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Study sets matching "geometry chapter 12 theorems"

10 terms
Geometry Theorems : Chapter 12
Surface Area of a Triangular Prism
Surface Area of a Cylinder
Surface Area of a Pyramid
Surface Area of a Right Cone
SA=2B+Ph
SA=2B+Ch
SA=B+1/2Pl
SA=B+1/2Cl
Surface Area of a Triangular Prism
SA=2B+Ph
Surface Area of a Cylinder
SA=2B+Ch
15 terms
Geometry Chapter 12 Theorems
If a line is tangent to a circle
If 2 segments are tengent to a circle…
Congruent central angles =
Congruent chords=
It is perpendicular to the radius drawn to the point of tange…
The segments are congruent
Congruent chords
Congruent arcs
If a line is tangent to a circle
It is perpendicular to the radius drawn to the point of tange…
If 2 segments are tengent to a circle…
The segments are congruent
37 terms
Geometry Chapter 12 Theorems
Inside
Outside
Chord
Secant
The interior of a circle is the set of all points ________ th…
The exterior of a circle is the set of all points ________ th…
A ________ is a segment whose end points lie on a circle
A ________ is a line that intersects a circle at two points
Inside
The interior of a circle is the set of all points ________ th…
Outside
The exterior of a circle is the set of all points ________ th…
11 terms
Chapter 12 Geometry Theorems
Circle Tangency Thm
Converse of the Circle Tangency Thm
Snow Cone Theorem
Central Angle Chord Arc Theorem
If a line is tangent to a circle, then the line is perpendicu…
If a line is in a plane of a circle is perpendicular to a rad…
The two segments tangent to a circle from a point outside the…
Within a circle/in congruent circles:... 1) Congruent cent ang h…
Circle Tangency Thm
If a line is tangent to a circle, then the line is perpendicu…
Converse of the Circle Tangency Thm
If a line is in a plane of a circle is perpendicular to a rad…
14 terms
Geometry Chapter 12 Theorems
LA of prism
TA of prism
V of prism
La of cylinder
sum of faces that are not base
LA + 2 bases
BH
2 pi r h
LA of prism
sum of faces that are not base
TA of prism
LA + 2 bases
20 terms
Geometry Chapter 12 Theorems
If a line is tangent to a circle, then…
If two tangent segments to a circle sh…
Within a circle, congruent angles have…
Within a circle, congruent central ang…
Then the line is perpendicular to the radius at the point of…
Then the two segments are congruent.
Have congruent arcs. (HO)
Have congruent chords. (HO)
If a line is tangent to a circle, then…
Then the line is perpendicular to the radius at the point of…
If two tangent segments to a circle sh…
Then the two segments are congruent.
13 terms
Geometry chapter 12 theorems
Eulers theorem
Surface area of a right prism
Surface area of a right cylinder
Surface area of a regular pyramid
The number of faces, verticies, and edges of a polyhedron are…
The surface area of a right prism is the sum of the base area…
The surface area of a right cylinder is the sum of the base a…
The surface area of a regular pyramid is the sum of the base…
Eulers theorem
The number of faces, verticies, and edges of a polyhedron are…
Surface area of a right prism
The surface area of a right prism is the sum of the base area…
Geometry Chapter 12 Postulates and Theorems
Total area of a prism =
Lateral area of a right prism =
Volume of a right prism =
Lateral area of a cylinder =
lateral area + 2 times the area of a base (T.A. = L.A. + 2B).
the perimeter of a base times the height of the prism (L.A. =…
the area of a base times the height of the prism (V = B*h).
the circumference of a base times the height of the cylinder…
Total area of a prism =
lateral area + 2 times the area of a base (T.A. = L.A. + 2B).
