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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…

AA~

SSS~

SAS~

Theorem 7-3

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

If the corresponding sides of two triangles are proportional,…

If an angle of one triangle is congruent to an angle of a sec…

The altitude to the hypotenuse of a right triangle divides th…

AA~

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

SSS~

If the corresponding sides of two triangles are proportional,…

Angle-Angle Similarity Theorem/AA∼ Post.

Side-Side-Side Similarity Theorem/ SSS…

Side-Angle-Side Similarity Theorem/ SA…

Triangle Proportionality Theorem/ ∆Pro…

If two angles of one triangle are similar to two angles of an…

If three sides of one triangle are proportional to three corr…

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 Similarity Theorem/AA∼ Post.

If two angles of one triangle are similar to two angles of an…

Side-Side-Side Similarity Theorem/ SSS…

If three sides of one triangle are proportional to three corr…

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…

SSS Congruence Theorem

SAS Congruence Theorem

ASA Congruence Theorem

AAS Congruence Theorem

If, in two triangles, three sides of one are congruent to thr…

If, in two triangles, two sides and the included angle of one…

If, in two triangles, two angles and the included side of one…

If, in two triangles, two angles and a nonincluded side of on…

SSS Congruence Theorem

If, in two triangles, three sides of one are congruent to thr…

SAS Congruence Theorem

If, in two triangles, two sides and the included angle of one…

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…

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…

Angle-Angle Similarity (AA ~) Postulat…

Side-Angle-Side Similarity (SAS ~) The…

Side-Side-Side Similarity (SSS ~) Theo…

Theorem 7-3

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

If an angle of one triangle is congruent to an angle of a sec…

If the corresponding sides of two triangles are proportional,…

The altitude to the hypotenuse of a right triangle divides th…

Angle-Angle Similarity (AA ~) Postulat…

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

Side-Angle-Side Similarity (SAS ~) The…

If an angle of one triangle is congruent to an angle of a sec…

7-1 (SAS Similarity Theorem)

7-2 (SSS Similarity Theorem)

7-3 (Triangle Proportionality Theorem)

7-3 Corollary

If an angle of one triangle is congruent to an angle of anoth…

If the sides of 2 triangles are in proportion, then the trian…

If a line parallel to one side of a triangle intersects the o…

If three parallel lines intersect two transversals, then they…

7-1 (SAS Similarity Theorem)

If an angle of one triangle is congruent to an angle of anoth…

7-2 (SSS Similarity Theorem)

If the sides of 2 triangles are in proportion, then the trian…

diagonal definition

equilateral polygon definition

equiangular polygon definition

regular polygon definition

a segment that joins 2 nonconsecutive vertices

all sides are congruent

all interior angles are congruent

equilateral and equiangular; must be convex

diagonal definition

a segment that joins 2 nonconsecutive vertices

equilateral polygon definition

all sides are congruent

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…

if, in two triangles, three sides of o…

if, in two triangles, two sides and th…

if, in two triangles, two angles and t…

if, in two triangles, two angles and t…

SSS Congruence Theorem

SAS Congruence Theorem

ASA Congruence Theorem

AAS Congruence Theorem

if, in two triangles, three sides of o…

SSS Congruence Theorem

if, in two triangles, two sides and th…

SAS Congruence Theorem

7.1 - Pythagorean Theorem

7.2 - Converse of the Pythagorean Theo…

7.3

7.4

In a right triangle, the square of the length of the hypotenu…

if the square of the longest side of a triangle is equal to t…

c2<a2+b2 means acute (same as 7.2, but with this equation

c2>a2+b2 then obtuse

7.1 - Pythagorean Theorem

In a right triangle, the square of the length of the hypotenu…

7.2 - Converse of the Pythagorean Theo…

if the square of the longest side of a triangle is equal to t…

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…

Ratio

Proportion

Similar

Similarity Ratio

Comparison of two qualities

Statement stating two ratios equal

Two figures having the same shape but not same size. Correspo…

Ratio of lengths of corresponding sides

Ratio

Comparison of two qualities

Proportion

Statement stating two ratios equal

Pythagorean Theorem (Theorem 7.1)

Pythagorean Triple

Converse of the Pythagorean Theorem (T…

Theorem 7.3

In a right triangle, the square of the length of the hypotenu…

a set of three positive integers (a, b, and c) that satisfies…

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

If the square of the length of the longest side is less than…

Pythagorean Theorem (Theorem 7.1)

