# Study sets matching "geometry triangle proofs"

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Direct conclusion drawn from midpoint

Direct conclusion drawn from segment bi…

Direct conclusion drawn from angle bise…

Direct conclusion drawn from perpendicu…

2 congruent segments

2 congruent segments

2 congruent angles

right angles

Direct conclusion drawn from midpoint

2 congruent segments

Direct conclusion drawn from segment bi…

2 congruent segments

reflexive

symmetric

substitution

partition

a quantity is equal to itself. ex: a=a

an equality may be expressed in either order. ex: if a=b, then…

equal quantities can be substituted. ex: if a+b=c and b=d, the…

a whole equals the sum of its parts. a whole is greater than a…

reflexive

a quantity is equal to itself. ex: a=a

symmetric

an equality may be expressed in either order. ex: if a=b, then…

SSS

SAS

ASA

AAS

if all 3 sides are equal in length

if any 2 corresponding SIDES and their included 1 ANGLE are th…

if any 2 ANGLES and their included SIDE are the same in both t…

if there are PAIRS of corresponding ANGLES and a pair of corre…

SSS

if all 3 sides are equal in length

SAS

if any 2 corresponding SIDES and their included 1 ANGLE are th…

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.

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.…

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

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

M is the midpoint of AB

CD bisects AB at P

BE bisects <ABC

AB and CD intersect at E

Statement: AM congruent MB... Reason: A mdpt divides a line segem…

S: AP congruent PB... CP congruent PD... R: A bisector divides a li…

S: <ABE congruent <EBC... R: a bisector divides and angle into tw…

S: <1 congruent <3... <2 congruent <4... R: intersecting lines from…

M is the midpoint of AB

Statement: AM congruent MB... Reason: A mdpt divides a line segem…

CD bisects AB at P

S: AP congruent PB... CP congruent PD... R: A bisector divides a li…

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

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

if 2 angles of one triangle are congrue…

corresponding parts of congruent triang…

if 3 sides of a triangle are congruent…

if 2 sides and the included angle of a…

third angles theorem

CPCTC

SSS

SAS

if 2 angles of one triangle are congrue…

third angles theorem

corresponding parts of congruent triang…

CPCTC

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

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…

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…

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…

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…

SSS

SAS

ASA

AAS

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

If 2 sides and the included angle of 1 triangle are congruent…

If 2 angles and the included side of 1 triangle are congruent…

If 2 angles and another included side of 1 triangle are congru…

SSS

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

SAS

If 2 sides and the included angle of 1 triangle are congruent…

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 included…

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 included…

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…

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

M is the midpoint of segment AB

CD bisects AB at P

BE bisects angle ABC

AB and CD intersect at E

AM is congruent to MB; a midpoint divides a line segment into…

AP is congruent to PB; a bisector divides a line segment into…

Angle ABE is congruent to EBC; a bisector divides an angle int…

Angle 1 is congruent to angle 3, angle 2 is congruent to angle…

M is the midpoint of segment AB

AM is congruent to MB; a midpoint divides a line segment into…

CD bisects AB at P

AP is congruent to PB; a bisector divides a line segment into…

definition

theorem

proposition

lemma

an explanation of the mathematical meaning of a word

a very important true statement

a less important but nonetheless interesting true statement

a true statement used in proving other true statements

definition

an explanation of the mathematical meaning of a word

theorem

a very important true statement