#### Study sets matching "geometry postulates chapter 8"

#### Study sets matching "geometry postulates chapter 8"

Cross Product Property of proportions

Reciprocal property of proportions

Switching Property of proportions

Add property of proportions

The product of the extremes equals the product of the means.…

If 2 ratios are equal then their reciprocals are also equal.…

If a/b=c/d, then a/c=b/d

If a/b=c/d, then a+b/b=c+d/d

Cross Product Property of proportions

The product of the extremes equals the product of the means.…

Reciprocal property of proportions

If 2 ratios are equal then their reciprocals are also equal.…

geometric mean

simplest form radicals

common Pythagorean triples (5)

if the altitude is drawn to the hypote…

if a, b, and x are positive numbers and a/x = x/b , then x is…

1. No perfect square factor other than 1 is under the radical…

1. 3 - 4- 5... 2. 5 - 12 - 13 ... 3. 8 - 15 - 17... 4. 7 - 24 - 25... 5.…

then the 2 triangles formed are similar to the original trian…

geometric mean

if a, b, and x are positive numbers and a/x = x/b , then x is…

simplest form radicals

1. No perfect square factor other than 1 is under the radical…

Theorem 59

Theorem 60

Theorem 61

Postulate

In a proportion, the product of the means is equal to the pro…

If the product of a pair of nonzero numbers is equal to the p…

The ratio of the perimeters of two similar polygons equals th…

If there exists a correspondence between the vertices of two…

Theorem 59

In a proportion, the product of the means is equal to the pro…

Theorem 60

If the product of a pair of nonzero numbers is equal to the p…

*

**theorem 8-1****

**corollary 1 to theorem 8-1****

**corollary 2 to theorem 8-1****

**theorem 8-2 : pythagorean theorem***if the altitude is drawn to the hypotenuse of a right triangl…

when the altitude is drawn to the hypotenuse of a right trian…

when the altitude is drawn to the hypotenuse of a right trian…

in a right triangle , the square of the hypotenuse is equal t…

*

**theorem 8-1***if the altitude is drawn to the hypotenuse of a right triangl…

*

**corollary 1 to theorem 8-1***when the altitude is drawn to the hypotenuse of a right trian…

Transformation

Isometry

Reflection

Translation

A(n) __________________ is a one-to-one correspondence betwee…

A(n) _____________________ is a transformation that preserves…

The _______________________ of P through line L is P itself i…

A(n) __________________________ is the composite of two succe…

Transformation

A(n) __________________ is a one-to-one correspondence betwee…

Isometry

A(n) _____________________ is a transformation that preserves…

Diagonal

Polygon Interior Angles Theorem

Interior Angles of a quadrilateral

Polygon Exterior Angles Theorem

segment that joins two nonconsecutive vertices of a polygon

The sum of the measures of the interior angles of a convex n-…

The sum of the measures of the interior angles of a quadrilat…

the sum of the measures of the exterior angles of a convex po…

Diagonal

segment that joins two nonconsecutive vertices of a polygon

Polygon Interior Angles Theorem

The sum of the measures of the interior angles of a convex n-…

Interior Angle Theorem

Exterior Angle Theorem

Theorem 8.3

Theorem 8.4

If a convex polygon has n sides and S is the sum of the measu…

If a polygon is convex, then the sum of the measures of the e…

Opposite sides of parallelogram are congruent.

Opposite angles of a parallelogram are congruent.