Lateral area of a right prism =
the perimeter of a base times the height of the prism (L.A. =…
15 terms
Geometry Chapter 12 Formulas and Theorems
F+V=E+2
(1/2)aP
aP+Ph
2πr²+2πrh
Euler's Theorem
Area of Regular Polygon
Surface Area of Right Prism
Surface Area of Right Cylinder
F+V=E+2
Euler's Theorem
(1/2)aP
Area of Regular Polygon
15 terms
Geometry Chapter 12 Formulas and Theorems
F+V=E+2
(1/2)aP
aP+Ph
2πr²+2πrh
Euler's Theorem
Area of Regular Polygon
Surface Area of Right Prism
Surface Area of Right Cylinder
F+V=E+2
Euler's Theorem
(1/2)aP
Area of Regular Polygon
46 terms
Geometry Chapter 12 Vocab & Theorems
Arc
Arc length
Central Angle of a Circle
Chord
unbroken part of the circle consisting of 2 points on the cir…
The distance along an arc measured in linear units.
An angle whose vertex is the center of a circle.
A segment whose endpoints lie on a circle.
Arc
unbroken part of the circle consisting of 2 points on the cir…
Arc length
The distance along an arc measured in linear units.
13 terms
Geometry Chapter 12 Formulas and Theorems
B+LA
2πr²+2πrh
B+(1/2)bh
πr²+πrL
Surface Area of Right Prism
Surface Area of Right Cylinder
Surface Area of Regular Pyramid
Surface Area of Right Cone
B+LA
Surface Area of Right Prism
2πr²+2πrh
Surface Area of Right Cylinder
Geometry Chapter 12 theorems and definitions
Euler's Theorem
Cross section
Lateral Faces
Lateral Edges
F+V=E+2
the intersection of a solid and a plane
parallelograms formed by connecting the corresponding vertice…
segments connecting cooresponding vertices of the bases of a…
Euler's Theorem
F+V=E+2
Cross section
the intersection of a solid and a plane
16 terms
Adv. Geometry - Chapter 12 Theorems
If a line is tangent to a circle, then…
If a line in a plane is perpendicular…
If two segments tangent to a circle fo…
In a circle, or congruent circles, if…
the line is perpendicular to the radius drawn to the point of…
the line is tangent to the circle
then the segments are congruent
you have congruent chords
If a line is tangent to a circle, then…
the line is perpendicular to the radius drawn to the point of…
If a line in a plane is perpendicular…
the line is tangent to the circle
27 terms
Chapter 12 geometry vocab and theorems
Chord
Tangent
Secant
Point of tangency
A segment whose endpoints lie on a cirlce
A line in the same plane as a circle that intersects it at ex…
A line that intersects a circle at two points
Line which touches a circle or ellipse at just one point, alw…
Chord
A segment whose endpoints lie on a cirlce
Tangent
A line in the same plane as a circle that intersects it at ex…
19 terms
Chapter 12 Geometry Honors Theorems
Chord
Secant
Tangent
Point of tangency
A segment whose endpoints lie on a circle
A line that intersects a circle at two points
A line in the same plane as a circle but only intersects the…
The point where the tangent and a circle intersect
Chord
A segment whose endpoints lie on a circle
Secant
A line that intersects a circle at two points
18 terms
All Chapter 12 Geometry Theorems
Formulas of a square base prism for P,…
Formulas of a trapezoidal prism for P,…
Formulas of a cylinder for C, B, LA, S…
Formulas of a square base pyramid for…
P- Add sides ... B- length by width... LA- Perimeter of base (P) ti…
P- Add the sides ... B- 1/2 height of the trapezoid (base 1+ bas…
C- 2r π... B- π r²... LA- Circumfrence times height ... SA- Lateral Ar…
P- number of sides times the side length... B- Side length²... LA-…
Formulas of a square base prism for P,…
P- Add sides ... B- length by width... LA- Perimeter of base (P) ti…
Formulas of a trapezoidal prism for P,…
P- Add the sides ... B- 1/2 height of the trapezoid (base 1+ bas…
43 terms
Geometry Chapter 12 Vocabulary and theorems
Interior of a circle ... 12-1
Exterior of a circle ... 12-1
Chord ... 12-1
Secant... 12-1
the set of all points inside the circle
is the set of all points outside the circle
a segment whose endpoints lie on a circle
a line that intersects a circle at two points
Interior of a circle ... 12-1
the set of all points inside the circle
Exterior of a circle ... 12-1
is the set of all points outside the circle
13 terms
Geometry Quiz Chapter 12.3 Theorems and Terms
The area of a sector is a...
