# Study sets matching "honors geometry chapter 4 postulates theorems"

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Acute Triangle

Right Triangle

Obtuse Triangle

Equilangular Triangle

If a triangle has 3 acute angles, then it is an acute triangle.

If a triangle has one right angle, then it is a right triangle.

If a triangle has one obtuse angle, then it is an obtuse trian…

If a triangle has three congruent and acute angles, then it is…

Acute Triangle

If a triangle has 3 acute angles, then it is an acute triangle.

Right Triangle

If a triangle has one right angle, then it is a right triangle.

Theorem 4.1 (Angle Sum Theorem)

Theorem 4.2 (Exterior Angles Theorem)

Corollary 4.1

Corollary 4.2

all three angles of a triangle equal 180 degrees

The exterior angle is equal to the sum of the 2 remote interio…

In a right triangle, the 2 acute angles are complementary

A triangle can have at most one right angle or one obtuse angle

Theorem 4.1 (Angle Sum Theorem)

all three angles of a triangle equal 180 degrees

Theorem 4.2 (Exterior Angles Theorem)

The exterior angle is equal to the sum of the 2 remote interio…

Polygons whose corresponding parts are…

The same or equal.

If two angles of one triangle are congr…

If three sides of one triangle are cong…

Congruent Polygons

Congruent

Triangle Third Angle Sum Theorem

SSS Congruence Postulate

Polygons whose corresponding parts are…

Congruent Polygons

The same or equal.

Congruent

Right Angle Congruence Theorem

Vertical Angles Theorem

Congruent Supplements Theorem

Congruent Complements Theorem

If 2 angles are right angles, then they are congruent

If 2 angles are vertical angles, then they are congruent

If 2 angles are supplementary to the same angle or congruent a…

If 2 angles are complementary to the same angle or congruent a…

Right Angle Congruence Theorem

If 2 angles are right angles, then they are congruent

Vertical Angles Theorem

If 2 angles are vertical angles, then they are congruent

Third Angles Theorem

Side-Side-Side Postulate

Side-Angle-Side Postulate

Angle-Side-Angle Postulate

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

If the three sides of one triangle are congruent to the three…

If two sides and the included angle of one triangle are congru…

If two angles and the included side of one triangle are congru…

Third Angles Theorem

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

Side-Side-Side Postulate

If the three sides of one triangle are congruent to the three…

Same-side Interior Angle Postulate... If a…

Alternate Interior Angles Theorem... If a…

Corresponding Angles Theorem... If a trans…

Alternate Exterior Angles Theorem... If a…

supplementary... m∠1 + m∠2 = 180

congruent

corresponding

exterior

Same-side Interior Angle Postulate... If a…

supplementary... m∠1 + m∠2 = 180

Alternate Interior Angles Theorem... If a…

congruent

triangle sum theorem

exterior angles theorem

corollary to the triangle sum theorem

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 two angles of one triangle are congruent tot two angles of…

triangle sum theorem

the sum of the measures of the interior angles of a triangle i…

exterior angles theorem

the measure of an exterior angle of a triangle is equal to the…

Through any two points there is exactly…

Through any three noncollinear points t…

If two points lie in a plane, then the…

If two lines intersect, they then inter…

Through any two points there is exactly one line

Through any three noncollinear points there is exactly one pla…

If two points lie in a plane, then the line containing those p…

If two lines intersect, they then intersect at exactly one poi…

Through any two points there is exactly…

Through any two points there is exactly one line

Through any three noncollinear points t…

Through any three noncollinear points there is exactly one pla…

Triangle Sum Theorem

Corollary #1 Triangle Sum Theorem

Corollary #2 Triangle Sum Theorem

Exterior Angle Theorem

The sum of the angle measures of a triangle is 180°.

The acute angles of a right triangle are complementary.

The measures of each angle of an equiangular triangle is 60°.

The measure of an exterior angle of a triangle is equal to the…

Triangle Sum Theorem

The sum of the angle measures of a triangle is 180°.

Corollary #1 Triangle Sum Theorem

The acute angles of a right triangle are complementary.

triangle sum theorem

exterior angles theorem

corollary to the triangle sum theorem

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 two angles of one triangle are congruent tot two angles of…

triangle sum theorem

the sum of the measures of the interior angles of a triangle i…

exterior angles theorem

the measure of an exterior angle of a triangle is equal to the…

Theorem 6-1: The Exterior Angle Theorem

Theorem 6-2

Theorem 6-3

Corollary 1

The measure of an exterior angle of a triangle is greater than…

If one side of a triangle is longer than a second side, then t…

If one angle of a triangle is larger than a second angle, then…

The perpendicular segment from a point to a line is the shorte…

Theorem 6-1: The Exterior Angle Theorem

The measure of an exterior angle of a triangle is greater than…

Theorem 6-2

If one side of a triangle is longer than a second side, then t…

Theorem 7-1: SAS Similarity Theorem

Theorem 7-2: SSS Similarity Theorem

Theorem 7-3: Triangle Proportionality T…

Theorem 7-4: Triangle Angle-Bisector Th…

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 triangle intersects the othe…

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

Theorem 7-1: SAS Similarity Theorem

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

Theorem 7-2: SSS Similarity Theorem

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

Triangle Sum Theorem

Exterior Angle Theorem

Corollary to Triangle Sum Theorem

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

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…

Triangle Sum Theorem

Corollary #1 Triangle Sum Theorem

Corollary #2 Triangle Sum Theorem

Exterior Angle Theorem

The sum of the angle measures of a triangle is 180°.