In a right triangle, the square of the length of the hypotenu…

Pythagorean Triple

a set of three positive integers (a, b, and c) that satisfies…

Theorem 24

Theorem 25

Theorem 26

Theorem 27

The sum of the angles of a quadrilateral is 360 degrees

The opposite sides and angles of a parallelogram are equal

The diagonals of a parallelogram bisect each other

A quadrilateral is a parallelogram if its opposite sides are…

Theorem 24

The sum of the angles of a quadrilateral is 360 degrees

Theorem 25

The opposite sides and angles of a parallelogram are equal

Polygon Interior Angles Theorem

Corollary to the Polygon Interior Angl…

Polygon Exterior Angles Theorem

Parallelogram Opposite Sides Theorem

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…

Polygon Interior Angles Theorem

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

Corollary to the Polygon Interior Angl…

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

Pythagorean triple

Trigonometric ratio

Tangent

Sine

set of three integers a, b, c which form the sides of a right…

relate the sides of a right triangle to its angles. Specifica…

a straight line or plane that touches a curve or curved surfa…

the trigonometric function that is equal to the ratio of the…

Pythagorean triple

set of three integers a, b, c which form the sides of a right…

Trigonometric ratio

relate the sides of a right triangle to its angles. Specifica…

AA~

SAS~

SSS~

Theorem 7.3

if two angles of one triangle are congruent to two angles of…

if an angle of one triangle is congruent to an angle of anoth…

if all of the corresponding sides of two triangles are propor…

the altitude to the hypotenuse of a right triangle divides th…

AA~

if two angles of one triangle are congruent to two angles of…

SAS~

if an angle of one triangle is congruent to an angle of anoth…

Angle-Angle Similarity Postulate

Side-Angle-Side Similarity Theorem

Side-Side-Side Similarity Theorem

Theorem 7-3

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

If an angle of one triangle is congruent to the angle of a se…

If the measures of the corresponding sides of two triangles a…

The altitude to the hypotenuse of a right triangle divides th…

Angle-Angle Similarity Postulate

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

Side-Angle-Side Similarity Theorem

If an angle of one triangle is congruent to the angle of a se…

Cross Products Property

Key Concept: Properties of Proportions

Similar Polygons

Angle-Angle Similarity (AA~) Postulate

• In a proportion, the product of the extremes equals the pro…

• a/b=c/d is equivalent to b/a=d/c. ... • a/b=c/d is equivalent…

• Two polygons are similar polygons if: ... • Corresponding angl…

• If two angles of one triangle are congruent to two angles o…

Cross Products Property

• In a proportion, the product of the extremes equals the pro…

Key Concept: Properties of Proportions

• a/b=c/d is equivalent to b/a=d/c. ... • a/b=c/d is equivalent…

pythagorean theorem (formula)

pythagorean theorem definition

converse of pythagorean theorem

acute triangle theorem

a^2+b^2=c^2

in a right triangle, the square of the length of the hypotenu…

if the square of the length of the hypotenuse is equal to the…

if the square ofmthe length of the longest sideof a triangle…

pythagorean theorem (formula)

a^2+b^2=c^2

pythagorean theorem definition

in a right triangle, the square of the length of the hypotenu…

Cross Products Property

Equivalent Proportions

Similar Polygons

Perimeters of Similar Polygons

In a proportion, the product of the extremes equals the produ…

Equivalent proportions have identical cross products

Two polygons are similar if and only if their corresponding a…

If two polygons are similar, then their perimeters are propor…

Cross Products Property

In a proportion, the product of the extremes equals the produ…

Equivalent Proportions

Equivalent proportions have identical cross products

pythagorean theorem

converse of the pythagorean theorem

theorem 7.3

theorem 7.4

in a right triangle, the square of the length of the hypotenu…

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…

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

pythagorean theorem

in a right triangle, the square of the length of the hypotenu…

converse of the pythagorean theorem

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

** cross-product property of proportio…

*** reciprocal property of proportions ***

*** other properties of proportions ***

** postulate 15 : AA similarity postul…

a/b = c/d is equivalent to ad = bc ... ( product of extremes =…

if a/b = c/d , then b/a = d/c ... ( a/b and b/a are reciprocals )

if a/b = c/d then :... a.) a/c = b/d ... b.) a+b/b = c+d/d... if a/…

if 2 angles of 1 triangle are congruent to 2 angles of anothe…

** cross-product property of proportio…

a/b = c/d is equivalent to ad = bc ... ( product of extremes =…

*** reciprocal property of proportions ***

if a/b = c/d , then b/a = d/c ... ( a/b and b/a are reciprocals )

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

Theorem 7-3 (Sorry no name for it)

