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Study sets matching "geometry triangle proofs"

14 terms
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…
15 terms
Geometry Triangle Proofs
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…
5 terms
Geometry Triangle Proofs
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…
28 terms
Geometry Triangle Proofs
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
6 terms
Geometry Triangle Proofs
SSS (Side-Side-Side)
SAS (Side-Angle-Side)
ASA (Angle-Side-Angle)
AAS (Angle-Angle- Side)
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 a nonincluded side of one triangle are cong…
SSS (Side-Side-Side)
if three sides of one triangle are congruent to three sides o…
SAS (Side-Angle-Side)
if two sides and the included angle of one triangle are congr…
36 terms
Analytic Geometry: Triangle Proofs
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
8 terms
Geometry triangle proofs
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
9 terms
geometry triangle proofs
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…
11 terms
Geometry (similar triangle proofs)
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
15 terms
geometry triangle proofs
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
17 terms
Geometry triangle proofs
Equilateral Triangles
Equiangular Triangles
Scalene Triangle
Isosceles triangle
...
...
...
...
Equilateral Triangles
...
Equiangular Triangles
...
11 terms
Geometry triangle proofs
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
13 terms
Geometry (triangle proofs)
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…
13 terms
Geometry: Triangle Proofs Quiz
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…
5 terms
Geometry Triangle Proof Definitions
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…
31 terms
Geometry Proofs and Congruent Triangles
acute triangle
obtuse triangle
right triangle
equiangular
all angles are less than 90
one angle is greater than 90
one angle of a triangle = 90
all angles are congruent
acute triangle
all angles are less than 90
obtuse triangle
one angle is greater than 90
32 terms
Geometry Triangle Proof Reasons
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
6 terms
Geometry Proofs: Triangles
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…
Geometry proofs (isosceles triangles)
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.
18 terms
Geometry Triangle proof vocabulary
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
8 terms
Geometry Triangle Proof Terms
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
14 terms
Geometry: Triangle congruence proofs, Triangle Relationships
SSS
SAS
ASA
AAS
Side, Side, Side
Side, Angle, Side
Angle, Side, Angle
Angle, Angle, Side
SSS
Side, Side, Side
SAS
Side, Angle, Side
18 terms
Triangle Proofs
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…
17 terms
Geometry-unit3B:triangle proofs
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
11 terms
Geometry Triangle Proofs Part 1
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
18 terms
Congruent Triangles & Triangle Proofs
SSS Postulate
SAS Postluate
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 Postluate
if 2 sides and the includes angle of 1 triangle are congruent…
19 terms
Triangle Proofs
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…
18 terms
Triangle Proofs
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
Geometry Terms Triangle Congruence & Proofs
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
36 terms
Geometry Unit: Proofs and Triangle Congruence
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)
14 terms
Geometry: Triangle congruence proofs, Triangle Relationships
SSS
SAS
ASA
AAS
Side, Side, Side
Side, Angle, Side
Angle, Side, Angle
Angle, Angle, Side
SSS
Side, Side, Side
SAS
Side, Angle, Side
18 terms
Geometry Triangle/ Theorems to use in Proofs
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…
26 terms
Geometry 9: Test 3: Proofs & Congruent Triangles
Given
midpoint
segment bisector
angle bisector
next statements
2 congruent segments
2 congruent segments
2 congruent angles
Given
next statements
midpoint
2 congruent segments
14 terms
Triangle Proofs
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
9 terms
Geometry Lesson 3-4 Triangle Proofs
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…
48 terms
GSE Analytic Geometry - Unit 2: Similarity, Congruence, and Proofs, Proofs - Triangles
angle
Adjacent Angles
Alternate Exterior Angles
Alternate Interior Angles
Angles are created by two distinct rays that share a common e…
Angles in the same plane that have a common vertex and a... comm…
Alternate exterior angles are pairs of angles formed... when a t…
Alternate interior angles are pairs of angles formed... when a t…
angle
Angles are created by two distinct rays that share a common e…
Adjacent Angles
Angles in the same plane that have a common vertex and a... comm…
13 terms
Triangle Proofs
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
17 terms
Congruent Triangles & Triangle Proofs
SSS Postulate
SAS Postluate
ASA Postulate
AAS Theorem
if 3 sides of 1 triangle are congruent to 3 sides of a 2nd tr…
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 a non-included side of one triangle are congr…
SSS Postulate
if 3 sides of 1 triangle are congruent to 3 sides of a 2nd tr…
SAS Postluate
if 2 sides and the included angle of 1 triangle are congruent…
18 terms
Triangle Proofs
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
7 terms
Triangle Proofs
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…
17 terms
Triangle Proofs
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
18 terms
Congruent Triangles & Triangle Proofs
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
18 terms
Congruent Triangles & Triangle Proofs
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…
23 terms
Geometry Chapter 4: Properties of a Triangle, Triangle Congruency, Proofs
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…
14 terms
Geometry Properties of Proofs (Types of Triangle Congruence)
SAS Triangle Congruence
AAS Triangle Congruence
ASA Triangle Congruence
SSS Triangle Congruence
two pairs of corresponding sides congruent and the AND the an…
two pairs of corresponding angles congruent and one pair of c…
two pairs of corresponding angles congruent AND the sides bet…
three pairs of corresponding sides congruent
SAS Triangle Congruence
two pairs of corresponding sides congruent and the AND the an…
AAS Triangle Congruence
two pairs of corresponding angles congruent and one pair of c…
8 terms
Similar Triangle Proofs
Intersecting Lines Create
Parallel Lines Create
When triangles share an angle you use
Similarity Proving Methods
Vertical Angles
Alternate Interior Angles or... Corresponding Angles
The Reflexive Property
AA, SAS and SSS Similarity
Intersecting Lines Create
Vertical Angles
Parallel Lines Create
Alternate Interior Angles or... Corresponding Angles
15 terms
Congruent Triangle Proofs
right triangle
isosceles triangle
reflexive sides
perpendicular lines
right triangle
isosceles triangle
38 terms
Geometry Proofs
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
20 terms
Geometry Proofs
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Addition Property of Equality
a = a
If a = b... Then b = a
If a = b, and b = c ... Then a = c
If a = b ... Then a + 3 = b + 3
Reflexive Property of Equality
a = a
Symmetric Property of Equality
If a = b... Then b = a
21 terms
Geometry- Unit 3 (angles and triangles proofs)
perpendicular lines form right angles
how to tell that two angles are supp (2)
how to tell that two angles are comp
how to tell that perp angles are equal…
perp lines def
1. the exterior sides of 2 adj angles are opposite rays -> su…
the exterior sides of 2 adj angles are perp -> comp
1. they are right angles -> all right angles are =... 2. two adj…
perpendicular lines form right angles
perp lines def
how to tell that two angles are supp (2)
1. the exterior sides of 2 adj angles are opposite rays -> su…
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