Geometry: Unit 4: Proofs
Ways to Prove Congruency In a Rhombus
- all 4 sides are congruent - parallelogram with 2 consecutive sides congruent
Ways to Prove a Quadrilateral Is a Parallelogram
- both pairs of opposite sides are congruent - both pairs of opposite sides are parallel - one pair of opposite sides are congruent and perpendicular
Alternate Exterior Angles
congruent
Isosceles Triangle
2 congruent sides and 2 congruent base angles
CPCTC
Corresponding Parts of Congruent Triangles are Congruent: used when you are at or near the end of a proof which asks the student to show that two angles or two sides are congruent; we use it because it means that if two triangles are known to be congruent, then all corresponding angles/sides are also congruent
(True or False) vertical angles are method to prove lines are parallel to each other
False
Congruent
Having the same size and shape
Linear Pair Postulate
If 2 angles make a straight line then they are supplementary
Hypotenuse Leg Theorem
If the hypotenuse and a leg of one right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.
Valid Congruence Criteria
SSS, SAS, ASA, AAS, HL
Hypotenuse
The side opposite the right angle in a right triangle.
(True or False) parallelograms can be proven by showing only one pair of sides is congruent and parallel
True
Supplementary
Two angles whose sum is 180 degrees
Perpendicular Bisector
a line (or segment or ray) which is perpendicular to the given segment and intersects the given segment at its midpoint, creating 2 congruent segments
Auxiliary Line
a line drawn in a figure to aid in a proof
Median
a line segment joining a vertex to the midpoint of the opposing side, bisecting it. Every triangle has exactly three medians, one from each vertex and they all intersect each other at the triangles centroid
Midpoint
a point that divides a segment into 2 congruent pairs
Altitude
a segment from any vertex perpendicular to the line containing the opposite side
Angle Bisector
a segment that divides an angle into 2 congruent angles
Partition Postulate
a segment/angle is equal to the sum of its parts
Segment Bisector
an object that intersects a segment at it's midpoint
Alternate Interior Angles
congruent
Corresponding Angles
congruent
Parallel Lines
equidistant; same slope
Transversal
intersects two lines so that corresponding angles are congruent, then the lines are parallel. If interior angles on the same side of the transversal are supplementary, then the lines are parallel
Perpendicular Lines
lines that intersect at right angles
In order to prove lines are parallel, you must prove....
one of the pairs of angles are congruent
Reflexive Property
property that states any object is congruent to itself
Addition Postulate
sum of congruent items are congruent
Same Side Exterior Angles
supplementary
Same Side Interior Angles
supplementary
Substitution Property
when you plug equal items in for each other
Subtraction Postulate
when you subtract common or congruent items