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.