This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
This will help you in differentiating subsets of a line such as line segments, ray and opposite rays. Also in finding the number of line segments and rays in a given line.
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This learner's module talks about the topic Reasoning. It also includes the definition of Reasoning, Types of Reasoning (Inductive and Deductive Reasoning) and Examples of Reasoning for each type of reasoning.
This powerpoint presentation is an introduction for the topic TRIANGLE CONGRUENCE. This topic is in Grade 8 Mathematics. I hope that you will learn something from this sides.
This will help you in differentiating subsets of a line such as line segments, ray and opposite rays. Also in finding the number of line segments and rays in a given line.
For more instructional resources, CLICK me here! 👇👇👇
https://tinyurl.com/y9muob6q
LIKE and FOLLOW me here! 👍👍👍
https://tinyurl.com/ycjp8r7u
https://tinyurl.com/ybo27k2u
This learner's module talks about the topic Reasoning. It also includes the definition of Reasoning, Types of Reasoning (Inductive and Deductive Reasoning) and Examples of Reasoning for each type of reasoning.
What is the missing reason in the proof Given with diagonal .docxalanfhall8953
What is the missing reason in the proof?
Given: with diagonal
Prove:
Statements
Reasons
1.
1. Definition of parallelogram
2.
2. Alternate Interior Angles Theorem
3.
3. Definition of parallelogram
4.
4. Alternate Interior Angles Theorem
5.
5. ?
6.
6. ASA
A. Reflexive Property of Congruence
B. Alternate Interior Angles Theorem
C. ASA
D. Definition of parallelogram
Find the values of a and b. The diagram is not to scale.
A.
B.
C.
D.
Complete this statement: A polygon with all sides the same length is said to be ____.
A. regular
B. equilateral
C. equiangular
D. convex
Which statement is true?
A. All squares are rectangles.
B. All quadrilaterals are rectangles.
C. All parallelograms are rectangles.
D. All rectangles are squares.
What is LM?
A. 176
B. 98
C. 88
D. 32
Which description does NOT guarantee that a trapezoid is isosceles?
A. congruent bases
B. congruent legs
C. both pairs of base angles congruent
D. congruent diagonals
Which description does NOT guarantee that a quadrilateral is a square?
A. has all sides congruent and all angles congruent
B. is a parallelogram with perpendicular diagonals
C. has all right angles and has all sides congruent
D. is both a rectangle and a rhombus
Which statement can you use to conclude that quadrilateral XYZW is a parallelogram?
A.
B.
C.
D.
and Find
The diagram is not to scale.
A. 60
B. 10
C. 110
D. 20
WXYZ is a parallelogram. Name an angle congruent to
A.
B.
C.
D.
The Polygon Angle-Sum Theorem states: The sum of the measures of the angles of an n-gon is ____.
A.
B.
C.
D.
Which Venn diagram is NOT correct?
A.
B.
C.
D.
Classify the figure in as many ways as possible.
A. rectangle, square, quadrilateral, parallelogram, rhombus
B. rectangle, square, parallelogram
C. rhombus, quadrilateral, square
D. square, rectangle, quadrilateral
In the rhombus, Angle 1 = 140. What are Angles 2 and 3?
The diagram is not to scale.
A. Angle 2 = 40 and Angle 3 = 70
B. Angle 2 = 140 and Angle 3 = 70
C. Angle 2 = 40 and Angle 3 = 20
D. Angle 2 = 140 and Angle 3 = 20
Use less than, equal to, or greater than to complete this statement: The sum of the measures of the exterior angles of a regular 9-gon, one at each vertex, is ____ the sum of the measures of the exterior angles of a regular 6-gon, one at each vertex.
A. cannot tell
B. less than
C. greater than
D. equal to
Lucinda wants to build a square sandbox, but she has no way of measuring angles. Explain how she can make sure that the sandbox is square by only measuring length.
A. Arrange four equal-length sides so the diagonals bisect each other.
B. Arrange four equal-length sides so the diagonals are equal lengths also.
C. Make each diagonal the same length as four equal-length sides.
D. Not possible; Lucinda has to be able to measure a right angle.
Whi.
Name the intersection of plane ACG and plane BCG.ACBGCGD. .docxrosemarybdodson23141
Name the intersection of plane ACG and plane BCG.
AC
BG
CG
D. The planes need not intersect
Which diagram shows plane PQR and plane QRS intersecting only in ?
A
B
C
D
If Z is the midpoint of what are x, RZ, and RT?
