#### Study sets matching "geometry triangle proofs"

#### Study sets matching "geometry triangle proofs"

SSS (side, side, side)

ASA (angle, side, angle)

SAS (side, angle, side)

AAS (angle, angle, side)

If 3 sides of one triangle are congruent to the corresponding…

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

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

If two angles and a side opposite one of the angles in one tr…

SSS (side, side, side)

If 3 sides of one triangle are congruent to the corresponding…

ASA (angle, side, angle)

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

definition of congruence

definition of midpoint

definition of angle bisector

definition of perpendicular lines

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

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 degrees

definition of congruence

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

definition of midpoint

the point that divides a segment into two congruent segments

Addition Postulate

Subtraction Postulate

Division Postulate

Supplement Theorem

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

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

Halves of equals are equals

Supplements of congruent angles are congruent (write out defi…

Addition Postulate

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

Subtraction Postulate

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

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 o…

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

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

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

side side side (SSS)

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

side angle side (SAS)

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

Angle Bisector

Segment Bisector

Midpoint

Perpendicular

Any line or part of aline that divides an angle into two cong…

Any line or part of a line that intersects a segment at the m…

A point that divides a segment into two congruent segments.

Two lines that intersect to form right angles.

Angle Bisector

Any line or part of aline that divides an angle into two cong…

Segment Bisector

Any line or part of a line that intersects a segment at the m…

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.

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 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°

definition of congruency

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

definition of midpoint

The point that divides a segment into two congruent segments

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 o…

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

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

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

Side-Side-Side (SSS) Congruence

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

Side-Angle-Side (SAS) Congruence

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

SAS

SSS

ASA

AAS

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

requires three sides

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

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

SAS

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

SSS

requires three sides

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

Congruence

Midpoint

Angle Bisector

Perpendicular Lines

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

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…

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 o…

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

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

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

Side Side Side Congruence (SSS)

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

Side Angle Side Congruence (SAS)

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

CPCTC

CSSPT

AA~

SAS~

Corresponding parts of congruent triangles ar congruent

Corresponding sides of similar triangles are proprtional

Angle angle similar

Side angle side similar

CPCTC

Corresponding parts of congruent triangles ar congruent

CSSPT

Corresponding sides of similar triangles are proprtional

SAS

ASA

AAS

SSS

Two triangles are congruent if two sides in the included angl…

Two triangles are congruent if two angles and the included si…

Two triangles are congruent if two angles and the consecutive…

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

SAS

Two triangles are congruent if two sides in the included angl…

ASA

Two triangles are congruent if two angles and the included si…

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 = A…

Vertical Angles > 2 = Angles

Segment Bisector

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

Angle Bisector

Angle Bisector > 2 = angles

Altitude of a triangle

Angle bisector of a triangle

Median of a triangle

Right angles

A line segment drawn from any vertex of a triangle ,perpendic…

A line segment that bisects any angle of the triangle and ter…

A line segment that joins any vertex of the triangle to the m…

all right angles are congruent

Altitude of a triangle

A line segment drawn from any vertex of a triangle ,perpendic…

Angle bisector of a triangle

A line segment that bisects any angle of the triangle and ter…

Side-Side-Side (SSS)

Side-Angle-Side (SAS)

Angle-Side-Angle (ASA)

Angle-Angle-Side (AAS)

prove three (3) sets of corresponding sides congruent to each…

prove two (2) sets of corresponding sides congruent to each o…

prove two (2) sets of corresponding angles congruent to each…

prove two sets of corresponding angles congruent to each othe…

Side-Side-Side (SSS)

prove three (3) sets of corresponding sides congruent to each…

Side-Angle-Side (SAS)

