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Math
Geometry
Geometry Semester 1
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Chapters 1-6. Thereoms, postulates and formulas.
Terms in this set (76)
ruler postulate
You can draw things!
segment addition postulate
If B is between A and C, AB + BC = AC.
distance formula
√(x₂ - x₁)² + (y₂ - y₁)²
pythagorean thereom
a² + b² = c²
angle addition postulate
m∠RSP + m∠PST = m∠RST
midpoint formula
(x₁ + x₂/2, y₁ + y₂/2)
conditional
p → q
inverse
≈p → ≈q
converse
q → p
contrapositive
≈q → ≈p
biconditional
p ↔ q
law of detachment
If p → q is a true statement and p is true, then q is true.
law of syllogism
If p → q and q → r are true statements, then p → r is true.
addition property of equality
If a=b, then a + c = b + c.
subtraction property equality
If a=b, then a - c = b - c.
multiplication property of equality
If a=b, then ac=bc.
division property of equality
If a=b, then a ÷ c = b ÷ c.
reflexive property of equality
a=a
symmetric property of equality
If a=b, then b=a.
transitive property of equality
If a=b and b=c, then a=c.
substitution property of equality
If a=b, then a can be substituted for b.
right angle congruence thereom
Right angles are congruent.
congruent supplements thereom
If 2 angles are supplementary to the same angle (or congruent angles) they are congruent.
linear pair postulate
If 2 angles form a linear pair, they are supplementary.
vertical angles thereom
Vertical angles are congruent.
parallel postulate
There is exactly 1 line through P parallel to L.
perpendicular postulate
There is exactly one line through P perpendicular to L.
corresponding angles postulate
If 2 parallel lines are cut by a transversal, the pairs of corresponding angles are congruent.
perpendicular transversal thereom
If a transversal is perpendicular to 1 of 2 parallel lines, then it is perpendicular to the other.
converse of corresponding angles postulate
If 2 lines are cut by a transversal so that corresponding angles are congruent, the lines are parallel.
slope
rise/run
slopes of parallel lines postulate
2 nonvertical lines are parallel if and only if they have the same slope. Any 2 vertical lines are parallel.
slopes of perpendicular lines postulate
2 nonvertical lines are perpendicular if and only if the product of their slopes is -1. Vertical and horizontal lines are perpendicular.
equilateral triangle
Triangle with 3 congruent sides.
isoceles triangle
Triangle with 2 congruent sides.
scalene triangle
Triangle with no congruent sides.
acute triangle
Triangle with 3 acute angles.
equiangular triangle
Triangle with 3 congruent angles. Also acute.
right triangle
Triangle with 1 90° angle.
obtuse triangle
Triangle with 1 obtuse angle.
triangle sum thereom
The sum of the measures of the interior angles of a triangle is 180°.
exterior angle thereom
The measure of an exterior angle of a triangle is equal to the sum of the measures of the 2 nonadjacent interior angles.
corollary to the triangle sum thereom
The acute angles of a right triangle are complementary.
third angles thereom
If 2 angles of one triangle are congruent to 2 angles of another triangle, then the 3rd angles are also congruent.
reflexive property of congruent triangles
Every triangle is congruent to itself.
symmetric property of congruent triangles
If ∆ABC ≅ ∆DEF, then ∆DEF ≅ ∆ABC.
transitive property of congruent triangles
If ∆ABC ≅ ∆DEF and ∆DEF ≅ ∆JKL, then ∆ABC ≅ ∆JKL.
base angles
If 2 sides of a triangle are congruent, then the angles opposite them are congruent.
converse of base angles thereom
If 2 angles of a triangle are congruent, then the sides opposite them are congruent.
HL congruence thereom
If the hypotenuse and leg of a right triangle are congruent to the hypotenuse and a leg of a 2nd right triangle, then the 2 triangles are congruent.
perpendicular bisector thereom
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
converse of perpendicular bisector thereom
If a point is equidistant from the endpoints of a segment, then it is on the perpendicular bisector of the segment.
angle bisector thereom
If a point is on the bisector of an angle, then it is equidistant from the 2 sides of the angle.
converse of angle bisector thereom
If a point is in the interior of an angle and is equidistant from the sides of the angle, then it lies on the angle's bisector.
concurrent lines
When 3 or more lines intersect at the same point.
point of concurrency
Where concurrent lines intersect.
cirumcenter
Point of concurrency of the perpendicular bisectors.
concurrency of perpendicular bisectors of a triangle thereom
The perpendicular bisectors of a triangle intersect at a point that is equidistant from the vertices of the triangle.
incenter
Point of concurrency of the angle bisectors. Always lies inside the triangle.
concurrency of angle bisectors of a triangle thereom
The angle bisectors of a triangle intersect at a point that is equidistant from the sides of the triangle.
midsegment thereom
The segment connecting the midpoints of 2 sides of a triangle is parallel to the 3rd side and half as long.
exterior angle inequality thereom
The measure of an exterior angle of a triangle is greater than the measure either of the 2 nonadjacent interior angles.
triangle inequality thereom
The sum of the lengths of any 2 sides of a triangle is greater than the length of the 3rd side.
equilateral
All sides congruent.
equiangular
all angles congruent.
regular
Both equilateral and equiangular.
interior angles of a quadrilateral thereom
The sum of the measures of a quadrilateral's interior angles is 360°.
rhombus
Quadrilateral with 4 congruent sides.
rectangle
Quadrilateral with 4 right angles.
square
Quadrilateral with 4 congruent sides and 4 right angles.
rhombus corollary
It's a rhombus if and only if it has 4 congruent sides.
rectangle corollary
It's a rectangle if and only if it has 4 right angles.
square corollary
It's a square if and only if it is a rhombus and a rectangle.
trapezoid
Quadrilateral with 1 pair of parallel sides.
isoceles trapezoid
Quadrilateral with 1 pair of parallel sides and congruent legs.
midsegment thereom for trapezoids
A trapezoid's midsegment is parallel to each base and its length is half the sum of the lengths of the bases.
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