#### 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…

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…

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…

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,…

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…

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-…

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…

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…

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

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

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…

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…

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

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…

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

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…

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…

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 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.

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…

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…