prove two (2) sets of corresponding sides congruent to each o…

SAS

SSS

ASA

HL

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

If the three sides of one triangle is congruent to threats si…

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

If the hypotenuse and the leg of one triangle are congruent t…

SAS

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

SSS

If the three sides of one triangle is congruent to threats si…

Definition of Congruence

Definition of Midpoint

Definition of Angle Bisector

Definition of Perpendicular Lines

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

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 degrees

Definition of Congruence

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

Definition of Midpoint

The point that divides a segment into two congruent segments

Midpoint

Bisector

Intersecting

Perpendicular

Cuts a segemt perfectly in half into 2 congruent parts

Cuts a segment or angle perfectly in half into 2 congruent pa…

Forms vertical angles that are congruent

Forms right angles that are congruent

Midpoint

Cuts a segemt perfectly in half into 2 congruent parts

Bisector

Cuts a segment or angle perfectly in half into 2 congruent pa…

Reflective Property

Vertical Angles are Congruent

Right Angles are Congruent

Alternate Interior Angles or Parallel…

AB = BA When the triangles have an angle or side in common

When two lines are intersecting

When you are given right triangles and/or a square/ rectangle

When the givens inform you that two lines are parallel

Reflective Property

AB = BA When the triangles have an angle or side in common

Vertical Angles are Congruent

When two lines are intersecting

Definition of congruence

Midpoint

Angle bisector

Perpendicular lines

Having the exact same shape and size which allows the exact s…

A point that divides an angle into two congruent segments

A line that divides an angle into two congruent angle measure…

Lines that intersect to form 90° angles

Definition of congruence

Having the exact same shape and size which allows the exact s…

Midpoint

A point that divides an angle into two congruent segments

CPCTC

SSS

SAS

ASA

Corresponding Parts of Congruent Triangles are Congruent

Side Side Side - have to prove all 3 sides are congruent

Side Angle Side - 2 congruent sides with angles they create c…

Angle Side Angle - 2 congruent angles with the sides between…

CPCTC

Corresponding Parts of Congruent Triangles are Congruent

SSS

Side Side Side - have to prove all 3 sides are congruent

Right Angle Congruence Theorem

Linear pair theorem

Definition of perpindicular lines

Adjacent

If two angles are right angles, then they are congruent. (Mus…

If two angles form a linear pair, then they are supplementary.

Perpindicular lines form right angles.

If two lines are perpinducular, then they form congruent adja…

Right Angle Congruence Theorem

If two angles are right angles, then they are congruent. (Mus…

Linear pair theorem

If two angles form a linear pair, then they are supplementary.

Adjacent angles

Linear pairs

Supplementary angles

Complementary angles

Angles that share a common ray

2 adjacent angles that form a line=180

2 angles that add up to 180

2 angles that add up to 90

Adjacent angles

Angles that share a common ray

Linear pairs

2 adjacent angles that form a line=180

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 (…

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

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 is congruent to SAS

AAS is congruent to AAS

HL is congruent to HL

SSS is congruent to SSS

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

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

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

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

SAS is congruent to SAS

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

AAS is congruent to AAS

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

The Properties of Operations

Associative property of addition

Commutative prop. of addition

Additive identity property of 0

...

(a+b)+c=a+(b+c) ... (3+5)+7=3+(5+7)

a+b=b+a... (4x-5)+9=9+(4x-5)

a+0=0+a=a... -12+0=-12 0-12=-12

The Properties of Operations

...

Associative property of addition

(a+b)+c=a+(b+c) ... (3+5)+7=3+(5+7)

SAS

AAS

HL

SSS

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

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

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

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

SAS

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

AAS

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

Riflexive Property

Subtraction Property

Equilateral

Isosceles

when a side length takes equal part in both triangles, and th…

m1 + m2 + m3 = m3 + m4 ... -m3 -m3... m1 + m2 = m4... (shows congru…

Triangle with all three congruent sides

Triangle with atleast two congruent sides

Riflexive Property

when a side length takes equal part in both triangles, and th…

Subtraction Property

m1 + m2 + m3 = m3 + m4 ... -m3 -m3... m1 + m2 = m4... (shows congru…

Definition of Congruent Polygons

CPCTC

Third Angles Theorem

Exterior Angle Theorem

Two polygons are congruent if and only if their corresponding…

Congruent Parts of Congruent Triangles are Congruent

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

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

Definition of Congruent Polygons

Two polygons are congruent if and only if their corresponding…

CPCTC

Congruent Parts of Congruent Triangles are Congruent

What does CPCTC stand for?

Tells you to draw a box and prove 2 <'…

Extend lines. Proves 2 <'s AI.

Tells you to label two sides equal (co…

Corresponding Parts of Congruent Triangles are Congruent.

Perpendicular

Parallel

Midpoint

What does CPCTC stand for?

Corresponding Parts of Congruent Triangles are Congruent.