A. x = 18, RZ = 134, and RT = 268
B. x = 22, RZ = 150, and RT = 300
C. x = 20, RZ = 150, and RT = 300
D. x = 20, RZ = 300, and RT = 150
In the figure shown, . Which of the following statements is false?
A.
B. BEC and AED are vertical angles.
C. AEB and BEC are vertical angles.
D.
____ two points are collinear.
A. Any
B. Sometimes
C. No
What is the name of the ray that is opposite ?
A.
B.
C.
D.
Name an angle adjacent to
A.
B.
C.
D.
What is the intersection of plane STXW and plane SVUT?
A.
B.
C.
D.
bisects and Solve for x and find The diagram is not to scale.
A. x = 13,
B. x = 13,
C. x = 14,
D. x = 14,
How are the two angles related?
A. supplementary
B. adjacent
C. vertical
D. complementary
Name an angle complementary to
A.
B.
C.
D.
Find the coordinates of the midpoint of the segment whose endpoints are H(6, 4) and K(2, 8).
A. (4, 4)
B. (2, 2)
C. (8, 12)
D. (4, 6)
What is a counterexample for the conjecture? Conjecture: The product of two positive numbers is greater than the sum of the two numbers.
A. 3 and 5
B. 2 and 2
C. A counterexample exists, but it is not shown above.
D. There is no counterexample. The conjecture is true.
Which conditional has the same truth value as its converse?
A. If x = 7, then .
B. If a figure is a square, then it has four sides.
C. If x – 17 = 4, then x = 21.
D. If an angle has a measure of 80, then it is acute.
Name the Property of Congruence that justifies the statement: If .
A. Symmetric Property
B. Transitive Property
C. Reflexive Property
D. none of these
Substitution Property of Equality If , then ______.
A.
B.
C.
D.
Identify the hypothesis and conclusion of this conditional statement: If two lines intersect at right angles, then the two lines are perpendicular.
A. Hypothesis: The two lines are perpendicular. Conclusion: Two lines intersect at right angles.
B. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are perpendicular.
C. Hypothesis: The two lines are not perpendicular. Conclusion: Two lines intersect at right angles.
D. Hypothesis: Two lines intersect at right angles. Conclusion: The two lines are not perpendicular.
Which biconditional is NOT a good definition?
A. A whole number is even if and only if it is divisible by 2.
B. A whole number is odd if and only if the number is not divisible by 2.
C. An angle is straight if and only if its measure is 180.
D. A ray is a bisector of an angle if and only if it splits the angle into two angles.
Transitive Property of Congruence If ______.
A.
B.
C.
D.
Which statement is an example of the.
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2. Pre-test
2
1. What do you call the statements that are assumed to
be true and do not
need proof?
A. axioms
B. defined terms
C. theorems
D. undefined terms
3. Pre-test
3
2. There are four parts of the Mathematical system.
Which of the following is not a part of the mathematical
system?
A. corollary
B. theorems
C. axioms or postulate
D. defined and undefined terms
4. Pre-test
4
3. Which of the following statements is true about axioms
or postulates?
A. These are concepts that need to be defined.
B. These are statements accepted after it is proved
deductively.
C. These are concepts that can be defined using the
undefined terms.
D. These are statements assumed to be true and need
no further proof.
5. Pre-test
5
4. Which of the following statements is true about a
postulate?
A. It is never accepted to be true.
B. It is accepted as true without a formal proof.
C. It is only accepted as true after being formally proven.
D. It is usually not obvious as true, so it must be proven.
6. Pre-test
6
5. Which of the following best describes a theorem?
A. It is the same thing as a postulate.
B. It is a statement that is accepted as true without a
formal proof.
C. It is a statement that is impossible to be proven by
mathematical reasoning.
D. It is a statement that has been formally proven using
mathematical reasoning.
7. Pre-test
7
6. Which of the following is NOT a property of
Mathematical system?
A. conjecture C. postulates
B. define terms D. theorems
8. Pre-test
8
7. Which of the following statements is true about
defined terms?
A. These are concepts that need to be defined.
B. These are statements accepted after it is proved
deductively.
C. These are concepts that can be defined using the
undefined terms.
D. These are statements assumed to be true and need
no further proof.
9. Pre-test
9
8. Which of the following illustrates reflexive property?
A. (𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = (𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷
B. (𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = (𝐵𝐶 + 𝐴𝐵) + 𝐶𝐷
C. (𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = 𝐴𝐵 + 𝐵𝐶 + 𝐶𝐷
D. (𝐴𝐵 + 𝐵𝐶) + 𝐶𝐷 = 𝐶𝐷 + (𝐴𝐵 + 𝐵𝐶)
10. Pre-test
10
9. Which of the following illustrates distributive property
of equality?
