
Bisectors of Triangles
Perpendicular bisectors segment perpendicular to another segment at its midpoint.
Theorem 5.1 Perpendicular Bisector Theorem
C
A
D
B
Theorem 5.1 Converse of the Perpendicular Bisector Theorem
Concurrent lines 3 or
Chapter 5 Triangle Restrictions
Name_
Answer all the following questions using a compound inequality.
Use the picture below for #1 3.
1) Find the range of possible values of x.
0
y
_
5
7
2) Find the range of possible values of y.
x0
w0
_
3) Find the range
Rectangle- parallelogram with 4 right angles
Rectangles
Diagonals of a rectangle are congruent
If diagonals of a parallelogram are congruent, then its a rectangle
Midsegment of a trapezoid- segment whose endpoints are the midpoints of
non- parallel sides
The triangle inequality theorem
The sum of any 2 sides of a triangle is greater than the 3rd
side
If the longest side is known, add the 2 smallest to check
5
<X<
x+ 2x + 5 > 4x 3
x + 4x 3 > 2x + 5
3x +5 > 4x 3
5x 3 > 2x +5
x<3
x > 8/3
29
Quadrilateral - polygon with 4 sides
Parallelograms quadrilateral with 2 pairs of parallel sides.
Symbol:
What does it take for a quadrilateral to be a parallelogram?
Two pairs of parallel lines
2 pairs of opposite sides congruent then its a parallelogram
Proving Triangles Congruent
Steps for Finding Congruent Sides/Angles
*Label all congruent sides and angles of needed triangles with an A or an S*
1) Use given congruent sides/angles
2) Use given terms and their definitions
midpoint, bisectors definitions
S
C
1)
Statement:
Conclusion:
Angle2
R
2)
12
Statement:Misthemidpointof
Angle1iscongruenttoConclusion:LineAMiscongruenttolineMB
Reason:Verticalanglesarecongruent
Reason:Def.ofmidpoint
NextConclusion:Measureofangle1isequaltothemeasureofangle2
Rea