The acute angles of a right triangle are complementary.

The measures of each angle of an equiangular triangle is 60°.

The measure of an exterior angle of a triangle is equal to the…

Triangle Sum Theorem

The sum of the angle measures of a triangle is 180°.

Corollary #1 Triangle Sum Theorem

The acute angles of a right triangle are complementary.

Ruler Postulate

Segment Addition Postulate

Protractor Postulate

Angle Addition Postulate

The points on a line can be put into a one-to-one corresponden…

If B is between A and C, then AB + BC = AC

Given line AB and a point O on line AB, all rays that can be d…

If S is in the interior of <PQR, then m<PQS + m<SQR = m<PQR

Ruler Postulate

The points on a line can be put into a one-to-one corresponden…

Segment Addition Postulate

If B is between A and C, then AB + BC = AC

Congruent Polygons

Third Angles Theorem

Side-Side-Side (SSS) Postulate

Side-Angle-Side (SAS) Postulate

Have congruent corresponding parts--their matching sides and a…

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

If the three sides of one triangle are congruent to the three…

If two sides and the included angle of one triangle are congru…

Congruent Polygons

Have congruent corresponding parts--their matching sides and a…

Third Angles Theorem

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

Pythagorean Inequalities Theorem

Triangle Sum Theorem

The acute angles of a right triangle ar…

The measure of each angle of an equiang…

In triangle ABC, c is the length of the longest side. If c^2 >…

The sum of the measures in the triangle is 180

The acute angles of a right triangle are complementary

The measure of each angle of an equiangular triangle is 60

Pythagorean Inequalities Theorem

In triangle ABC, c is the length of the longest side. If c^2 >…

Triangle Sum Theorem

The sum of the measures in the triangle is 180

Congruent Polygons

Corollary

Equilateral Triangle

Isosceles Triangle

Polygons that have corresponding sides congruent and correspon…

Theorem that can proved easily using another theorem.

A triangle whose sides are all congruent.

Triangle that has two congruent sides.

Congruent Polygons

Polygons that have corresponding sides congruent and correspon…

Corollary

Theorem that can proved easily using another theorem.

Congruent Polygon

Theorem 4-1... Third Angled Theorem

Postulate 4-1 ... Side Side Side Postulate…

Postulate 4-2 ... Side Angle Side (SAS)

all of its corresponding sides are congruent all corresponding…

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

If 3 sides of one triangle are congruent to 3 sides of another…

If 2 sides and an included angle of one triangle are congruent…

Congruent Polygon

all of its corresponding sides are congruent all corresponding…

Theorem 4-1... Third Angled Theorem

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

triangle sum theorem

exterior angles theorem

corollary to the triangle sum theorem

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 two angles of one triangle are congruent tot two angles of…

triangle sum theorem

the sum of the measures of the interior angles of a triangle i…

exterior angles theorem

the measure of an exterior angle of a triangle is equal to the…

Congruent Polygon

Third Angled Theorem

Side Side Side Postulate (SSS)

Side Angle Side (SAS)

all of its corresponding sides are congruent all corresponding…

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

If 3 sides of one triangle are congruent to 3 sides of another…

If 2 sides and an included angle of one triangle are congruent…

Congruent Polygon

all of its corresponding sides are congruent all corresponding…

Third Angled Theorem

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

Triangle Sum Theorem (4.1)

Exterior Angle Theorem (4.2)

Corollary to the triangle sum theorem

Complementary Angles =

The sum of the measures of the interior angles of a triangle i…

The measures of an exterior angle of a triangle is equal to th…

The acute angles of a right triangle are complementary

Add up to 90

Triangle Sum Theorem (4.1)

The sum of the measures of the interior angles of a triangle i…

Exterior Angle Theorem (4.2)

The measures of an exterior angle of a triangle is equal to th…

Triange-Angle Sum Theorem

Exterior Angle of a Triangle Corollary

Acute Angles of a Right Triangle Coroll…

Third Angles Theorem

the sum of the measures of the interior angles of a triangle i…

if two angles of of triangle are congruent with two angles of…

Triange-Angle Sum Theorem

the sum of the measures of the interior angles of a triangle i…

Exterior Angle of a Triangle Corollary

Postulate

Postulate

Postulate

Postulate

A line segment can be extended to any length in either directi…

Through two given points, one and only one line can be drawn.…

Two lines cannot intersect in more than one point

One and only one circle can be drawn with any given point as c…

Postulate

A line segment can be extended to any length in either directi…

Postulate

Through two given points, one and only one line can be drawn.…