Geometry Proofs

Question 1

Three types of proofs

Answer 1

Flow proof, Paragraph proof, Two Column Proof

Question 2

What are postulates 2.1 through 2.15 about?

Answer 2

Basic rules about points and lines, and other rules about segments and angles

Question 3

Postulates 2.1-2.7

Answer 3

-if there are two points there is exactly one line going through them
-if there are 3 non collinear points there is exactly one plane going through them
-Every line has at least 2 points that define it
-Every plane has at least three points that define it
-If there are two points on a plane, the line containing them is also on that plane
-Two lines intersect ant one point
-Two planes intersect at one line

Question 4

Ruler postulate (2.8)

Answer 4

The distance between two points on a line can be measured
-Used rarely

Question 5

Segment Addition Postulate (2.9)

Answer 5

If A, B, and C are collinear and B is between A and C then AB+ BC= AC
-Used to simplify connecting segments into one segment

Question 6

Protractor Postulate (2.10)

Answer 6

Angles can be measures
- Used Rarely

Question 7

Angle Addition Postulate (2.11)

Answer 7

point D is on the interior of angle ABC if and only if ABD + DBC = ABC
-Used to simplify adjacent angles and split them apart

Question 8

Corresponding Angles Postulate

Answer 8

If two parallel Lines are cut by a transversal then each pair of corresponding angles are congruent.
-Use to find angle measures

Question 9

Converse of Corresponding Angles Postulate

Answer 9

If the pairs of corresponding angles are congruent, the the lines being cut by a transversal are parallel.
-Used to prove parallel lines

Question 10

Parallel Postulate

Answer 10

If Given a line and a non collinear point, the point has exactly one line running through it that would be parallel to the given line
-Rarely Used

Question 11

Perpendicular Postulate

Answer 11

If Given a line and a non collinear point, the point has exactly one line running through it that would be parallel to the given line
-Rarely Used

Question 12

What are the properties of real numbers

Answer 12

-addition, subtraction, multiplication, division

• reflexive (a=a), symmetric (a=b, b=a), transitive (a=b, b=c, then a=c), substitution, distributive (a(b+c)=ab+ac)

Question 13

Midpoint theorem

Answer 13

2.1 M is the midpoint of AB if and only if AM=MB
-use to convert _ is the mid point of _ into an equation
-often first step

Question 14

2.2 Properties of segment congruence

Answer 14

Reflexive, Symmetric, Transitive
-not commonly used

Question 15

2.3 Supplement Theorem, and 2.4 Complement theorem

Answer 15

• If there is a linear pair, the two angles are supplementary

-If the non common sides of adjacent angles form a right angle, the angles are complementary

-Used to convert image/given to equation

Question 16

2.5 Properties of segment congruence theorem

Answer 16

Reflexive Symmetric, Transitive
-not commonly used

Question 17

2.6 Congruent Supplements, and 2.7 Congruent Complements (THEOREMS)

Answer 17

If two angles complement/supplement to the same angle then they are are congruent

-used from drawings

Question 18

2.8 Vertical Angle theorem

Answer 18

Vertical Angles are congruent
- used from drawings

Question 19

2.9 through 2.13, right angle theorems

Answer 19

• Perpendicular lines intersect to form 4 right angles
• All right angles are congruent
• perpendicular lines form congruent adjacent angles
• if two angles are congruent and supplementary they are right
• If two angles are congruent and form a linear pair they are right

Question 20

2.14 Alternate Interior Angles theorem and 2.20 Alternate Interior Angles Converse theorem

Answer 20

-AIA are always congruent if transversal cuts parallel lines
-If AIA are congruent then transversal cuts parallel lines

-used to prove angle measure or that lines are parallel

Question 21

2.17 CIA theorem, and 2.21 converse theorem

Answer 21

-CIA are always congruent if transversal cuts parallel lines
-If CIA are congruent then transversal cuts parallel lines

-used to prove angle measure or that lines are parallel

Question 22

2.16 AEA Theorem, and 2.22 AEA converse theorem

Answer 22

-AEA are always congruent if transversal cuts parallel lines
-If AEA are congruent then transversal cuts parallel lines

-used to prove angle measure or that lines are parallel

Question 23

2.17 Perpendicular transversal theorem

Answer 23

If a transversal is perpendicular to one of two parallel lines it is perpendicular to the other

-used to prove angle measure=90

Question 24

2.18 slope of parallel lines, and 2.19 slope of perpendicular lines

Answer 24

-parallel lines have the same slope
-perpendicular lines have opposite slope

Question 25

2.24 Two Lines Equidistant from a Third Theorem

Answer 25

If two lines are equidistant from a third they are parallel

Question 26

Definition of congruence

Answer 26

Used Often! switch from congruence to equals and back

Question 27

4.1 Triangle Sum theorem

Answer 27

The sum of all the angles in a triangle is 180

Question 28

4.2 Exterior angle theorem

Answer 28

The exterior angle is the sum of the two remote interior angles

Question 29

4.3 Third angles theorem

Answer 29

If two of the angles in a triangle are congruent to the angles in another triangle, the third angles are congruent too

Question 30

4.4 Triangles properties of congruence theorem

Answer 30

reflexive, symmetric, transitive

Question 31

Definition of congruent polygons

Answer 31

Used like definition of congruence but for polygons

Question 32

AAS, SSS, SAS, ASA (THEOREMS/POSTULATES?)

Answer 32

A= angle S= side If two triangles have AAS, SSS, SAS, or ASA congruent then the triangles are congruent

Question 33

CPCTC

Answer 33

stands for, corresponding parts of congruent triangles are congruent. - use to prove corresponding parts of triangles are equal in measure

Question 34

What do L, A, S, and H stand for?

Answer 34

L- leg (right triangle) H- hypotenuse (right triangle A- angle S- side

Question 35

What are the right triangle congruence theorems?

Answer 35

LL, LA, HL, AH right triangles are congruent if any of these parts are given congruent.

Question 36

What are the properties of an equilateral triangle

Answer 36

The legs are congruent, the angle not opposite to either leg is the vertex, the angles that are opposite to the legs are the base angles

Question 37

4.10 Isosceles triangle theorem

Answer 37

The base angles in an isosceles triangles are congruent

Question 38

4.3 properties of an equilateral triangle

Answer 38

a triangle is equilateral if an only if its equal-angular

Question 39

4.4 properties of an equilateral triangle

Answer 39

each angle of an equilateral triangle measures 60