# Study sets matching "geometry postulates chapter 8"

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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. I…

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

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. I…

Reciprocal property of proportions

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

geometric mean

simplest form radicals

common Pythagorean triples (5)

if the altitude is drawn to the hypoten…

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. 9…

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

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…

Pythagorean Theorem

Converse of the Pythagorean Theorem

Theorem 8-3

Theorem 8-4

In a right triangle, the sun of the squares of the lengths of…

If the square of the length of one side of a triangle is equal…

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

If the square of the longest side of a triangle is less than t…

Pythagorean Theorem

In a right triangle, the sun of the squares of the lengths of…

Converse of the Pythagorean Theorem

If the square of the length of one side of a triangle is equal…

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Transformation

Isometry

Reflection

Translation

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

A(n) _____________________ is a transformation that preserves…

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

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

Transformation

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

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 squares…

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

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

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

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 a…

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

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 a…

Theorem 59

Theorem 60

Theorem 61

Postulate

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

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

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

If there exists a correspondence between the vertices of two t…

Theorem 59

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

Theorem 60

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

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 measur…

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

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 measur…

Exterior Angle Theorem

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

Pythagorean Theorem

Pythagorean Theorem (alternate statemen…

Pythagorean Converse Theorem

Isosceles Right Triangle Theorem (a.k.a…

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

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 + b…

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

Pythagorean Theorem

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

Pythagorean Theorem (alternate statemen…

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 su…

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 tri…

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

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 tri…

Geometric Means Corollary Pt.1

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

Theorum 8.1: Polygon interior angles th…

Corollary to the Theorem 8.1: interior…

Theorem 8.2: Polygon Exterior Angles Th…

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 side…

Theorum 8.1: Polygon interior angles th…

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…

Theorem 8-1: The Pythagorean Theorem

Theorem 8-2: Converse of the Pythagorea…

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 Pythagorea…

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

The product of the extremes equals the…

If two ratios are equal, then their rec…

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

Two polygons are________if their corres…

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 rec…

Reciprocal Property

Postulate 1-1 Through any two points, t…

Postulate 1-2 If two distinct lines int…

Postulate 1-3 If two distinct _______in…

Postulate 1-4 Through any ________point…

line

point

planes

three noncollinear

Postulate 1-1 Through any two points, t…

line

Postulate 1-2 If two distinct lines int…

point

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 form…

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 form…

angle of depression

angle of elevation

Cosine

Law of Cosine

The angle formed by a horizontal line and the line of sight to…

the angle formed by a horizontal line and the line of sight to…

The ratio of the adjacent side of an angle to the hypotenuse o…

a²=b²+c²-2bcCosA

angle of depression

The angle formed by a horizontal line and the line of sight to…

angle of elevation

the angle formed by a horizontal line and the line of sight to…

radius (regular polygon)

polygon

remote interior angles

linear scale factor

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

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

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

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

radius (regular polygon)

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

polygon

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

corresponding lengths in similar triang…

perimeters of similar polygons

areas of similar polygons

AA similarity theorem

if two polygons are similar, then the ratio of any two corresp…

if two polygons are similar, then the ratio of... their perimeter…

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

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

corresponding lengths in similar triang…

if two polygons are similar, then the ratio of any two corresp…

perimeters of similar polygons

if two polygons are similar, then the ratio of... their perimeter…

A right triangle where the length of th…

A right triangle where the length of th…

The angle formed by a horizontal line a…

The angle formed by a horizontal line a…

30-60-90 Triangle

45-45-90 Triangle

Angle of Depression

Angle of Elevation

A right triangle where the length of th…

30-60-90 Triangle

A right triangle where the length of th…

45-45-90 Triangle

Triangle Sum Theorem

Exterior Angle Theorem

Triangle Sum Theorem Corollary

Third Angles Theorem

The sum of the measures of the interior angles of a triangle i…

The measure of an exterior angle of a triangle is equal to the…

The acute angles of a right triangle are complementary

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

Triangle Sum Theorem

The sum of the measures of the interior angles of a triangle i…

Exterior Angle Theorem

The measure of an exterior angle of a triangle is equal to the…

A right triangle where the length of th…

A right triangle where the length of th…

The angle formed by a horizontal line a…

The angle formed by a horizontal line a…

30-60-90 Triangle

45-45-90 Triangle

Angle of Depression

Angle of Elevation

A right triangle where the length of th…

30-60-90 Triangle

A right triangle where the length of th…

45-45-90 Triangle

Pythagorean Theorem

Converse of the Pythagorean Theorem

A triangle is obtuse if

A triangle is acute if

a^2 + b^2 = c^2 in a right triangle

If a^2 + b^2 = c^2, then the triangle is a right triangle.

c^2 > a^2 + b^2

c^2 < a^2 + b^2

Pythagorean Theorem

a^2 + b^2 = c^2 in a right triangle

Converse of the Pythagorean Theorem

If a^2 + b^2 = c^2, then the triangle is a right triangle.

radius (regular polygon)

polygon

remote interior angles

linear scale factor

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

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

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

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

radius (regular polygon)

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

polygon

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