# Algebra and Geometry Exercises Solutions

```Jasmine Althea Derige / Kei Rivas
Date Started: January 3, 2021
Date Completed: January
If-then Statements
III. Activity
A.
1.
2.
3.
Hypothesis
: Today is Saturday.
Conclusion
: The day after today is Sunday.
Hypothesis
: It’s sunny.
Conclusion
: You should apply sun block on your skin.
Hypothesis
: A closed figure is a rhombus.
Conclusion
B.
1. If a shape is an octagon, then it has eight sides.
2. If the lines are perpendicular, then it forms right angles.
3. If a number is even, then it is divisible by 2.
4. If a triangle is an equilateral, then it has three congruent sides.
Converse, Inverse, and Contrapositive Statements
III. Activity
1. Inverse
hexagon.
Converse
Contrapositive
sides.
2. Inverse
same length.
Converse:
Contrapositive
congruent.
: If a polygon does not have six sides, then it is not a
: If a polygon is a hexagon, then it has six sides.
: If a polygon is not a hexagon, then it does not have six
: If segments are not congruent, then they do not have the
: If segments have the same length, then they are congruent.
: If segments do not have the same length, then they are not
3. Inverse
Converse
Contrapositive
4. Inverse
Converse
Contrapositive
5. Inverse
Converse
Contrapositive
teacher.
: If I will not win the game, then I will not get a prize.
: If I’ll get the prize, then I win the game.
: If I will not get a prize, then I will not win the game.
: If you are not a dog, then you know how to fly.
: If you do not know how to fly, then you are a dog.
: If you know how to fly, then you are not a dog.
: If a woman is not a teacher, then she is not a college
: If a woman is a college graduate, then she is a teacher.
: If a woman is not a college graduate, then she is not a
Mathematical Reasoning
I.
Activity
CONDITIONAL
INVERSE
1. If it is 2016, then If it is not
it is a leap year. 2016, then it
is not a leap
year.
2. If it is 10x=5,
If it is not
then it is x=2.
10x=5, then
it is not x=2.
3. If a polygon has If a polygon
congruent sides does not
and angles, then have
it is regular.
congruent
sides and
angles, then
it is not
regular.
4. If the angles are If the angles
vertical, then
are not
they are equal.
vertical,
then they
are not
equal.
5. If an animal is a If an animal
bird, then it has is not a bird,
feathers.
then it has
no feathers.
CONVERSE
If it is a leap year,
then it is 2016.
CONTRAPOSITIVE
If it is not a leap year,
then it is not 2016.
If it is x=2, then it
is 10x=5.
If it is not x=2, then it is
not 10x=5.
If a polygon is
regular, then it
has congruent
sides and angles.
If a polygon is not
regular, then it does not
have congruent sides
and angles.
If the angles are
equal, then they
are vertical.
If the angles are not
equal, then they are not
vertical.
If an animal has
feathers, then it is
a bird.
If an animal does not
have feathers, then it is
not a bird.
POST-TEST
KNOWLEDGE
1. If you eat too much, then you will get fat.
2. If lines p and q intersect, then lines p and q have at least one point in common.
3. If two angles are supplements of the same angle, then they are equal.
PROCESS
1. Inverse
: If you will not turn the television off, then you will not be
able to study better.
Converse
: If you will be able to study better, then you turn the
television off.
Contrapositive
: If you will not be able to study better, then you will not turn
the television off.
2. Inverse
: If a triangle is not isosceles, then it does not have two equal
angles.
Converse
: If a triangle has two equal angles, then it is isosceles.
Contrapositive
: If a triangle does not have two equal angles, then it is not
isosceles.
3. Inverse
: If lines on the same plain intersect, then they are not called
parallel.
Converse
: If lines are called parallel, then they intersect on the same
plane.
Contrapositive
: If lines are not called parallel, then they do not intersect on
the same plane.
PROCESS
1.
(4,5)
)
(-2,-8)
2.
(5,10)
(4,8)
(3,6)
(2,4)
(1,2)
3.
(0,2)
(6,0)
4.
(-3,0)
(-1,1)
```