To find the area of a sector whose cen…
Sector of a circle
Sector of a circle picture:
Fraction of the circle containing the sector.
A region bounded by two radii of the circle and their interce…
The area of a sector is a...
Fraction of the circle containing the sector.
To find the area of a sector whose cen…
12 terms
Geometry Quiz Chapter 12.4 Theorems and Terms
Inscribed angle
Intercepted arc
A chord or arc /subtends/ an angle if...
The measure of an inscribed angle is _…
An angle whose vertex is on a circle and whose sides contain…
Consists of endpoints that lie on the sides of an inscribed a…
Its endpoints lie on the sides of the angle.
Half
Inscribed angle
An angle whose vertex is on a circle and whose sides contain…
Intercepted arc
Consists of endpoints that lie on the sides of an inscribed a…
24 terms
Geometry Quiz Chapter 12.2 Theorems and Terms
Central angle
Arc
Minor arc definition
Minor arc measure
An angle whose vertex is the center of a circle.
An unbroken part of a circle consisting of two points called…
An arc whose points are on or in the interior of a central an…
The measure of a minor arc is equal to the measure of its cen…
Central angle
An angle whose vertex is the center of a circle.
Arc
An unbroken part of a circle consisting of two points called…
12 terms
Geometry Quiz Chapter 12.6 Theorems and Terms
The following theorem describes the re…
Chord-Chord Product Theorem:... If two ch…
Applying the chord-chord product theor…
Secant segment
...
Then the products of the segments of the chords are equal.
A segment of a secant with at least one endpoint on the circle.
The following theorem describes the re…
...
Chord-Chord Product Theorem:... If two ch…
Then the products of the segments of the chords are equal.
14 terms
Geometry Quiz Chapter 12.5 Theorems and Terms
If a tangent and a secant (or chord) i…
Using tangent-secant and tangent-chord…
If two secants or chords intersect in…
Finding angle measures inside a circle…
Then the measure of the angle formed is half the measure of i…
The measure of each angle formed is half the sum of the measu…
If a tangent and a secant (or chord) i…
Then the measure of the angle formed is half the measure of i…
Using tangent-secant and tangent-chord…
10 terms
Geometry Chapter 12 Vocabulary and Theorem
Lateral faces
Base edges
Altitude
Height
faces that are not bases
where a lateral edge intersects a base
a segment from one base to another that is perpendicular to b…
the length of the altitude
Lateral faces
faces that are not bases
Base edges
where a lateral edge intersects a base
14 terms
Geometry Chapter 12 Theorems, Definitions, and Postulates
Similar
Proportionality
Theorem 12-1
Geometric mean
same shapes, not necessarily same size
given a, b, c and p, q, r, of positive real #'s, if a/p = b/q…
Similarity is an equivalence relation
if a, b, c, are positive #'s and a/b= b/c, then b is the geom…
Similar
same shapes, not necessarily same size
Proportionality
given a, b, c and p, q, r, of positive real #'s, if a/p = b/q…
18 terms
Geometry Chapter 12: Postulates, Theorems, and Corollaries
Thm. 12-1-1
Thm. 12-1-2
Thm. 12-1-3
Arc Addition Postulate
If a line is tangent to a circle, then it is perpendicular to…
If a line is perpendicular to the radius of a circle at a poi…
If segments are tangent to a circle from the same external po…
The measure of an arc formed by 2 adjacent arcs is the sum of…
Thm. 12-1-1
If a line is tangent to a circle, then it is perpendicular to…
Thm. 12-1-2
If a line is perpendicular to the radius of a circle at a poi…
12 terms
Geometry Quiz Chapter 12.4 Theorems and Terms
Inscribed angle
Intercepted arc
A chord or arc /subtends/ an angle if...