Interior Angle Theorem

If a convex polygon has n sides and S is the sum of the measu…

Exterior Angle Theorem

If a polygon is convex, then the sum of the measures of the e…

means-extremes product theorem

similar polygons definition

perimeter theorem

3 methods of proving triangles congruent

product of means is equal to the product of extremes

1. corresponding angles are congruent... 2. corresponding sides…

the ratio of the perimeters of any 2 similar polygons equals…

1. AA similarity... 2. SSS similarity... 3. SAS similarity

means-extremes product theorem

product of means is equal to the product of extremes

similar polygons definition

1. corresponding angles are congruent... 2. corresponding sides…

Right Triangle Altitude Theorem

Pythagorean Theorem

Converse of the Pythagorean Theorem

Pythagorean Theorem Corollary

If the altitude is drawn to the hypotenuse of a right triangl…

In a right triangle, the square of the hypotenuse is equal to…

If the square of one side of a triangle is equal to the sum o…

If c²=a²+b², then m∠C=90°, and ∆ABC is right.... If c²<a²+b², th…

Right Triangle Altitude Theorem

If the altitude is drawn to the hypotenuse of a right triangl…

Pythagorean Theorem

In a right triangle, the square of the hypotenuse is equal to…

Postulate 1-1 Through any two points,…

Postulate 1-2 If two distinct lines in…

Postulate 1-3 If two distinct _______i…

Postulate 1-4 Through any ________poin…

line

point

planes

three noncollinear

Postulate 1-1 Through any two points,…

line

Postulate 1-2 If two distinct lines in…

point

Pythagorean Theorem

Pythagorean Theorem (alternate stateme…

Pythagorean Converse Theorem

Isosceles Right Triangle Theorem (a.k.…

In any right triangle with legs of lengths a and b and hypote…

In any right triangle, the sum of the areas of the squares on…

Suppose a triangle has sides of lengths a, b, and c. If a² +…

In any isosceles right triangle, if a leg has length x, then…

Pythagorean Theorem

In any right triangle with legs of lengths a and b and hypote…

Pythagorean Theorem (alternate stateme…

In any right triangle, the sum of the areas of the squares on…

Area postulate

Uniqueness Property

Congruence Property

Additive Property

Uniqueness, congruence, and additive properties and rectangle…

Given a unit region, every polygonal region has a unique area

Congruent figures have the same area

The area of the Union of two non-overlapping regions is the s…

Area postulate

Uniqueness, congruence, and additive properties and rectangle…

Uniqueness Property

Given a unit region, every polygonal region has a unique area

Thm. 8-1-1

Geometric Means Corollary Pt.1

Geometric Means Corollary Pt.2

The Law of Sines

The altitude to the hypotenuse of a right triangle forms 2 tr…

The length of the altitude to the hypotenuse of a right trian…

The length of a leg of a right triangle is the geometric mean…

For any triangle ABC with side lengths a, b, and c:

Thm. 8-1-1

The altitude to the hypotenuse of a right triangle forms 2 tr…

Geometric Means Corollary Pt.1

The length of the altitude to the hypotenuse of a right trian…

Theorum 8.1: Polygon interior angles t…

Corollary to the Theorem 8.1: interior…

Theorem 8.2: Polygon Exterior Angles T…

Theorem 8.3

The sum of the measures of interior angles of a n-gon is (n-2…

The sum of the measures of interior angles of a quadrilateral…

The sum of the measures of exterior angles of a polygon is 360

If a quadrilateral is a parallelogram, then it's opposite sid…

Theorum 8.1: Polygon interior angles t…

The sum of the measures of interior angles of a n-gon is (n-2…

Corollary to the Theorem 8.1: interior…

The sum of the measures of interior angles of a quadrilateral…

The product of the extremes equals the…

If two ratios are equal, then their re…

If A/B = C/D , then A/C = B/D .

Two polygons are________if their corre…

Cross Product Property

Reciprocal Property

Interchange Means Property

Similar

The product of the extremes equals the…

Cross Product Property

If two ratios are equal, then their re…

Reciprocal Property

Perimeters of Similar Polygons

Areas of Similar Polygons

Angle-Angle Similarity Theorem

Side-Side-Side Similarity Theorem (SSS)

If 2 polygons are similar, then the ratio of their perimeters…

If two polygons are similar, then the ratios of their areas i…

If 2 angles of one triangle are congruent to 2 angles of anot…

If the corresponding sides lengths of two triangles are propo…

Perimeters of Similar Polygons

If 2 polygons are similar, then the ratio of their perimeters…

Areas of Similar Polygons

If two polygons are similar, then the ratios of their areas i…

Theorem 8-1: The Pythagorean Theorem

Theorem 8-2: Converse of the Pythagore…

Theorem 8-3

Theorem 8-4

If a triangle is a right triangle, then a² + b² = c².

