#### 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…

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 square…

if the sum of the squares of the lengths of two sides of a tr…

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 square…

converse of the pythagorean theorem

if the sum of the squares of the lengths of two sides of a tr…

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

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…

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…

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

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…