A. 3 + 4 = 4(3) + 3(4)
B.5(2) + 6(7) = 5(7) + 6(2)
C.8(𝑥 + 𝑦 + 𝑧) = 8𝑥 + 8𝑦 + 8𝑧
D.−8(𝑥 + 𝑦 + 𝑧) = −8𝑥 + 𝑧 + 𝑦
11. Pre-test
11
10. Which of the following is a commutative axiom?
A. 2 + 3 = 2 + 3 C. 2 ∙ 3 = 2 ∙ 3
B. 2 + 3 = 3 + 2 D. (2 + 3) = 2(3) + 3(2)
12. Objectives:
12
1.Define each part of the mathematical system;
a. Undefined terms
b. Defined terms
c. Postulates
d. Theorems;
2. Illustrate how the four parts of mathematical
system related to one another.
13. MATHEMATICAL SYSTEM
13
UNDEFINED
TERMS
DEFINED
TERMS
AXIOMS/
POSTULATES
THEOREMS
in geometry, we
come across with
terms which
cannot be
precisely defined.
In modern
mathematics. We
do accept certain
undefined terms by
description.
Unlike undefined
terms (which do
not have formal
definition), these
have a formal
definition. They
are used to define
even more terms.
A statement which
is accepted as
true without
proof. These
statements can be
used as reasons in
proving some
mathematical
statements.
a statement that
can be proven.
Once a theorem is
proven, it can also
be used as a
reason in proving
other statements.
20. Directions: Identify whether each of the following
represents a point, line or a plane.
1. Stars in the sky
2. Curtain rod
3. Edge of a ruler
4. Cartolina
5. A knot on a piece of thread
6. A clothesline
20
7. Top of a box
8. Page of a book
9. A magic wand
10. Button
11. Mole
12. Handkerchief
Point
Line
Line
Plane
Point
Line
Plane
Plane
Line
Point
Point
Plane
22. Point
22
• A point is a position in space. It has only location but no
dimension; length, width, thickness and does not occupy
an area.
• It is named using a CAPITAL LETTER and it can be
modeled by a dot.
A
B
C
D
• All other geometric figures are made up of a collection of
points.
23. Line
23
• A straight, continuous arrangement of infinitely many
points. Its length is infinite. It extends infinitely in two
directions. And it has no thickness.
• The arrowhead symbolizes infinity
• Lines are named by a single lower case script letter or by
any two points on a line
25. Plane
● A flat surface that extends along its length and
width. It is like an “infinite sheet of paper”.
● It has length and width but no thickness
● It is named by a single script CAPITAL LETTER or by
any three points in the plane which are not on the
same line.
25
26. Plane
● A flat surface that extends along its length and
width. It is like an “infinite sheet of paper”.
● It has length and width but no thickness
● It is named by a single script CAPITAL LETTER or by
any three points in the plane which are not on the
same line.
26
D
plane D
L I
E F
plane LIF
plane IFE
plane LEF
plane EFI
plane LIFE
● At least three noncollinear
points determine a plane.
27. Defined Terms
27
Collinear Points Non-collinear Points
A B C
Points A, B, and C are colinear
points
A B
C
Points A, B, and C are non-
colinear points
are points that lie on the same line are points that do not lie on the
same line
28. 28
Defined Terms
Coplanar Points Non-coplanar Points
A
B
C
Points A, B, and C are coplanar
points
B
C
A
Points A, B, and C are non-
coplanar points
are points that lie in the same
plane
are points that do not lie in the
same plane
29. Subsets of a Line
LINE SEGMENT
29
A B
A B A B B
A C
A line segment is a part of a
line consisting two
endpoints and all the points
in between.
A line segment may be called:
AB or BA
Its endpoints are A and B.
RAY
A ray is a part of a line with
one endpoint and extending
in only one direction.
A ray is named with its endpoint
first, followed by another point
on the ray.
The ray can be named AB read
as “ray AB”
OPPOSITE RAY
are rays with a common
endpoint but extending in
opposite directions.
Common Endpoint: B
Opposite rays:
BA and BC
B is between points A and C
30. 30
Let’s Try!
1. Name all the points.
A, W, X, Y and Z
2. Name all the lines using a script letter.
line a line b line c line d
3. What is the other name for line a?
line WZ or line ZW
4. Using a script letter, name a plane form
by the four lines.
plane L
5. Name the plane in three different ways
using three points.
plane WXY plane XYZ plane WZY
W X
Z Y
L
A
c
d
a b