If a² + b² = c², then the triangle is a right triangle.

If c² > a² + b², then the triangle is obtuse.

If c² < a² + b², then the triangle is acute.

Theorem 8-1: The Pythagorean Theorem

If a triangle is a right triangle, then a² + b² = c².

Theorem 8-2: Converse of the Pythagore…

If a² + b² = c², then the triangle is a right triangle.

Pythagorean Theorem

Pythagorean Theorem (alternate stateme…

Pythagorean Converse Theorem

Isosceles Right Triangle Theorem (a.k.…

In any right triangle with legs of lengths a and b and hypote…

In any right triangle, the sum of the areas of the squares on…

Suppose a triangle has sides of lengths a, b, and c. If a² +…

In any isosceles right triangle, if a leg has length x, then…

Pythagorean Theorem

In any right triangle with legs of lengths a and b and hypote…

Pythagorean Theorem (alternate stateme…

In any right triangle, the sum of the areas of the squares on…

Pythagorean Theorem

Pythagorean Theorem (alternate stateme…

Pythagorean Converse Theorem

Isosceles Right Triangle Theorem (a.k.…

In any right triangle with legs of lengths a and b and hypote…

In any right triangle, the sum of the areas of the squares on…

Suppose a triangle has sides of lengths a, b, and c. If a² +…

In any isosceles right triangle, if a leg has length x, then…

Pythagorean Theorem

In any right triangle with legs of lengths a and b and hypote…

Pythagorean Theorem (alternate stateme…

In any right triangle, the sum of the areas of the squares on…

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…

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…

Postulate 1.1

Postulate 1.2

Postulate 1.3

Postulate 1.4

Through any two points, there is exactly one line

If two lines intersect, they intersect in exactly one point

If two planes intersect, they intersect at exactly one line

Through any three noncollinear points, there is exactly one p…

Postulate 1.1

Through any two points, there is exactly one line

Postulate 1.2

If two lines intersect, they intersect in exactly one point

Theorem 8-1-1

Geometric Means (Corollary 8-1-2) (Ign…

Geometric Means (Corollary 8-1-3) (Ign…

Trigonometric Ratios (Sine)

The altitude to the hypotenuse of a right triangle forms two…

The length of the altitude to the hypotenuse of a right trian…

The length of a leg of a right triangle is the geometric mean…

The Sine of an angle is the ratio of the length of the leg op…

Theorem 8-1-1

The altitude to the hypotenuse of a right triangle forms two…

Geometric Means (Corollary 8-1-2) (Ign…

The length of the altitude to the hypotenuse of a right trian…

Theorem 8-1

Corollary 1 to Theorem 8-1

Corollary 2 to Theorem 8-1

Theorem 8-2 Pythagorean Theorem

If the altitude is drawn to the hypotenuse of a right triangl…

When the altitude is drawn to the hypotenuse of a right trian…

When the altitude is drawn to the hypotenuse of a right trian…

In a right triangle, the square of the hypotenuse is equal to…

Theorem 8-1

If the altitude is drawn to the hypotenuse of a right triangl…

Corollary 1 to Theorem 8-1

When the altitude is drawn to the hypotenuse of a right trian…

radius (regular polygon)

polygon

remote interior angles

linear scale factor

a line segment that connects the center of a regular polygon…

a two-dimensional closed figure of three or more line segment…

when a triangle has an exterior angles, these angles are the…

the ratio of similarity. the ratio of any pair of correspondi…

radius (regular polygon)

a line segment that connects the center of a regular polygon…

polygon

a two-dimensional closed figure of three or more line segment…

Parallel lines

Skew lines

Alternate interior angles

Same side interior angles

Coplanar lines that do not intersect

noncoplanar and non parallel lines

nonadjacent interior angles that lie on opposite sides of the…

Interior angles that lie on the same side of the transversal

Parallel lines

Coplanar lines that do not intersect

Skew lines

noncoplanar and non parallel lines

Postulate 1-1

Postulate 1-2

Postulate 1-3

Linear Pair Postulate

Through any 2 points there is a line

If 2 lines intersect, they intersect in exactly 1 point

If 2 planes intersect, they intersect in exactly 1 line

If two angles form a linear pair, then they are supplementry

Postulate 1-1

Through any 2 points there is a line

Postulate 1-2

If 2 lines intersect, they intersect in exactly 1 point

Postulate 1-1

Postulate 1-2

Postulate 1-3

Postulate 1-4

There is exactly one line through any two points.

