Study sets matching "geometry triangle proofs"

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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…
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
14 terms
Triangle Proofs-Geometry
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…
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…
10 terms
Geometry: Triangle Proofs
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…
10 terms
Proofs, Triangle Congruency, Geometry 1
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.
15 terms
analytic geometry triangle proofs
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
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…
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
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
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
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…
17 terms
Geometry triangle proofs
Equilateral Triangles
Equiangular Triangles
Scalene Triangle
Isosceles triangle
...
...
...
...
Equilateral Triangles
...
Equiangular Triangles
...
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
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…
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
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…
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…
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
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
Geometry triangle proof terms
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…
40 terms
Geometry- Triangles Proofs
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
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
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
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.
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
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
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…
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)
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
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…
23 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…
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
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
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…
Congruent Triangles & Triangle Proofs
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…
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
19 terms
Triangle Proofs
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…
15 terms
Geometry Definitions - Unit 3/4 Triangles & Proof
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…
Geometry triangle proofs and postulates 12/9/16
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
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…
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
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
25 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
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…
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
Triangle Proofs
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
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