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

If an angle of one triangle is congruent to an angle of a sec…

If the corresponding sides of two triangles are proportional,…

The altitude to the hypotenuse of a RIGHT triangle divides th…

AA Similarity Postulate

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

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of a sec…

ratio

proportions

extended ratios

similar polygons

a comparison of two quantities using division

an equation stating that two ratios are equal

compares three or more quantities

have the same shape, but not necessarily the same size

ratio

a comparison of two quantities using division

proportions

an equation stating that two ratios are equal

Postulate 7-1:Angle-Angle Similarity P…

Theorem 7-2:Side-Angle-Side Similarity…

Theorem 7-3: Side-Side-Side Similarity…

Theorem 7-3

if two angles of one triangle are congruent to two angles of…

if an angle of one triangle is congruent to an angle of a sec…

if the corresponding sides of two triangles are proportional,…

the altitude to the hypotenuse of a right triangle divides th…

Postulate 7-1:Angle-Angle Similarity P…

if two angles of one triangle are congruent to two angles of…

Theorem 7-2:Side-Angle-Side Similarity…

if an angle of one triangle is congruent to an angle of a sec…

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

Corollary to the Polygon Interior... Angl…

Polygon Exterior Angles Theorem

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…

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

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

Means-Extremes Property of Proportions

Properties of proportions (a/b = c/d i…

AA Similarity Postulate

CASTC

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

a/b = c/d is equivalent to:... 1. ad = bc... 2. a/c = b/d... 3. b/a…

If two angles of one triangle are respectively congruent to t…

Corresponding Angles of Similar Triangles are Congruent

Means-Extremes Property of Proportions

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

Properties of proportions (a/b = c/d i…

a/b = c/d is equivalent to:... 1. ad = bc... 2. a/c = b/d... 3. b/a…

Postulate 7-1:Angle-Angle Similarity P…

Theorem 7-2:Side-Angle-Side Similarity…

Theorem 7-3: Side-Side-Side Similarity…

Theorem 7-3

if two angles of one triangle are congruent to two angles of…

if an angle of one triangle is congruent to an angle of a sec…

if the corresponding sides of two triangles are proportional,…

the altitude to the hypotenuse of a right triangle divides th…

Postulate 7-1:Angle-Angle Similarity P…

if two angles of one triangle are congruent to two angles of…

Theorem 7-2:Side-Angle-Side Similarity…

if an angle of one triangle is congruent to an angle of a sec…

The sum of the angles of a quadrilateral

a quadrilateral is equiangular iff

the opposite sides and angles of a par…

the diagonals of a parallelogram

is 360

it is a rectangle

are equal

bisect each other

The sum of the angles of a quadrilateral

is 360

a quadrilateral is equiangular iff

it is a rectangle

squares of the legs

Pythagorean Theorem

Right Triangle

½(b)(h)

Pythagorean Theorem: In a right triangle, the square of the l…

What theorem is this?

The Pythagorean Theorem is only true for what type of triangle?

Area of a triangle

squares of the legs

Pythagorean Theorem: In a right triangle, the square of the l…

Pythagorean Theorem

What theorem is this?

SAS

SSS

Altitude hypotenuse

Corollary to altitude hypotenuse

If an angle of one triangle is congruent to angle of a second…

If the sides of two triangles are portional, then the triangl…

The altitude to the hypotenuse of a right triangle divides th…

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

SAS

If an angle of one triangle is congruent to angle of a second…

SSS

If the sides of two triangles are portional, then the triangl…

The measure of an exterior angle of a…

Midline theorem

No choice theorem

S(i) = ____________

the sum of the remote interior angles

If a segment joins the midpoints of two sides of a triangle,…

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

(n-2)180 - sum of interior angles

The measure of an exterior angle of a…

the sum of the remote interior angles

Midline theorem

If a segment joins the midpoints of two sides of a triangle,…

Angle Angle Similarity Postulate

Side Side Side Similarity Theorem

Side Angle Side 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 Similarity Postulate

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

Side Side Side Similarity Theorem

If the three sides of one triangle are proportional to the th…

Theorem 7.3

Theorem 7.5

Composition Theorem

Cross Product Property

If lines k and m intersect at point P, then a reflection in l…

If lines k and m are parallel, then a reflection in line k fo…

the composition of two (or more) isometries is an isometry

the product of the extremes equals the product of the means

Theorem 7.3

If lines k and m intersect at point P, then a reflection in l…

Theorem 7.5

If lines k and m are parallel, then a reflection in line k fo…

ratio (of one number to another)