Two distinct intersecting lines intersect at exactly one line.

Two distinct intersecting planes intersect at exactly one line.

There is one plane through any three noncollinear points.

Postulate 1-1

There is exactly one line through any two points.

Postulate 1-2

Two distinct intersecting lines intersect at exactly one line.

Pythagorean Theorem

Converse of The Pythagorean ... Theorem

Theorem 8-3

Theorem 8-4

If a triangle is a right triangle then the sum of the squares…

Converse of Pythagorean Theorem If the sum of the squares of…

If the square of the length of the longest side of a triangle…

If the square of the length of the longest side of a triangle…

Pythagorean Theorem

If a triangle is a right triangle then the sum of the squares…

Converse of The Pythagorean ... Theorem

Converse of Pythagorean Theorem If the sum of the squares of…

Definition of Perimeter

Area Postulate

Right Triangle Angle Formula

Triangle Area Formula

The perimeter of a polygon is the sum of the lengths of its s…

a. Uniqueness Property... Given a unit region, every polygonal…

The area of a right triangle is half the product of the of th…

The area of a triangle is half the product of the length of a…

Definition of Perimeter

The perimeter of a polygon is the sum of the lengths of its s…

Area Postulate

a. Uniqueness Property... Given a unit region, every polygonal…

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

Perimeters of Similar Polygons

Areas of Similar Polygons

Angle-Angle (AA) Similarity Theorem

Side-Side-Side (SSS) Similarity Theorem

If two polygons are similar, then the ratio of their perimete…

If two polygons are similar, then the ratio of their areas is…

If two angles of one triangle are... congruent to two angles of…

If the corresponding side lengths of... two triangles are propor…

Perimeters of Similar Polygons

If two polygons are similar, then the ratio of their perimete…

Areas of Similar Polygons

If two polygons are similar, then the ratio of their areas is…

radius (regular polygon)

polygon

remote interior angles

linear scale factor

a line segment that connects the center of a regular polygon…

a two-dimensional closed figure of three or more line segment…

when a triangle has an exterior angles, these angles are the…

the ratio of similarity. the ratio of any pair of correspondi…

radius (regular polygon)

a line segment that connects the center of a regular polygon…

polygon

a two-dimensional closed figure of three or more line segment…

Corresponding Angles Postulate - If tw…

Alternate Interior Angles Theorem - If…

Alternate Exterior Angles Theorem - If…

Same-Side Interior Angles Theorem - If…

then the pairs of corresponding angles are congruent.

then the alternate interior angles are congruent.

then the alternate exterior angles are congruent.

then the pairs of same-side interior angles are supplementary.

Corresponding Angles Postulate - If tw…

then the pairs of corresponding angles are congruent.

Alternate Interior Angles Theorem - If…

then the alternate interior angles are congruent.

