Download MATH 241 Midterm Review Know these things. When appropriate

MATH 241
Midterm Review
Know these things. When appropriate be able to draw a diagram to illustrate the fact. Be able to use these facts. Be able to prove the items that
are starred.
Know and be able to state all theorems that have a name! You may be
asked to state and prove such a theorem (e.g. “State and prove the angle
side inequality theorem.”), if you do not know what the theorem by name
you will not be able to answer the question.
Chapter 1
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Playfair’s Parallel Axiom and the parallel postulate.
opposite angles in an X are equal.
Know what it means for two things to be congruent.
SAS, SSS, ASA, SAA, SSA* and HSR.
The triangle inequality.
The isosceles triangle theorem and it’s converse.
The angle side inequality and it’s converse.
Theorem 1.3.1/2 (parallel lines)
The angles in a triangle sum to 180 degrees.
The exterior angle theorem and the exterior angle inequality.
Thales’ Theorem
Thales’ corollary (1.3.7) and its converse (1.3.8).
Know what a convex, simple or non-simple quadrilateral is.
The interior angles of a simple quadrilateral sum to 360◦ .
What it means for a shape to be cyclic.
A quad is cyclic if and only if it’s opposite interior angles sum to
180◦ .
Characterization of the right bisector Theorem.
Characterization of the angle bisector Theorem.
Construction problems 1.5.1 to 1.5.8
Assignments 2 and 3.
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Chapter 2
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l1 k l2 , m1 ⊥ l1 and m2 ⊥ l2 then m1 k m2 .
m1 ⊥ l1 and m2 ⊥ l2 then l1 k l2 if and only if m1 k m2 .
A triangle’s three perpendicular bisectors are concurrent.
Know what is, and how to construct a triangle’s circumcircle.
All of theorem 2.2.1 (chords of circles).
A triangle’s three angle bisectors are concurrent.
Know what a triangle’s incircle is, how it’s center is found and how
the incircle would be constructed.
Each pair of exterior angle bisectors of a triangle intersect.
The external angle bisectors of two angles of a triangle and the internal angle bisector of the third are concurrent.
Know what a triangle’s excircle is, how it’s center is found and how
the excircle would be constructed.
In a parallelogram 1) opposite sides are congruent, 2) opposite angles
are congruent, 3) the diagonals bisect each other.
A simple quadrilateral is a parallelogram, if any of the following
are true: 1) Opposite sides are congruent, 2) opposite angles are
congruent, 3) one pair of opposite sides are congruent and parallel,
4) the diagonals bisect each other.
The three altitudes of a triangle are concurrent.
Know what the orthocenter of a triangle is.
The midline theorem. (any proof)
The three medians are concurrent and trisect each other.
In 4ABC if P is the midpoint of AB and Q is on AC such that P Q
is parallel to BC, then Q is the midpoint of AC.
Construct a parallelogram given three of the four vertices.
Construct a line Through a point P parallel to a given line l.
For a point P outside of a circle C(0, r), construct a line Through P
tangent to C(0, r).
What a Thales’ Locus is.
How to construct a Thales’ Locus on a line segment AB with a given
angle θ.
Construction problem 2.5.6.
Assignments 4 and 5.