Test 3

Question 1

four ways to prove congruent triangles

Answer 1

AAS
SSS
SAS
ASA

Question 2

four ways to prove similar triangles

Answer 2

AA
AAA
sss
sAs

Question 3

circle

Answer 3

set of points whose distance from a given point is the same

Question 4

using vs proving a theorem

Answer 4

Prove:
-If: suppose this is true
-Then: argue this must be true
Use: argue the If, the then automatically follows and is true

Question 5

Why does SSA not work?

Answer 5

You can have to triangles with SSA that do not look nothing alike

Question 6

congruent

Answer 6

same shape and size

Question 7

similar

Answer 7

same shape

Question 8

how can you prove right triangles?

Answer 8

HA
HL
LL
LA

Question 9

E15
E27
E29

Answer 9

-vertical angles
-alt. interior angles, then parallel
-parallel, then congruent alt. and corresponding angles

Question 10

Which proofs require a construction?

Answer 10

E9 - bisect an angle
E1 - equilateral triangle
E10 - bisect a segment

Question 11

Prove the Pythagorean theorem part 1

Question 12

Axiomatic Geometry

Answer 12

theorems are proved using definitions, axioms, postulates, and previously proven theorems by means of accepted rules of logic

Question 13

Similarities and Differences between different types of geometry

Answer 13

SIMILAR
-definitions are the same
-spherical: certain shapes are the same with the same properties
-taxicab: parallel lines

DIFFERENT
-spherical: no parallel lines
-taxicab: no round circles
-spherical: sum of all angles in a triangle is greater than 180

Question 14

Kissing Cousins

Answer 14

parallel - alternate interior angles
perpendicular - adjacent, linear, and congruent angles

Question 15

Invariant Properties:
translation
rotation
reflection
dilation

Answer 15

angle measure stays the same for all four

line segment stays the same except for dilation

axis orientation is a yes for translation and dilation but a no for rotation and reflection

point orientation stays the same except for reflection

parallel and perpendicular stay the same for all four

Question 16

What do you have to do before using cpctc?

Answer 16

prove the triangles congruent
state the corresponding parts

Question 17

two difference between definition and property

Answer 17

-definition has been accepted as true, whereas, property must be proven to be true
-there are multiple properties, whereas, there is only one definition

Question 18

Pythagorean Theorem (2 if-thens)

Answer 18

if you have a right triangle, then a^2+b^2=c^2

if there is any tirangle that works with a^2+b^2=c^2, then it is a right triangle

Question 19

Why are definition important?

Answer 19

-definitions are proven to be true
-you can use them in different contexts
-

Question 20

Postulate 5

Answer 20

if you have two lines crossed by a transversal form 2 interior angles on the same side of the transversal so that their sum is less than 2 right angles, then:
a) the lines intersect and
b) the lines intersect on the same side as the angles

Question 21

Axiom 5

Answer 21

Whole is greater than any of its parts

Question 22

What are you supposed to know about the remaining parts if ASA?

Answer 22

the other matching parts are congruent whether it be sides or angles

Question 23

What is true about the other parts after AA?

Answer 23

-all the other matching sides are in proportion
-all the other matching angles are congruent