pattern
find one counterexample to show that each conjecture is false.
5. for two real numbers a and b, a is either equal to b or greater than b.
6. all quadrilaterals are parallelograms.
1 - 5 additional practice conditional statements
write each sentence as a conditional.
1. a regular hexagon has exactly six congruent sides.
2. two supplementary angles form a line.
determine the truth value of each conditional. explain your reasoning or give a counterexample.
3. if a figure has four congruent angles, then the figure is a square.
4. if the sidewalks are wet, then it has been raining.

Question

Accepted Answer

# 1. Write each sentence as a conditional
## 1.
# Brief Explanations:
A conditional statement has the form "If $p$, then $q$". Here, $p$ is "a figure is a regular hexagon" and $q$ is "it has exactly six congruent sides".
# Answer:
If a figure is a regular hexagon, then it has exactly six congruent sides.

## 2.
# Brief Explanations:
For the statement "Two supplementary angles form a line",  $p$ is "two angles are supplementary" and $q$ is "they form a line".
# Answer:
If two angles are supplementary, then they form a line.

# 2. Determine the truth - value of each conditional
## 3.
# Brief Explanations:
A counter - example is a rectangle. A rectangle has four congruent angles (each $90^{\circ}$), but it is not a square (a square has four congruent sides in addition to four congruent angles). So the statement "If a figure has four congruent angles, then the figure is a square" is false.
# Answer:
False. A rectangle has four congruent angles but is not a square.

## 4.
# Brief Explanations:
A counter - example is when someone has washed the sidewalks. The sidewalks are wet, but it has not been raining. So the statement "If the sidewalks are wet, then it has been raining" is false.
# Answer:
False. The sidewalks could be wet because they were washed.

# 3. Find one counter - example
## 5.
# Brief Explanations:
Let $a = 1$ and $b=2$. Here $a$ is not equal to $b$ ($1
eq2$) and $a$ is not greater than $b$ ($1<2$).
# Answer:
Let $a = 1$ and $b = 2$.

## 6.
# Brief Explanations:
A trapezoid is a quadrilateral (a four - sided figure). But in a trapezoid, only one pair of sides is parallel (while in a parallelogram, both pairs of opposite sides are parallel).
# Answer:
A trapezoid is a quadrilateral that is not a parallelogram.

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QUESTION IMAGE

Question

Explanation:

1. Write each sentence as a conditional

1.

Answer:

2.