Points, Lines, Planes, Line segments
Which is the correct way to label a plane?
1. plane 5
2. plane BCD
3. plane G
4. plane abc
2.
The _ between two points is the length of the segment between the points. The coordinates of the points can be user to find the length of the segment.
Distance, Coplanar, Segment or Endpoints
Distance
Answer true or false.
1. If an object is red, then it is not blue.
2. If an object is not red, then it is not blue.
3. If an object is not blue, then it is not red.
4. If an object is blue, then it is not red.
5. Rewrite this statement as a true if-then statement.
An even number is divisible by 2.
Warm Up
1. True
2. False
3. False
4. True
5. If a Number is even, then it is divisible by 2. If a Number is divisible by 2, then it is even
The sum of two odd numbers is always an _ number
1. Odd 2. Even 3. Congruent 4. Bisecting
2. Even
If A→B is a true statement and _ is true, then _ is
true.
A and B
1. _ points are points that lie on the same line.
2. _ points are points that lie in the same plane.
Collinear and Coplanar
What is the midpoint of XZ?
|X| |Z|
-4-3-2-1 0 1 2 3 4 5 6 7 8 9
The midpoint of XZ is 2.5
• If he earns a 3.5 GPA or higher this semester, then he
will be accepted.
• If Aarón is accepted into culinary school, then he has
earned a 3.5 GPA or higher for the semester.
what is this?
Biconditional statement
An isosceles trapezoid is a trapezoid with _ opposite congruent legs.
2
Complementary have a sum of what?
Supplementary have a sum of what?
Complementary = 90 degrees
Supplementary = 180 degrees
Find the measure of XZ if Line segment XY is 11.3cm and YZ is 3.8cm.
15.1 cm
(0, -6)
Find the distance between each pair of points.
1. –35 and 21 on a number line
2. A(5, 0) and B(8, 0)
3. M(6, –2) and N(6, 8)
4. X(4, 4) and Y(9, 16)
1. 56 units
2. 3 units
3. 10 units
4. 13 units
A _ statement is the conjunction of a
conditional and its converse.
Biconditional
a. Given: If three points are noncollinear, then they determine a plane.
Points A, B, and C lie in plane G.
Conclusion: Points A, B, and C are noncollinear.
A. Valid; points A, B, and C determine plane G. Therefore, they are
noncollinear.
B. Valid; because points A, B, and C are noncollinear, they determine
plane G.
C. Invalid; points A, B, and C determine plane G. Therefore, they are
noncollinear.
D. Invalid; points A, B, and C can be collinear and lie in plane G.
D.
Find the measure of PQ if PR is 24.3 cm and QR is 17.8 cm.
6.5 cm
Find Distance on a Number Line
|A| |B| |C| |D| |E|
-6-5-4-3-2-1 0 1 2 3 4 5 6 7 8
Find AE
A. -12 B. 2 C. 12 D. 13
C. 12
CK is 174 cm
1. Find CG.
2. Find GK.
Use the number line.
Is each statement true or false?
3. CE + EH =CH
4. DJ + JG = DG
1. 109cm
2. 65cm
3. true
4. false
Write the conditional and converse for the statement. Determine
the truth values of the conditional and converse. If false, find a
counterexample. Write a biconditional statement if possible.
Isosceles triangles have at least two congruent sides.
Conditional: If a triangle is isosceles, then it has at least two congruent
sides.
Converse: If a triangle has at least two congruent sides, then it is
isosceles.
The conditional is true, and the converse is true.
Biconditional: A triangle is isosceles if and only if it has at least two
congruent sides.
4x + 5 = 4(17) + 5 Substitute 17 for x.
= 68 + 5 Multiply.
= 73 Solve.
The measures of the angles are 17° and 73°.
Find the value of x and BC if B is between A and C,
AC = 4x −12, AB = x, and BC = 2x + 3.
x=15
A B C D E F G H I J K L M
-8-7-6-5-4-3-2-1 0 1 2 3 4
True or False
1. D is the midpoint of BG
2. E is the midpoint of AI
1. False
2. True
b. Given: If Dakota goes to the video game store, then he will buy a
new game.
Dakota went to the video game store this afternoon.
Conclusion: Dakota bought a new game.
C. Valid; because the statement Dakota went to the video game
store this afternoon satisfies the hypothesis of the conditional
statement, the conclusion is true.
D. Invalid; because the statement Dakota went to the video game
store this afternoon satisfies only the hypothesis, the conclusion
is not true.
C.
Write the conditional and converse for each statement.
Determine the truth values of the conditionals and
converses. If false, find a counterexample. Write a
biconditional statement if possible.
a. Rasha listens to music when she is in study hall.
b. If two lines are parallel, then they have the same
slope and different y-intercepts.
a. Rasha listens to music when she is in study hall.
Conditional: If Rasha is in study hall, then she is listening to music.
Is the conditional statement true or false? If false, provide a
counterexample. true
Converse: If Rasha is listening to music, then she is in study hall.
Is the converse true or false? If false, provide a counterexample.
False; sample answer: Rasha could be listening to music in the
cafeteria.
Because the converse is false, a biconditional statement cannot
be written.
Given: If you do not get
enough sleep,
p: You do not get enough
sleep.
then you will be tired. q: You will be tired.
If you are tired, then
you will not do well on
your test.
r: You will not do well on your
test.
THis is the law of?
Syllogism