The ratio of 3:4

The ratio of 3 to 4 to 5

proportion

Is the quotient when the first number is divided by the secon…

3:4... 3 to 4... 3/4

3:4:5

an equation stating that two ratios are equal (a/b = c/d)

ratio (of one number to another)

Is the quotient when the first number is divided by the secon…

The ratio of 3:4

3:4... 3 to 4... 3/4

Theorem 7-1: SAS Similarity Theorem

Theorem 7-2: SSS Similarity Theorem

Theorem 7-3: Triangle Proportionality…

Theorem 7-4: Triangle Angle-Bisector T…

If an angle of one triangle is congruent to an angle of anoth…

If the sides of two triangles are in proportion, then the tri…

If a line parallel to one side of triangle intersects the oth…

If a ray bisects an angle of a triangle, then it divides the…

Theorem 7-1: SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anoth…

Theorem 7-2: SSS Similarity Theorem

If the sides of two triangles are in proportion, then the tri…

ratio

extended ratio

proportion

extremes

is a comparison of two quantities by division

compares three (or more) numbers by division

an equation that states that two ratios are equal

the first and last numbers in a proportion

ratio

is a comparison of two quantities by division

extended ratio

compares three (or more) numbers by division

ratio

extended ratio

proportion

extremes

a comparison of 2 quantities using division

can be used to compare 3 or more quantities

equation stating that 2 ratios are equal

a and d in which a over b=c over d

ratio

a comparison of 2 quantities using division

extended ratio

can be used to compare 3 or more quantities

SSS Congruence Theorem

SAS Congruence Theorem

ASA Congruence Theorem

AAS Congruence Theorem

If, in two triangles, three sides of one are congruent to thr…

If, in two triangles, two sides and the included angle of one…

If, in two triangles, two angles and the included side of one…

If, in two triangles, two angles and a non-included side of o…

SSS Congruence Theorem

If, in two triangles, three sides of one are congruent to thr…

SAS Congruence Theorem

If, in two triangles, two sides and the included angle of one…

Postulate 7-1 (AA~)

Theorem 7-1 (SAS~)

Theorem 7-2 (SSS~)

Theorem 7-3

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

If an angle of one triangle is congruent to an angle of a sec…

If the corresponding sides of two triangles are proportional,…

The altitude to the hypotenuse of a right triangle divides th…

Postulate 7-1 (AA~)

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

Theorem 7-1 (SAS~)

If an angle of one triangle is congruent to an angle of a sec…

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

Triangle Proportionality Corollary

If an angle of one triangle is congruent to an angle of anoth…

If the sides of two triangles are in proportion, then the tri…

If a line parallel to one side of a triangle intersects the o…

If three parallel lines intersect two transversals, then they…

SAS Similarity Theorem

If an angle of one triangle is congruent to an angle of anoth…

SSS Similarity Theorem

If the sides of two triangles are in proportion, then the tri…

Polygon interior angles theorem

Corollary to the polygon interior angl…

Polygon exterior angles theorem

Parallelogram opposite sides theorem

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 measure of the exterior angles of a convex pol…

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

Polygon interior angles theorem

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

Corollary to the polygon interior angl…

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

Angle- Angle (AA) Similarity Postulate

Side-Side-Side (SSS) Similarity Theorem

Side-Angle-Side (SAS) Similarity Theorem

Triangle Proportionality Theorem

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

If 3 sides of one triangle are proportional to 3 correspondin…

If 2 sides of one triangle are proportional to 2 sides of ano…

If a line parallel to a side of a triangle intersects the oth…

Angle- Angle (AA) Similarity Postulate

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

Side-Side-Side (SSS) Similarity Theorem

If 3 sides of one triangle are proportional to 3 correspondin…

Congruence of Segments Theorem

Congruence of Angles Theorem

Right Angle Congruence Theorem

Congruent Supplements Theorem

Segment congruence is reflexive, symmetric, and transitive.

Angle congruence is reflexive, symmetric, and transitive.

All right angles are congruent.

If two angles are supplementary to the same angle (or to cong…

Congruence of Segments Theorem

Segment congruence is reflexive, symmetric, and transitive.

Congruence of Angles Theorem

Angle congruence is reflexive, symmetric, and transitive.

Angle Angle Similarity Postulate

Side angle Side similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

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

If an angle of one triangle is congruent to an angle of anoth…

If the sides of two triangles are in proportion, then the tri…

If a line parallel to one side of a triangle intersects the o…

Angle Angle Similarity Postulate

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

Side angle Side similarity Theorem

If an angle of one triangle is congruent to an angle of anoth…