# Study sets matching "geometry theorems chapter 7 gifted"

7.1 - Reflection Theorem

7.2 - Rotation Theorem

7.3

7.4 - Translation Theorem

a reflection is an isometry

a rotation is an isometry

if lines k & m intersect at point p, then a reflection in k fo…

a translation is an isometry

7.1 - Reflection Theorem

a reflection is an isometry

7.2 - Rotation Theorem

a rotation is an isometry

Corollary to the Polygon Interior Angle…

Polygon Exterior Angles Theorem

Parallelogram Opposite Sides Theorem

Parallelogram Opposite Angles Theorem

the sum of the measure of the interior angles of a quadrilater…

the sum of the measures of the exterior angles of a convex pol…

if a quadrilateral is a parallelogram, then its opposite sides…

if a quadrilateral is a parallelogram, then its opposite angle…

Corollary to the Polygon Interior Angle…

the sum of the measure of the interior angles of a quadrilater…

Polygon Exterior Angles Theorem

the sum of the measures of the exterior angles of a convex pol…

Polygon Interior Angles Theorem

Corollary to the Polygon Interior Angle…

Polygon Exterior Angles Theorem

Parallelogram Opposite Sides Theorem

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…

The sum of the measures of the exterior angles of a convex pol…

If a quadrilateral is a parallelogram, then its opposite sides…

Polygon Interior Angles Theorem

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

Corollary to the Polygon Interior Angle…

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

Triangle proportionality theorem

Corollary

Angle bisector theorem

A Property of proportions

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

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

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

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 intersects…

Corollary

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

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-g…

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

The sum of the measures of the exterior angles of a convex pol…

If a quadrilateral is a parallelogram, then its opposite sides…

7.1 Polygon Interior Angles Theorem

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

Corollary 7.1 Corollary to the Polygon…

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

AA~

SSS~

SAS~

Theorem 7-3

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

If the corresponding sides of two triangles are proportional,…

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

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

AA~

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

SSS~

If the corresponding sides of two triangles are proportional,…

Diags rhombus perpendicular thm

Diags rhombus bisect opp angles thm.

Diags rectangle congruency thm.

What does a parallelogram have? Or cons…

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

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 perp…

Diags rhombus bisect opp angles thm.

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

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

Corollary to the Polygon Interior... Angle…

Polygon Exterior Angles Theorem

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…

The sum of the measures of the exterior angles of a convex pol…

Classifications of Quadrilaterals

Polygon Interior Angles Theorem

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

Definition of a Rhombus

Definition of a Rectangle

Definition of a Square

Rhombus Corollary

A parallelogram with four congruent sides

A parallelogram with four right angles

A parallelogram with four congruent sides and four right angles

A quadrilateral is a rhombus if and only if it has four congru…

Definition of a Rhombus

A parallelogram with four congruent sides

Definition of a Rectangle

A parallelogram with four right angles

Perimeters of Similar Polygons

Angle-Angle Similarity

Side-Side-Side Similarity

Side-Angle-Side Similarity

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

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

IF the corresponding side lengths of two triangles are proport…

If the lengths of two sides of one triangle are proportional t…

Perimeters of Similar Polygons

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

Angle-Angle Similarity

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

SSS Congruence Theorem

SAS Congruence Theorem

ASA Congruence Theorem

AAS Congruence Theorem

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

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 one…

SSS Congruence Theorem

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

SAS Congruence Theorem

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

Postulate 15 AA

Theorem 7-1 SAS Similarity

Theorem 7-2 SSS Similarity

Theorem 7-3 Triangle Proportionality Th…

If 2 angles of 1 triangle are congruent to 2 of another triang…

If an angle of 1 triangle is congruents to an angle of another…

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

If a line parallel to 1 side of a triangle intersects the othe…

Postulate 15 AA

If 2 angles of 1 triangle are congruent to 2 of another triang…

Theorem 7-1 SAS Similarity

If an angle of 1 triangle is congruents to an angle of another…

Polygon Interior Angles Theorem

Corollary to the Polygon Interior Angle…

Polygon Exterior Angles Theorem

Parallelogram Opposite Sides Theorem

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

The sum of the measure of the interior angles of a quadrilater…

The sum of the measures of the exterior angles of a convex pol…

If a quadrilateral is a parallelogram, then its opposite sides…

Polygon Interior Angles Theorem

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

Corollary to the Polygon Interior Angle…

The sum of the measure of the interior angles of a quadrilater…

Task 1

Task 2

Task 3

Task 4

Show that both pairs of opposite sides are parallel

show that both pairs of opposite sides are congruent

Show that both pairs of opposite angles are congruent

Show that one pair of opposite sides are congruent and parallel

Task 1

Show that both pairs of opposite sides are parallel

Task 2

show that both pairs of opposite sides are congruent

Cross products property

Similar polygons

Angle-angle similarity

Side-Side-Side similarity

In a proportion if A/B=C/D then AD=BC

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

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

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

Cross products property

In a proportion if A/B=C/D then AD=BC

Similar polygons

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

7.1 - Pythagorean Theorem

7.2 - Converse of the Pythagorean Theor…

7.3

7.4

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

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

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 hypotenus…

7.2 - Converse of the Pythagorean Theor…

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

SAS Similarity Theorem

SSS Similarity Theorem

Triangle Proportionality Theorem

Corollary

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

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

if a line parallel to one side of a triangle intersects the ot…

if three parallel lines intersect two transversals, then they…

SAS Similarity Theorem

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

SSS Similarity Theorem

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

Theorem 7.1 Perimeters of Similar Polyg…

Postulate 7.1 Angle-Angle (AA) Similari…

Theorem 7.2 Side-Side-Side (SSS) Simila…

Theorem 7.3 Side-Angle-Side (SAS) Simil…

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

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

IF the corresponding side lengths of two triangles are proport…

If the lengths of two sides of one triangle are proportional t…

Theorem 7.1 Perimeters of Similar Polyg…

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

Postulate 7.1 Angle-Angle (AA) Similari…

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

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-g…

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

The sum of the measures of the exterior angles of a convex pol…

If a quadrilateral is a parallelogram, then its opposite sides…

7.1 Polygon Interior Angles Theorem

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

Corollary 7.1 Corollary to the Polygon…

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

Theorem 7.1 Perimeters of Similar Polyg…

Postulate 7.1 Angle-Angle (AA) Similari…

Theorem 7.2 Side-Side-Side (SSS) Simila…

Theorem 7.3 Side-Angle-Side (SAS) Simil…

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

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

IF the corresponding side lengths of two triangles are proport…

If the lengths of two sides of one triangle are proportional t…

Theorem 7.1 Perimeters of Similar Polyg…

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

Postulate 7.1 Angle-Angle (AA) Similari…

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

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 i…

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

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

If three parallel lines intersect two transversals, the parall…

Pythagorean theorem

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

Side splitter theorem

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

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 congr…

If an angle of one triangle is congruen…

If the sides of two triangles are in pr…

If a line parallel to one side of a tri…

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 congr…

Then the triangles are similar.

If an angle of one triangle is congruen…

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=c…

2 polygons are similar iff their corresponding angles are cong…

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

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=c…

Definition of similar polygons

2 polygons are similar iff their corresponding angles are cong…