# Study sets matching "geometry triangle proofs"

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Supplementary Angles

Vertical angles

Consecutive Interior Angles

Alternate Interior Angles

Add up to 180

Opposite angles formed by intersencting lines.

Interior, same side, and supplementary.

Supplementary Angles

Add up to 180

Vertical angles

Opposite angles formed by intersencting lines.

Theorem

Proof

Inscribe

Equidistant

A known fact that has been previously proven

Deductive argument for a mathematical statement.

The verb that means: to draw the incircle.

Equal distance

Theorem

A known fact that has been previously proven

Proof

Deductive argument for a mathematical statement.

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (s…

2 pairs of congruent angles and one pair of congruent sides (s…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

CPCTC

Triangle Congruence Proofs

SSS (Side, Side, Side) Proof

SAS (Side, Angle, Side) Proof

Congruent parts of congruent triangles are congruent

There are five ways to find if two triangles are congruent: 1.…

If three sides of one triangle are equal to three sides of ano…

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

CPCTC

Congruent parts of congruent triangles are congruent

Triangle Congruence Proofs

There are five ways to find if two triangles are congruent: 1.…

Reflexive Property

Segment Addition Postulate

Def. of a Midpoint

Def. of Segment Bisector

A=A... AB=AB... <A is congruent to <A

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

if B is the midpoint of AC, then AB is congruent to BC

If BD bisected <ABC at D, then AD is congruent to DC

Reflexive Property

A=A... AB=AB... <A is congruent to <A

Segment Addition Postulate

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

Reflexive property

Vertical angles are congruent

Definition of midpoint

Definition of an angle bisector

When the triangles have an angle or side in common

When two lines are intersecting their angles are congruent

Results in two segments being congruent

Results into angles being congruent

Reflexive property

When the triangles have an angle or side in common

Vertical angles are congruent

When two lines are intersecting their angles are congruent

congruent triangles

third angles theorem

reflexive property of triangle congruen…

symmetric property of triangle congruen…

triangles that have the same shape and size

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

any segment equals itself

if triangle ABC is congruent to triangle EFG, triangle EFG is…

congruent triangles

triangles that have the same shape and size

third angles theorem

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

side side side (SSS)

side angle side (SAS)

hypotenuse leg (HL)

angle angle side (AAS)

if three sides of one triangle are congruent to three sides of…

If two sides and the included angle are congruent to two sides…

If the hypotenuse (the side across from the right angle) and a…

If two angles and a non included side of one triangle are cong…

side side side (SSS)

if three sides of one triangle are congruent to three sides of…

side angle side (SAS)

If two sides and the included angle are congruent to two sides…

Segment Bisector

Angle Bisector

Intersecting Lines

Vertical Angles

Segment Bisector > midpoint... Midpoint > 2 = segments

Angle Bisector > 2 = angles

Intersecting Lines > Vertical Angles... Vertical Angles > 2 = An…

Vertical Angles > 2 = Angles

Segment Bisector

Segment Bisector > midpoint... Midpoint > 2 = segments

Angle Bisector

Angle Bisector > 2 = angles

Midpoint

Segment bisector

Angle bisector

Perpendicular lines

A point that divides a segment into two congruent parts

A segment that divides a segment into two congruent parts

A segment that divides an angle into two congruent parts

Two lines that intersect to form right angles

Midpoint

A point that divides a segment into two congruent parts

Segment bisector

A segment that divides a segment into two congruent parts

Side-side-side (SSS)

Side-angle-side (SAS)

Angle-side-angle (ASA)

Side-angle-angle (SAA)

3 pairs of congruent sides

2 pairs of congruent sides and one pair of congruent angles

2 pairs of congruent angles and one pair of congruent sides (s…

2 pairs of congruent angles and one pair of congruent sides (s…

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

SAS

AAS

HL

SSS

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

if two angles and a non-included side of one triangle are cong…

If the hypotenuse and a leg of one right triangle are congruen…

Two triangles are congruent if all 3 sets of corresponding sid…

SAS

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

AAS

if two angles and a non-included side of one triangle are cong…

Side-Side-Side (SSS) Congruence

Side-Angle-Side (SAS) Congruence

Angle-Side-Angle (ASA) Congruence

Angle-Angle-Side (AAS) Congruence

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

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

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

If two angles and the non-included side of one triangle are co…

Side-Side-Side (SSS) Congruence

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

Side-Angle-Side (SAS) Congruence

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

Definition of Congruence

Definition of a Midpoint

Definition of Angle Bisector

Definition of Perpendicular Lines

Having the exact same size and shape and there by having the e…

The point that divides a segment into two congruent halves.