The measure of an inscribed angle is _…
An angle whose vertex is on a circle and whose sides contain…
Consists of endpoints that lie on the sides of an inscribed a…
Its endpoints lie on the sides of the angle.
Half
Inscribed angle
An angle whose vertex is on a circle and whose sides contain…
Intercepted arc
Consists of endpoints that lie on the sides of an inscribed a…
12 terms
Geometry Quiz Chapter 12.6 Theorems and Terms
The following theorem describes the re…
Chord-Chord Product Theorem:... If two ch…
Applying the chord-chord product theor…
Secant segment
...
Then the products of the segments of the chords are equal.
A segment of a secant with at least one endpoint on the circle.
The following theorem describes the re…
...
Chord-Chord Product Theorem:... If two ch…
Then the products of the segments of the chords are equal.
14 terms
Geometry Quiz Chapter 12.5 Theorems and Terms
If a tangent and a secant (or chord) i…
Using tangent-secant and tangent-chord…
If two secants or chords intersect in…
Finding angle measures inside a circle…
Then the measure of the angle formed is half the measure of i…
The measure of each angle formed is half the sum of the measu…
If a tangent and a secant (or chord) i…
Then the measure of the angle formed is half the measure of i…
Using tangent-secant and tangent-chord…
13 terms
Geometry Quiz Chapter 12.3 Theorems and Terms
The area of a sector is a...
To find the area of a sector whose cen…
Sector of a circle
Sector of a circle picture:
Fraction of the circle containing the sector.
A region bounded by two radii of the circle and their interce…
The area of a sector is a...
Fraction of the circle containing the sector.
To find the area of a sector whose cen…
24 terms
Geometry Quiz Chapter 12.2 Theorems and Terms
Central angle
Arc
Minor arc definition
Minor arc measure
An angle whose vertex is the center of a circle.
An unbroken part of a circle consisting of two points called…
An arc whose points are on or in the interior of a central an…
The measure of a minor arc is equal to the measure of its cen…
Central angle
An angle whose vertex is the center of a circle.
Arc
An unbroken part of a circle consisting of two points called…
15 terms
Geometry theorems chapter 12 (surface area and volume)
LA of a prism
TA of a prism
LA of pyramid
TA of pyramid
The sum of the areas of all the LATERAL faces
LA plus the areas of the two bases
Just add up all the areas of the lateral faces
LA plus the area of the ONE base
LA of a prism
The sum of the areas of all the LATERAL faces
TA of a prism
LA plus the areas of the two bases
13 terms
Geometry Theorems Chapter 2
Vertical Angles Theorem
Congruent Supplements Theorem
Congruent Complements Theorem
Right Angle Congruence Theorem
Vertical angles are conguent.
If two angles are supplements of the same angle or a congruen…
If two angles are complements of the same angle, then the two…
All right angles are congruent
Vertical Angles Theorem
Vertical angles are conguent.
Congruent Supplements Theorem
If two angles are supplements of the same angle or a congruen…
43 terms
Chapter 12 Vocab & Theorems
Interior of a Circle
Exterior of a Circle
Chord
Secant
Set of small points inside the circle.
Set of points outside the circle.
A segment who's points lie on the circle
A line that intersects a circle at 2 points.
Interior of a Circle
Set of small points inside the circle.
Exterior of a Circle
Set of points outside the circle.
