Topic 1 Review

A statement accepted without proof is a ________________.

• postulate

• theorem

• biconditional

• conjecture

Arriving at a conclusion by observing patterns is __________.

• Law of Detachment

• deductive reasoning

• inductive reasoning

• Law of Syllogism

A ___________ is the combination of a conditional and its converse.

• inverse

• conjecture

• contrapositive

• biconditional

According to the _____________, if a conditional statement and its hypothesis are true, then its conclusion is also true.

• Law of Syllogism

• Law of Detachment

• conjecture

• deductive reasoning

A conjecture that has been proven is a _____________.

• biconditional

• converse

• postulate

• theorem

A statement of the form "if not q, then not p" is a __________ of the conditional "if p, then q".

• contrapositive

• converse

• inverse

• biconditional

You use ___________ when you logically come to a valid conclusion based on given statements.

• Law of Detachment

• inductive reasoning

• Law of Syllogism

• deductive reasoning

LN = 45. Find x.

• 6

• $\frac{17}{2}$

• 14

• None of the above.

Answer explanation

LM + MN = LN
(3x + 2) + (x + 19) = 45
3x + 2 + x + 19 = 45
3x + x + 2 + 19 = 45
4x + 21 = 45
4x = 24
x = 6

 $m\angle GBH=28\degree;\ \ m\angle GBC=$  ___

•  $28\degree$  

•  $14\degree$  

•  $56\degree$  

• None of the above.

Answer explanation

 $m\angle GBH\ =\ 28\degree$  and has TWO arc marks. We also see that  $\angle HBC$  has TWO arc marks. 

Therefore, we ccan assume that  $\angle HBC\ =\ 28\degree$  . 

We are looking for the measure of  $\angle GBC$  , which consists of both  $\angle GBH\ \&\ \angle HBC$  . 

So 28 + 28 = 56, so our answer is  $56\degree$  .

Why must the compass width be larger than half the segment width to draw a perpendicular bisector?

• False; The compass must be less than half of the segment.

• To make a copy the segment.

• The arcs will intersect if the compass width is less than half of the segment width.

• The arcs will not intersect if the compass width is less than half of the segment width.