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BY
Leonard
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•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.
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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
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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
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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
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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)
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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
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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
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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
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-ior
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In other words:
Because AC and
BD bisect each other,
ABCD is a
parallel-ogram
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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.
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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
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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.
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