# geometry final

Just about everything on the sheet Ms. Modl gave us except for things that you can't put on the computer... like things with segments and stuff.

let me know if anything is wrong or misspelled and I'll fix it!

let me know if anything is wrong or misspelled and I'll fix it!

## Terms

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- converse of the perpendicular bisector theorem
- if a point is equidistant from the endpoints of a segment, then it lies of the perpendicular bisector of the segment
- SSS
- 3 sides of one triangle are congruent to 3 sides of another triangle
- alternate exterior angles theorem
- alternate exterior angles are congruent
- congruent angles
- angles with the same measure
- slope-intercept form
- y=mx+b
- reflex angle
- 180°< x < 360°
- perpendicular lines have:
- slopes that are opposite reciprocals
- right angle
- 90°
- obtuse angle
- 90°< x < 180°
- HL
- hypotenuse & leg of one right triangle is congruent to the hypotenuse & leg of another right triangle
- perimeter of rectangle
- P=2L+2w
- complementary angles
- 2 angles with a sum of 90°
- exterior angle theorem
- measure of the exterior angle is equal to the sum of the remote interior angles
- area of rectangle
- A=lw
- area of triangle
- A=½bh
- centroid theorem
- centroid is ²/₃ the distance from the vertex
- verticle angles theorem
- if ∠a and ∠b are verticle angles, then ∠a is congruent to ∠b
- converse of the isosceles triangle theorem
- if 2 ∠s of a triangle are congruent, the opposite sides are congruent
- inverse
- if not p, then not q
- SAS
- 2 sides and the included ∠ of one triangle are congruent to 2 sides and the included ∠ of another triangle
- ASA
- 2 ∠s and the included side of one triangle are congruent to 2 ∠s and the included side of another triangle
- CPCTC
- corresponding parts of congruent triangles are congruent
- parallel lines
- coplanar lines that do not intersect
- opposite rays
- 2 rays with a common enpoint
- vertical angles
- congruent, opposite, nonadjacent angles formed by 2 intersecting lines
- triangle midsegment theorem
- the midsegment is parallel to the opposite side of the triangle and its length is ½ the length of the opposite side
- isosceles triangle theorem
- if 2 sides of a triangle are congruent, the opposite angles are congruent
- median
- segment connecting vertex to the midpoint of the opposite side
- linear pair
- adjacent angles with a sum of 180°
- perimeter of triangle
- sum of sides
- law of syllogism
- if p the q and q then r are true, then p the r is true
- incenter theorem
- incenter is equidistant from the sides of the triangle
- incenter
- intersection of the angle bisectors of a triangle; always inside the triangle
- circumcenter theorem
- circumcenter is equidistant from the vertices of the triangle
- skew lines
- lines that are not coplanar, not parallel, and do not intersect
- slope of horizontal line
- y=b
- angle bisector theorem
- if a point is on the bisector of an angle, then it is equidistant from the sides of the angle
- theorem
- a statment that can be proven true
- coplanar
- points on the same plane
- converse of the angle bisector theorem
- if a point in the interior of an angles is equidistant from the sides of the angle, then it lies on the angle bisector
- perimeter of square
- P=4s
- Addition property
- if a=b, then a+c = b+c
- centroid
- intersection of the medians of a triangle; always inside the triangle
- subtraction property
- if a=b, then a−c = b−c
- proof
- to show a conclusion is true using deductive reasoning
- 2 lines can be proved parallel by the:
- conv. of the corr. ∠s post.; conv. of the alt. int. ∠s thm.; conv. of the alt. ext. ∠s thm; conv. of the same-side int. ∠s thm.
- segment
- with endpoints
- congruent segments
- segments with the same length
- slope
- y₂−y₁ over x₂−x₁
- area of square
- A=s²
- substitution property
- if a=b, then b can be substituted for a
- slope of vertical line
- x=a
- midpoint
- point that divides a segment into 2 congruent segments
- inductive reasoning
- conclusion based on patterns; maybe true; conclusion is a conjecture
- zero slope
- horizontal line
- right angle supplmentary theorem
- if ∠1 is congruent to ∠2, and ∠1 & ∠2 are supplementary, then ∠1 & ∠2 are right angles
- biconditional
- p if and only if q
- linear pair theorem
- if 2 angles form a linear pair, they are supplementary.
- angle
- formed by two rays with a common endpoint or vertex
- orthocenter
- intersection of the 3 altitudes of a triangle; may be outside the triangle
- right angle congruence theorem
- all right angles are congruent
- perpendicular lines
- lines that intersect at right angles
- collinear
- points on the same line
- line
- extends infinitely
- circumcenter
- intersection of the perpendicular bisectors of the sides of a triangle; may be outside the triangle
- third angles theorem
- if 2 angles of one triangle are congruent to 2 angles of another triangle, then the triangles are congruent.
- adjacent angles
- 2 angles that share a side and vertex
- ray
- endpoint at 1 end; extends infinitely at the other
- types of proof
- 2-column; flowchart; paragraph
- supplementary angles
- 2 angles with a sum of 180°
- parallel planes
- planes that do not intersect
- acute angle
- 0°< x < 90°
- converse of the equilateral triangle corollary
- if a triangle is equiangular, then it is equilateral
- postulate
- a statement accepted as true, without proof.
- parallel lines have:
- the same slope
- corresponding angles postulate
- corresponding angles are congruent
- conditional
- if p, then q
- contrapositive
- if not q, then not p
- definition of congruent triangles
- corresponding angles and corresponding sides are congruent
- converse
- if q, then p
- altitude
- the perpendicular segment from the vertex to the opposite side
- congruent complements theorem
- if 2 angles are complementary to the same angle, they are congruent.
- deductive reasoning
- conclusion based on logic, facts, definitions & properties; true; to prove a conjecture true
- midsegment
- segment that joins midpoints
- point-slope form
- y−y₁=m(x−x₁)
- multiplication property
- if a=b, then ac=bc
- transitive property
- if a=b and b=c then a=c
- law of detachment
- if p then q is true, and p is true, then q is true
- segment bisector
- ray, line, or segment that intersects a segment at its midpoint
- AAS
- 2 ∠s and the nonincluded side of one triangle are congruent to 2 ∠s and the nonincluded side of another triangle
- symmetric property
- if a=b, then b=a
- undefined slope
- vertical line
- Pythagorean Theorem
- a²+b²=c²
- alternate interior angles theorem
- alternate interior angles are congruent
- triangle sum theorem
- the sum of the angle measures of a triangle is 180°
- transversal
- line intersecting 2 coplanar lines at 2 different points
- perpendicular bisector theorem
- if a point is on the perpendicular bisector of a segment, then it is equidistant from the end points of the segment
- same-side interior angles theorem
- same-side interior angles are supplementary
- equilateral triangle corollary
- if a triangle is equilateral, then it is equiangular
- reflexive property
- a=a
- congruent supplements theorem
- if 2 angles are supplementary to the same angle, they are congruent.
- division property
- if a=b, then a/c = b/c