Deductive Geometry Unit 3

• Theorem 3: All points on the perpendicular bisector CD are equidistant from the endpoints of segment AD
• Theorem 4: If 2 points of a line, C and D, on CE, are equidistant from the endpoints of segment AB then the line, CE is the perpendicular bisector of AB
• Theorem 5: The perpendicular distance from a point to a line is the shortest segment joining them
• Theorem 6: If two lines are parallel, every perpendicular segment joining one line to the other has the same length
• rectangle iff all of its angles are equal
• rhombus iff all sides are equal
• square iff all sides and angles are equal
• trapezoid iff it has exactly one pair of parallel sides
• kite iff two pairs of distinct adjacent sides are equal
• isosceles trapezoid iff the non-parallel sides are =
• A midsegment of a triangle is the segment connecting the midpoints of two sides of the triangle
• MST: if a segment is the midsegment of a triangle then it is parallel to the base of the triangle and half the length of the base
• A median of a triangle is a line segment joining the vertex to the midpoint of the opposite side of the triangle
• A median of a trapezoid is a line segment joining the midpoints of the non-parallel sides.
• Median of a triangle theorem: the medians of a triangle are concurrent at a point called the centroid, which is 2/3 from the vertex, or medians are cut in a 1:2 ratio
• Median of a trapezoid theorem: the median of a trapezoid is parallel to the bases and equal to the average of the bases.
• C-MST: If a line passes through the midpoint of one side of a triangle and is parallel to another, then it intersects the midpoint of the third side
• Paper theorem: is parallel lines cut off congruent segments in one transversal, then any other transversal intersecting these lines are cut off into congruent segments
• the area of a trapezoid is (1/2(b1+b2))h
• the area of a rhombus is 2 x base x height or 1/2(d1*d2)
• the area of a kite is 1/2(d1*d2)
• the pythagorean theorem is a^2+b^2=c^2
• the sides of a 45-45-90 triangle are x-x the hypotenuse is xroot2
• the sides of a 30-60-90 traingle are x-xroot3-2x
• Side-Splitter Theorem: If a line segment intersects two sides of a triangle and is parallel to the third side, then it divides the two sides proportionally
• Similar Polygons: Polygons are similar iff all corresponding angles are equal and corresponding sides are proportional
• AAA Similarity: If three angles in a triangle are equal to the corresponding angles of a second triangle then the two triangles are similar
• AA Similarity Theorem: If two angles of a triangle are congruent to two corresponding angles then the triangles are similar in order of correspondence