MATH U10

Choose the statement that completes the following statement: If one straight angle measures 180° and another straight angle measures π rad, then we know that

180° = π

Consider the following axiom set: Axiom 1: Every cat has at least three cans of catnips. Axiom 2: Every can of catnips has at least two cats. Axiom 3: There exist at least two cats. What is the minimum number of cans of catnips?

3

These are statements accepted as true and do not need a proof.

Axioms

Select the conclusions that follow when the partition axiom is applied to the following data:

BD = 6 + 7 = 13 AD = 4 + 6 + 7 = 17 AC = 4 + 6 = 10

What axiom states the following: If equal quantities are multiplied by equal quantities, the products are equal. That is, if a = b and c = d, then ac = bd

Multiplication

Which of the following statements is not true?

No geometric figure can be moved without change in size or shape.

What axiom states the following: The whole equals the sum of its parts.

Partition

Draw out the correct conclusion from the following statements: 1. Points M, J, and B lie on the same line and MJ = JB. 2, R is the midpoint of MB

R and J represent the same point

These are statements proven by axioms.

Theorems

Consider the following axiom set: Axiom 1: Every cat has at least three cans of catnips. Axiom 2: Every can of catnips has at least two cats. Axiom 3: There exist at least two cats. Choose the correct proof for the axiom, "There exist at least two cans of catnips."

There exist at least two cats. Every cat has at least three cans of catnips; thus, there exist at least two cans of catnips

What axiom states the following: Things equal to the same or equal things are equal to each other. That is, if a = b and c = b, then a = c.

Transitive

Which of the following can only be described to have meanings.

Undefined terms

What are the undefined terms in the following axiom? Every bee belongs to two and only two hives.

bee, hives, belongs

What is the relation in the following axiom? Every path is between two ants.

between

What are the undefined terms in the following axiom? There are at least two buildings on campus.

buildings, campus, on

Consider the following axiom set: Axiom 1: Every cat has at least three cans of catnips. Axiom 2: Every can of catnips has at least two cats. Axiom 3: There exist at least two cats. What are the undefined terms in the axiom set?

cat, can of catnips, has

What is/are the element(s) in the following axiom? For any herd, there exists a sheep not in the herd.

herd, sheep

How many straight lines can be drawn through any two points?

only one

Choose the statement that completes the following sentence: If two polygons of equal area both quadruple in size, then ____

the two polygons will still have the same area

What conclusion follows when the transitive axiom is applied to the following data? 1. ∠A, ∠B, and ∠C measure 90° each 2. A right angle is an angle that measures 90°.

∠A, ∠B, and ∠C are right angles