by leonard i was unable to place the bar over the letters for a line segment. i hope you understand...
TRANSCRIPT
BY
Leonard
•I was unable to place the bar over the letters for a line segment. I hope you understand that where it is supposed to say segment AB, it just says AB.
•Next to each key term, I placed a P, T, or Q to show what topic it is from. P stands for Parallelism, T stands for Triangles, and Q stands for Quadrilaterals
• I had trouble picking what kind of background I would use for each slide, so I decided to make the background colorful and unique.
Key TermsKey Terms
Skew lines: 2 lines that are in different planes and never intersect
Parallel: when 2 lines are coplanar and never intersect
Transversal: a line that intersects 2 parallel lines (T is the transversal in this diagram)
Early Version of Exterior Angle Earl Warren
Key Terms ContinuedKey Terms Continued
Alternate interior angles: nonadjacent angles on the opposite sides of the transversal that are in the interior of the lines the trans- versal runs through
Corresponding angles: angles on the same side of the transversal, but one
angle is interior and the other is exterior.
Del Mar’s Diagonal 15th Street
Encinitas Median Moonlight Beach
More Key Terms
Quadrilateral: the union of 4 segments
Sides: segments of a shape (for example, AD & DC)
Vertices: where the segments meet each other (a, b, c, d)
Angles: the combination of two segments (such as )
a b
cd
ABC
Convex: when a line is able to connect any 2 points in a plane or figure with out going out of the figure itself
convex
Transversal Torrey Pines State Beach
Key terms continued
Opposite (in terms of quadrilaterals): the description of sides that never intersect or angles that
do not have a common side (such as AB &CD and AD & BC or A & C and B & D)
Consecutive (in terms of quadrilaterals): the description of sides that have a common end point or angles that share a common side (E.g. AB &BC or D & C)
Diagonal (in terms of quadrilaterals): segments joining 2 nonconsecutive vertices (AC & BD for example)
Parallelogram: quadrilateral with both pairs of opposites sides parallel
Trapezoid: quadrilateral with one pair of parallel sides
Bases (of a trapezoid): the parallel sides (AB & CD)
Median (of a trapezoid): segment joining midpoints of nonparallel sides (the red line)
Rhombus: a parallelogram with all sides congruent
Rectangle: a parallelogram with all angles right angles
Square: parallelogram with all congruent sides and all right angles
Intercept: the term used to describe when points are on the transversal (Line A and B intercept segment CD on the transversal)
Concurrent: when lines contain a single point which lies on all of them
Point of Concurrency: the point which is contained by all of the lines
PCA Corollary: states that corresponding angles created by 2 parallel lines cut by a transversal are congruent
In other words: if L1 and L2 are parallel, then 3 and 4 are congruent
This is possible because of the PAI Theorem and the Vertical Angle Theorem
-ior
In other words:
Because AC and
BD bisect each other,
ABCD is a
parallel-ogram
Theorem: If there is one right angle in a parallelogram, then it has 4 right angles, which means that parallelogram is a
rectangle.
In other words: If <D is a right angle and ABCD is a parallelogram, then <A, <B, and <C are right angles, which means that ABCD is a rectangle.
This is because of the theorem that states interior angles on the same side of the
transversal are supplementary and the theorem that states supplementary congruent angles are
right angles.
180° Triangle Theorem: The sum of a triangle’s angles is 180.
All of these triangles’ angles’ sum of measures is 180.
150 °
50° 50 ° 90 ° 30 °
60 °
15 ° 15 °
80 °
a
bc
If a segment is between the midpoints on both sides of a triangle, then that segment is 1) parallel
to the base and 2) half as long as the base.
a
bc
x y
In other words: If AX=XE and AY=YB, then XY is parallel to CB and XY=CB.
This can be proved by using SAS, AIP, Definition of a
Parallelogram, and a couple parallelogram
theories.