The ray that divides an angle into two congruent halves.

Lines that intersect to form right angles or 90 degrees.

Definition of Congruence

Having the exact same size and shape and there by having the e…

Definition of a Midpoint

The point that divides a segment into two congruent halves.

Reflexive property of segment congruence

Alternate interior angles theorem

Vertical angles congruence theorem

Triangle Sum Theorem

For any segment such as line AB, AB congruent AB

If two parallel lines cut by a transversal then the pairs of a…

Vertical angles are congruent

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

Reflexive property of segment congruence

For any segment such as line AB, AB congruent AB

Alternate interior angles theorem

If two parallel lines cut by a transversal then the pairs of a…

Midpoint

Segment bisector

Angle bisector

Perpendicular lines

def of midpoint

A segment that divides a segment into two congruent parts

A segment that divides an angle into two congruent parts

Two lines that intersect to form right angles

Midpoint

def of midpoint

Segment bisector

A segment that divides a segment into two congruent parts

midpoint

segment bisector

angle bisector

vertical angles

a midpoiny divides a segment into two congruent parts

a bisector divides a segment into two congruent parts

a bisector divides an angle into two congruent parts

vertical angles are congruent

midpoint

a midpoiny divides a segment into two congruent parts

segment bisector

a bisector divides a segment into two congruent parts

Definition of congruence

Definition of midpoint

Definition of angle bisector

Perpindicular lines

Havinf the same size and shape and there by having the exact s…

The poing that divides a segment into two congruent segments

The ray that divides an angle into two congruent angles

Lines that intersect to form right angles or 90 degrees

Definition of congruence

Havinf the same size and shape and there by having the exact s…

Definition of midpoint

The poing that divides a segment into two congruent segments

SAS

SSS

ASA

AAS

requires two sides and an angle. The angle must be between the…

requires three sides

requires two angles and a side. The side must be between the t…

requires two angles and a side. The side is not between the tw…

SAS

requires two sides and an angle. The angle must be between the…

SSS

requires three sides

Addition Postulate

Subtraction Postulate

Division Postulate

Supplement Theorem

If equal parts are added to equal parts, then their sums are e…

If 2 equal parts are subtracted from 2 equal parts, then their…

Halves of equals are equals

Supplements of congruent angles are congruent (write out defin…

Addition Postulate

If equal parts are added to equal parts, then their sums are e…

Subtraction Postulate

If 2 equal parts are subtracted from 2 equal parts, then their…

Congruence

Midpoint

Angle Bisector

Perpendicular Lines

having the exact same size and shape and there by having the e…

the point that divides a segment into two congruent segments

the ray that divides an angle into two congruent angles

lines that intersect to form right angles or 90°

Congruence

having the exact same size and shape and there by having the e…

Midpoint

the point that divides a segment into two congruent segments

Side Side Side Congruence (SSS)

Side Angle Side Congruence (SAS)

Angle Side Angle Congruence (ASA)

Angle Angle Side Congruence (AAS)

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

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

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

If two angles and the non-included side of one triangle are co…

Side Side Side Congruence (SSS)

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

Side Angle Side Congruence (SAS)

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

Third Angles Theorem:

Isosceles Triangle Theorem:

Converse of Isosceles Triangle …

reflexive prop.

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

If two sides of a triangle are congruent, then the angles oppo…

If two angles of a triangle are... congruent, then the sides oppo…

when triangles have an angle of side in common

Third Angles Theorem:

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

Isosceles Triangle Theorem:

If two sides of a triangle are congruent, then the angles oppo…

definition of congruency

definition of midpoint

definition of angle bisector

definition of perpendicular lines

having the exact same size and shape in there by having the ex…

The point that divides a segment into two congruent segments

the Ray that divides an angle into two congruent angles

Lines that intersect to form right angles or 90°

definition of congruency

having the exact same size and shape in there by having the ex…

definition of midpoint

The point that divides a segment into two congruent segments