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