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

Expansion Postulate

Line Postulate

Plane Postulate

Flat Plane Postulate

A line contains at least two points. A plane contains at leas…

Any two points in space lie in exactly one line

Three distinct noncollinear points lie in exactly one plane

If two points lie in a plane, then the line containing these…

Expansion Postulate

A line contains at least two points. A plane contains at leas…

Line Postulate

Any two points in space lie in exactly one line

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…

Theorem 8.1 - Polygon Interior Angles…

Corollary to Theorem 8.1 - Interior An…

Theorem 8.2 - Polygon Exterior Angles…

Theorem 8.3

The sum of the measures of the interior angles of a convex n-…

The sum of the measures of the interior angles of a quadrilat…

The sum of the measures of the exterior angles of a convex po…

If a quadrilateral is a parallelogram, then its opposite side…

Theorem 8.1 - Polygon Interior Angles…

The sum of the measures of the interior angles of a convex n-…

Corollary to Theorem 8.1 - Interior An…

The sum of the measures of the interior angles of a quadrilat…

Theorem 8.1

Theorem 8.2

Theorem 8.3

Theorem 8.4

If the altitude is drawn to the hypotenuse of a right triangl…

The altitude drawn to the hypotenuse of a right triangle sepa…

The altitude drawn to the hypotenuse of a right triangle sepa…

Pythagorean Theorem... In a right triangle, the sum of the squar…

Theorem 8.1

If the altitude is drawn to the hypotenuse of a right triangl…

Theorem 8.2

The altitude drawn to the hypotenuse of a right triangle sepa…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line.

Through any three noncollinear points, there is exactly one p…

A line contains at least two points.

A plane contains at least three noncollinear points.

Postulate 2.1

Through any two points, there is exactly one line.

Postulate 2.2

Through any three noncollinear points, there is exactly one p…

point

line

plane

collinear

a location; has no length, no width, no thickness

extends in one dimension; has length but no width and no thic…

A flat surface that has length and width but no thickness

Points that lie on the same line.

point

a location; has no length, no width, no thickness

line

extends in one dimension; has length but no width and no thic…

they are congruent.... Right Angles Cong…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Supplem…

they are congruent.... Congruent Complem…

If two angles are right angles, then

If two angles are supplementary to the same angle, then

If two angles are supplementary to congruent angles, then

If two angles are complementary to the same angle, then

they are congruent.... Right Angles Cong…

If two angles are right angles, then

they are congruent.... Congruent Supplem…

If two angles are supplementary to the same angle, then

Theorem 8.1

Theorem 8.2

Theorem 8.3

Theorem 8.4

If the altitude is drawn to the hypotenuse of a right triangl…

The altitude drawn to the hypotenuse of a right triangle sepa…

The altitude drawn to the hypotenuse of a right triangle sepa…

Pythagorean Theorem... In a right triangle, the sum of the squar…

Theorem 8.1

If the altitude is drawn to the hypotenuse of a right triangl…

Theorem 8.2

The altitude drawn to the hypotenuse of a right triangle sepa…

Postulate 1-1 Through any two points,…

Postulate 1-2 If two distinct lines in…

Postulate 1-3 If two distinct _______i…

Postulate 1-4 Through any ________poin…

line

point

planes

three noncollinear

Postulate 1-1 Through any two points,…

line

Postulate 1-2 If two distinct lines in…

point

Parallel Postulate

Perpendicular Postulate

Corresponding Angles Postulate

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…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactly one line

Through any three non-collinear points, there is exactly one…

A line contains at least two points

A plane contains at least three non-collinear points

Postulate 2.1

Through any two points, there is exactly one line

Postulate 2.2

Through any three non-collinear points, there is exactly one…

Expansion Postulate

Line Postulate

Plan Postulate

Flat Plane Postulate

A line contains at least 2 points. A plane contains at least…

Any 2 points in space lie in exactly one line.

3 distinct noncollinear points lie in exactly one plane.

If 2 points lie in a plane, then the line containing these 2…

Expansion Postulate

A line contains at least 2 points. A plane contains at least…

Line Postulate

Any 2 points in space lie in exactly one line.

Theorem 8.1... If the altitude is drawn t…

Theorem 8.2... The altitude drawn to the…

Theorem 8.3... The altitude drawn to the…

Theorem 8.4... Pythagorean Theorem... In a r…

, then the two triangles formed are similar to the original t…

The length of this altitude is the geometric mean between the…

The length of a leg of this triangle is the geometric mean be…

equal to the square of the length of the hypotenuse.

Theorem 8.1... If the altitude is drawn t…

, then the two triangles formed are similar to the original t…

Theorem 8.2... The altitude drawn to the…

The length of this altitude is the geometric mean between the…