13 terms
Geometry Chapter 7 Theorems
Theorem 7.1 Perimeters of Similar Poly…
Postulate 7.1 Angle-Angle (AA) Similar…
Theorem 7.2 Side-Side-Side (SSS) Simil…
Theorem 7.3 Side-Angle-Side (SAS) Simi…
If two polygons are similar, then their perimeters are propor…
If two angles of one triangle are congruent to two angles of…
IF the corresponding side lengths of two triangles are propor…
If the lengths of two sides of one triangle are proportional…
Theorem 7.1 Perimeters of Similar Poly…
If two polygons are similar, then their perimeters are propor…
Postulate 7.1 Angle-Angle (AA) Similar…
If two angles of one triangle are congruent to two angles of…
17 terms
Geometry Quiz Chapters 12.1 Theorems
Interior of a circle
Exterior of a circle
Chord
Secant
The set of all points inside the circle.
The set of all points outside the circle.
A segment whose endpoints lie on a circle.
A line that intersects a circle at two points.
Interior of a circle
The set of all points inside the circle.
Exterior of a circle
The set of all points outside the circle.
15 terms
Geometry Theorems Chapters 7-12
Angle-Angle (AA) Similarity Postulate
Side-Side-Side (SSS) Similarity Theorem
Side-Angle-Side (SAS) Similarity Theorem
Triangle Proportionality Theorem
If two angles of one triangle are congruent to two angles of…
If the three sides of one triangle are proportional to the th…
If two sides of one triangle are proportional to two sides of…
If a line parallel to a side of a triangle intersects the oth…
Angle-Angle (AA) Similarity Postulate
If two angles of one triangle are congruent to two angles of…
Side-Side-Side (SSS) Similarity Theorem
If the three sides of one triangle are proportional to the th…
5 terms
Chapter 13 Geometry Theorems
The Distance Formula
General Equation of a Circle
Two non vertical lines are parallel if…
Two non vertical lines are perpendicul…
The distance d between points (x1, y1) and (x2, y2) is given…
An equation of the circle with center (a,b) and radius r is (…
Their slopes are equal
The product of their slopes is -1
The Distance Formula
The distance d between points (x1, y1) and (x2, y2) is given…
General Equation of a Circle
An equation of the circle with center (a,b) and radius r is (…
44 terms
Chapter 12 Vocab & Theorems
Interior of a Circle
Exterior of a Circle
Chord
Secant
Set of small points inside the circle.
Set of points outside the circle.
A segment who's points lie on the circle
A line that intersects a circle at 2 points.
Interior of a Circle
Set of small points inside the circle.
Exterior of a Circle
Set of points outside the circle.
18 terms
Geometry Chapter 6 Theorems
____ sides of a parallelogram are cong…
opposite angles of a parallelogram are…
diagonals of a parallelogram
If three or more parallel lines cut of…
opposite
congruent
bisect each other
they cut off congruent segments on every transversal
____ sides of a parallelogram are cong…
opposite
opposite angles of a parallelogram are…
congruent
19 terms
Geometry theorems Chapter 11 & 12
Area of rectangle in parallelogram
Area of a square
Area of a triangle
Area of a trapezoid
A=bh
A= ss
A= 1/2 bh
A= h( b1 + b2)
Area of rectangle in parallelogram
A=bh
Area of a square
A= ss
25 terms
Geometry Chapters 11 + 12 Theorems
surface area of prism
surface area of pyramid
surface area of cylinder
surface area of cone
LA = ph... TA = ph + 2B
LA = ½pl... TA = ½pl + B
LA = ph / Ch / 2πrh... TA = Ch + 2πr²
LA = ½pl / ½Cl / ½(2πr)l... TA = ½pl + 1B / ½Cl +πr²
surface area of prism
LA = ph... TA = ph + 2B
surface area of pyramid
LA = ½pl... TA = ½pl + B
26 terms
Chapter 12 Theorems and Terms
Tangent to a circle
If a line is tangent to a circle,
If a line in the plane of a circle is…
If two tangent segments to a circle sh…
Line that intersects a circle exactly one point
the line is perpendicular to the radius at the point of tange…