Tells you to draw a box and prove 2 <'…

Perpendicular

Right angle

angle bisector

segment bisector

perpendicular

if 1 angle - a right angle is 90 degrees... if 2 or more angles…

angle 1 and angle 2 are congruent ... - angle bisector bisects a…

line AM is congruent to line MB... - segment bisector bisects a…

(+) angle 1,2,3,4 are right angles... - perpendicular lines inte…

Right angle

if 1 angle - a right angle is 90 degrees... if 2 or more angles…

angle bisector

angle 1 and angle 2 are congruent ... - angle bisector bisects a…

SSS Postulate

SAS Postluate

ASA Postulate

AAS Theorem

if 3 sides of 1 triangle are congruent to another 3 sides of…

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

if 2 angles and one included side of 1 triangle are congruent…

If 2 angles and a non-included side of one triangle are congr…

SSS Postulate

if 3 sides of 1 triangle are congruent to another 3 sides of…

SAS Postluate

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

Midpoint

Segment Bisector

Angle Bisector

Perpendicular

A point that divides a segment into two congruent segments.

A line, ray, or segment that divides a segment into two congr…

Ray/segment/line that intersects an angle at the vertex and c…

Two lines that intersect and form right angles.

Midpoint

A point that divides a segment into two congruent segments.

Segment Bisector

A line, ray, or segment that divides a segment into two congr…

Isosceles Triangle

Base Angles

Exterior Angle

Adjacent Interior Angle

A triangle that has two sides of equal length

Two angles opposite the two congruent sides of an isosceles t…

An angle that forms a linear pair with one of the interior an…

The angle that shares a vertex with the exterior angle.

Isosceles Triangle

A triangle that has two sides of equal length

Base Angles

Two angles opposite the two congruent sides of an isosceles t…

Exterior angle theorem

Corollary to the triangle sum theorem

Reflexive property of triangle congrue…

Symmetric property of triangle congrue…

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

The acute angles of a right triangle are complementary

For any triangle ABC, ABC = ABC

If ABC = DEF, then triangle DEF = triangle ABC

Exterior angle theorem

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

Corollary to the triangle sum theorem

The acute angles of a right triangle are complementary

SSS

SAS

ASA

AAS

If 3 sides of the triangle are congruent to 3 sides of a seco…

If 2 sides and the included angle of one triangle are congrue…

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

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

SSS

If 3 sides of the triangle are congruent to 3 sides of a seco…

SAS

If 2 sides and the included angle of one triangle are congrue…

Triangle Angle-Sum Theorem

Exterior Angles

Remote Interior Angles

Scalene Triangle

The sum of all angles of a triangle is 180 degrees.

Angle formed by extending one side. Equal to the sum of its r…

Angles non-adjacent to exterior angle.

A triangle with no congruent sides.

Triangle Angle-Sum Theorem

The sum of all angles of a triangle is 180 degrees.

Exterior Angles

Angle formed by extending one side. Equal to the sum of its r…

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 (…

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

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 congr…

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

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

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

SAS

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

AAS

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

Midpoint

Congruent Angles

Perpendicular Lines

Vertical Angles

point that divides the segment into two congruent segments

angles that have = measurements

2 lines that intersect to form right ∠'s

Two congruent non adjacent angles of intersecting lines

Midpoint

point that divides the segment into two congruent segments

Congruent Angles

angles that have = measurements

SSS Postulate

SAS Postulate

ASA Postulate

AAS Theorem

if 3 sides of 1 triangle is congruent to another 3 sides of a…

if 2 sides and the includes angle of 1 triangle are congruent…

if 2 angles and one included side of 1 triangle are congruent…

If 2 angles and a non-included side of one triangle are congr…

SSS Postulate

if 3 sides of 1 triangle is congruent to another 3 sides of a…

SAS Postulate

if 2 sides and the includes 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 angles

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

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

Side-side-side (SSS)

3 pairs of congruent sides

Side-angle-side (SAS)

2 pairs of congruent sides and one pair of congruent angles

right angle

angle bistector

segment bisector

perpendicular

an angle of 90 degrees

a ray that divides an angle into two equal angles

a segment, line or ray that divides a segment into two equal…

lines that intersect to create right angles

right angle

an angle of 90 degrees

angle bistector

a ray that divides an angle into two equal angles