# 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…

hypotenuse

Geometric Means Corollary ... 8-1-2

Geometric Means Corollary... 8-1-3

The Law of Sines

The altitude to the _____________ of a right triangle forms tw…

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

The length of a leg of a right triangle is the length of the g…

For any (tri)ABC with the side lengths a, b, and c, sinA/a = s…

hypotenuse

The altitude to the _____________ of a right triangle forms tw…

Geometric Means Corollary ... 8-1-2

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

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…

consecutive vertices

diagnol

Polygon Interior Angles Theorem

Corollary to Polygon Interior Angles Th…

in a polygon, 2 vertices that are endpoints of the same side

in a polygon, a segment that joins 2 non consecutive vertices

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

the sum of the measures of the interior angles of a quadrilate…

consecutive vertices

in a polygon, 2 vertices that are endpoints of the same side

diagnol

in a polygon, a segment that joins 2 non consecutive vertices

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…

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…

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…

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 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…

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

Perimeters of Similar Polygons

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

Areas of Similar Polygons

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

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…

Theorem 8-1-1 (Altitude and Similarity)

Sine

Cosine

Tangent

If the altitude to the hypotenuse of a right triangle froms tw…

The ratio of the length of the leg opposite the angle to the l…

The ratio of the length of the leg adjacent to the angle to th…

The ratio of the length of the leg opposite the angle to the l…

Theorem 8-1-1 (Altitude and Similarity)

If the altitude to the hypotenuse of a right triangle froms tw…

Sine

The ratio of the length of the leg opposite the angle to the l…

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…

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

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…

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.

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…

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…

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…

Pythagorean Theorem

Converse of the Pythagorean Theorem

45-45-90 Triangle Theorem

30-60-90 Triangle Theorem

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…

In a 45-45-90 triangle, the legs are congruent and the length…

In a 30-60-90 triangle, the length of the hypotenuse is twice…

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…

Interior Angle Sum Theorem

Exterior Angle Sum Theorem

Thm 8.3

Thm 8.4

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

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

Opposite sides of a parallelogram are congruent

Opposite angles of a parallelogram are congruent

Interior Angle Sum Theorem

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

Exterior Angle Sum Theorem

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

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

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concave

convex

isosceles trapezoid

kite

A polygon where part of the diagonal is in the exterior

A polygon where the entire diagonal is in the interior

Trapezoid where the legs are congruent

Quadrilateral with exactly two pairs of consecutive sides

concave

A polygon where part of the diagonal is in the exterior

convex

A polygon where the entire diagonal is in the interior

Through any two points, there is exactl…

Through any three noncollinear points,…

A line contains at least 2 points

A plane contains at least three noncoll…

Postulate 2.1

Postulate 2.2

Postulate 2.3

Postulate 2.4

Through any two points, there is exactl…

Postulate 2.1

Through any three noncollinear points,…

Postulate 2.2

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…

base angle

bases

consecutive

diagonals

each trapezoid has two pairs of ______

parallel sides of a trapezoid

sides of a polygon that share a vertex

a segment joining two non consecutive vertices of a polygon

base angle

each trapezoid has two pairs of ______

bases

parallel sides of a trapezoid