then the line is tangent to the circle
then the two segments are congruent
Tangent to a circle
Line that intersects a circle exactly one point
If a line is tangent to a circle,
the line is perpendicular to the radius at the point of tange…
15 terms
Geometry Postulates and Theorems Chapter 3
Postulate 3-1 Same-side Interior Angle…
Theorem 3-1 Alternate Interior Angles…
Theorem 3-2 Corresponding Angles Theor…
Theorem 3-3 Alternate Exterior Angles…
supplementary... m∠1 + m∠2 = 180
congruent
corresponding
exterior
Postulate 3-1 Same-side Interior Angle…
supplementary... m∠1 + m∠2 = 180
Theorem 3-1 Alternate Interior Angles…
congruent
11 terms
Chapter 12 Theorems
T12-1
T12-2
T12-3
T12-4
the lateral area of a right prism equals the perimeter of a b…
the volume of a right prism equals the area of a base times t…
the lateral area of a regular pyramid equals half the perimet…
the volume of a pyramid equals one third the area of the base…
T12-1
the lateral area of a right prism equals the perimeter of a b…
T12-2
the volume of a right prism equals the area of a base times t…
6 terms
Geometry Chapter 3 - Theorems and Postulates
Parallel Postulate
Perpendicular Postulate
Corresponding Angles Theorem
Alternate Interior Angles Theorem
If there is a line and a point not on the line, then there is…
If there is a line and a point not on the line, then there is…
If two parallel lines are cut by a transversal, then the pair…
If two parallel lines are cut by a transversal, then the pair…
Parallel Postulate
If there is a line and a point not on the line, then there is…
Perpendicular Postulate
If there is a line and a point not on the line, then there is…
14 terms
Geometry Chapter 5 Theorems & Postulates
Midsegment Theorem
Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector…
Circumcenter Theorem
The segment connecting the midpoints of two sides of a triang…
In a plane, if a point is on the perpendicular bisector of a…
In a plane, if a point is equidistant from the endpoints of a…
The perpendicular bisectors of a triangle intersect at a poin…
Midsegment Theorem
The segment connecting the midpoints of two sides of a triang…
Perpendicular Bisector Theorem
In a plane, if a point is on the perpendicular bisector of a…
11 terms
Chapter 12 Theorems
Theorem 12-1
Theorem 12-2
Theorem 12-3
Theorem 12-4
The lateral area of a right prism equals the perimeter of a b…
The volume of a right prism equals the area of a base times t…
The lateral area of a regular pyramid equals half the perimet…
The volume of a pyramid equals one third the area of the base…
Theorem 12-1
The lateral area of a right prism equals the perimeter of a b…
Theorem 12-2
The volume of a right prism equals the area of a base times t…
9 terms
Chapter 5 Geometry Theorems
midpoint
Triangle Midsegment Theorem
Perpendicular Bisector Theorem
Converse of the Perpendicular Bisector…
a segment connecting the midpoint of two sides of a triangle
If a segment joins the midpoints of two sides of a... triangle,…
If a point is on the perpendicular bisector of a... segment, the…
If a point is equidistant from the... endpoints of a segment, th…
midpoint
a segment connecting the midpoint of two sides of a triangle
Triangle Midsegment Theorem
If a segment joins the midpoints of two sides of a... triangle,…
42 terms
Geometry Chapter 2 terms, postulates and theorems
Conclusion
Conditional Statement
Conjecture
Contrapositive
In a conditional statement (if-then statement), the statement…
A statement written in an if then form... A statement of the for…
An educated guess based on known information... pg 78
The statement formed by negating both the hypothesis(educated…
Conclusion
In a conditional statement (if-then statement), the statement…
Conditional Statement
A statement written in an if then form... A statement of the for…
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