#### Study sets matching "geometry theorems chapter 7 gifted"

#### Study sets matching "geometry theorems chapter 7 gifted"

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…

Triangle proportionality theorem

Corollary

Angle bisector theorem

A Property of proportions

If a line is parallel to one side of a triangle and intersect…

If 3 or more parallel lines intersect 2 transversals, then th…

An angle bisector in a triangle separates the opposite side i…

If a/b=c/d then, ... ad=bc... a/c=b/d... b/a=d/c... a+b/b=c+d/d

Triangle proportionality theorem

If a line is parallel to one side of a triangle and intersect…

Corollary

If 3 or more parallel lines intersect 2 transversals, then th…

Triangle Proportionality Theorem

Converse of the Triangle Proportionali…

Two-Transversal Proportionality Coroll…

Triangle Angle Bisector Theorem

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

If a line divides two sides of a triangle proportionally, the…

If three or more parallel lines intersect two transversals, t…

An angle bisector of a triangle divides the opposite sides in…

Triangle Proportionality Theorem

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

Converse of the Triangle Proportionali…

If a line divides two sides of a triangle proportionally, the…

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,…

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…

Diags rhombus perpendicular thm

Diags rhombus bisect opp angles thm.

Diags rectangle congruency thm.

What does a parallelogram have? Or con…

A parallelogram is a rhombus if and only if(iff)diagonals per…

A parallelogram is a rhombus iff each diagonal bisects a pair…

A parallelogram is a rectangle iff diagonals congruent.

Picas, post, poat, pidb, opp parallel.

Diags rhombus perpendicular thm

A parallelogram is a rhombus if and only if(iff)diagonals per…

Diags rhombus bisect opp angles thm.

A parallelogram is a rhombus iff each diagonal bisects a pair…

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…

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

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…

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

Theorem 7.2

Theorem 7.3

Theorem 7.4

If the altitude is drawn from the vertex of the right angle o…

The measure of the altitude drawn from the vertex of the righ…

If the altitude is drawn from the vertex of the right angle o…

Pythagorean Theorem - In a right triangle, the sum of the squ…

Theorem 7.1

If the altitude is drawn from the vertex of the right angle o…

Theorem 7.2

The measure of the altitude drawn from the vertex of the righ…

7.1 Polygon Interior Angles Theorem

Corollary 7.1 Corollary to the Polygon…

7.2 Polygon Exterior Angles Theorem

7.3 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…

7.1 Polygon Interior Angles Theorem

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

Corollary 7.1 Corollary to the Polygon…

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

Pythagorean theorem

Side splitter theorem

Triangle angle bisector theorem

Corollary to side splitter theorem

The square of the length of a hypotenuse of a right triangle…

If a line is drawn parallel to one side if a triangle, then i…

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

If three parallel lines intersect two transversals, the paral…

Pythagorean theorem

The square of the length of a hypotenuse of a right triangle…

Side splitter theorem

If a line is drawn parallel to one side if a triangle, then i…

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…

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

If two angles of one triangle are cong…

If an angle of one triangle is congrue…

If the sides of two triangles are in p…

If a line parallel to one side of a tr…

Then the triangles are similar.

Then the triangles are similar.

Then the triangles are similar.

Then it divides those sides proportionally.

If two angles of one triangle are cong…

Then the triangles are similar.

If an angle of one triangle is congrue…

Then the triangles are similar.

Equality of cross products

Definition of similar polygons

AA Similarity

SSS SImilarity

For any numbers a and c and any nonzero numbers b and d, a/b=…

2 polygons are similar iff their corresponding angles are con…

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

If the measures of the corresponding sides of 2 triangles are…

Equality of cross products

For any numbers a and c and any nonzero numbers b and d, a/b=…

Definition of similar polygons

2 polygons are similar iff their corresponding angles are con…

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…

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…

Triangle sum theorem

Exterior angle theorem

Midline theorem

No choice theorem

If a polygon is a triangle, then the sum of the measures of t…

The measure of an exterior angle of a triangle equals the sum…

If a segment is a midline: (1) then it is parallel to the thi…

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

Triangle sum theorem

If a polygon is a triangle, then the sum of the measures of t…

Exterior angle theorem

The measure of an exterior angle of a triangle equals the sum…

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…

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…

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…

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…

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…

Properties of Proportions:

Similar polygons

Angle-Angle similarity (AA~) Theorem

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

a/b =c/d is equivalent to b/a=d/c, ... a/c=b/d, and ... a+b/b = c+d/d

polygons in which corresponding angles are congruent and the…

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…

Properties of Proportions:

a/b =c/d is equivalent to b/a=d/c, ... a/c=b/d, and ... a+b/b = c+d/d

Similar polygons

polygons in which corresponding angles are congruent and the…

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…

AA ~

SSS~

SAS~

Triangle Proportionality Thm

Postulate: If 2 angles of a triangle are congruent to 2 angle…

Theorem: If the 3 sides of 1 triangle are proportional to the…

Theorem: If 2 sides of 1 triangle are proportional to 2 sides…

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

AA ~

Postulate: If 2 angles of a triangle are congruent to 2 angle…

SSS~

Theorem: If the 3 sides of 1 triangle are proportional to the…

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

Properties of proportions

AA Similarity Postulate

SAS Similarity Theorem

SSS Similarity Theorem

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

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 the sides of two triangles are in proportion then the tria…

Properties of proportions

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

AA Similarity Postulate

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

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…

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…

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 )

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

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

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…

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?

Ratio

Proportion

Similar polygons

Similarity Ratio

Comparison of numbers

Two equal ratios

Corresponding angles are congruent and their corresponding si…

Ratio of the lengths of the corresponding sides of two simila…

Ratio

Comparison of numbers

Proportion

Two equal ratios

Theorem 24

Corollary to theorem 24

Theorem 25

Theorem 26

The sum of the angles of a quadrilateral is 360°

A quadrilateral is equiangular iff it is a rectangle

The opposite sides and angles of a parallelogram are equal

The diagonals of a parallelogram bisect each other

Theorem 24

The sum of the angles of a quadrilateral is 360°

Corollary to theorem 24

A quadrilateral is equiangular iff it is a rectangle

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…

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…

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

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,…