bell work 1) name the congruent triangles and the congruence shortcut that verifies their...
TRANSCRIPT
![Page 1: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/1.jpg)
Bell Work• 1) Name the congruent triangles and the congruence shortcut
that verifies their congruence:
• 2) Use segment addition to find x• AB = x + 11; BC = 2x + 5; AC = 22
• 3) Angle A and Angle B are complementary: Angle A = 3x + 5 Angle B = 5x + 5. Find x
• 4) Find the value of x and y in the triangle:
![Page 2: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/2.jpg)
AGENDA
• Please turn in your Triangle Drawings!• Chapter 4- Practice Test- To gauge where
you are on those skills. We will go over these on Weds.
• Skill 1-13 Review- You will fill in the sheet as we go along and work on the practice problems.
• Begin Study Guides- Chapter 1 DUE Wednesday.
![Page 3: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/3.jpg)
Outcomes
• I will be able to:• 1) Use and understand skills 1 - 13
![Page 4: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/4.jpg)
Chapter 4 Practice Test
• It is important you try your best to see how you are doing on these skills.
• Like a regular test, this is to be done silently, independently and with shown work.
• You are to find something to do silently or work on your study guide if finished early.
![Page 5: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/5.jpg)
Take Out Your Targeted Review Sheet
• We will do examples and practice problems.
• Please record your answers in the targeted review sheet.
![Page 6: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/6.jpg)
Skill #1 Inductive Reasoning• Inductive Reasoning – Observing data,
recognizing patterns, and making generalizations about that data
• 3 Stages of Inductive Reasoning• 1) Look for a pattern – Look at examples and
use diagrams, tables, and pictures to help discover a pattern.
• 2) Make a conjecture - Use your observations to make “guess” about the pattern.
• 3) Verify the conjecture - Use logical reasoning skills to decide if your conjecture is valid.
![Page 7: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/7.jpg)
Skill #1 Inductive ReasoningPractice
• 1) Find the next 3 numbers in the sequence and describe the pattern:
• -5, 10, -20, 40…• A) -70, 110, -160• B) -80, 160, -320• C) -50, 60, -70• D) -60, 90, -120
• 2) Find the next figure
• A) B)
• C) D)
![Page 8: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/8.jpg)
Skill #2 Writing Conjectures• Conjecture – an unproven statement
based on observations. Conjectures can be modified until they are concrete.
• ***The process of describing what is being observed
• Make a conjecture about the sums of any two odd numbers.
• 1+1 = 2 3 + 7 = 10 • 1 + 3 = 4 5 + 9 = 14• 3 + 5 = 8 7 + 9 = 16
Conjecture: If two odd numbers are added, thenthe result is an even number.
![Page 9: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/9.jpg)
Skill #2 Writing ConjecturesPractice
• 3) Write a conjecture based upon the pattern seen below:
• 4) Write a conjecture based upon the pattern seen below:
![Page 10: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/10.jpg)
Skill #3 Recognizing Points, Lines, and Planes
• You need to be able to use the symbols for points, lines, rays, segments, and planes
• Symbols:• Point: O• Line: PR• Ray: NR• Segment: MN• Plane: STO(must contain at least 3 points
that are on the plane). Unless the plane has a name.
X
![Page 11: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/11.jpg)
Skill #3 Recognizing Points, Lines and Planes
• Collinear: 3 or more points on the same line
• Coplanar: 3 or more points on the same plane
![Page 12: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/12.jpg)
Skill #3 Recognizing Points, Lines, and Planes(Problems)
• 5) Name a ray
• 6) Name 3 coplanar points
• 7) Name 3 noncollinear points
• 8) Name a plane
![Page 13: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/13.jpg)
Skill #4 Counterexamples
• Not all conjectures are true
• Counterexample – an example that shows that a conjecture is false
• Example: If two numbers are positive, then their difference is always positive.
• Counterexample: 1 – 2 = -1
![Page 14: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/14.jpg)
Skill #4 CounterexamplePractice
• 9) Find a counterexample for the following conjecture:
• If a number is prime, then it is odd
• 10) Find a counterexample for the following conjecture:
• If you square root a number, then it is always less than the number
![Page 15: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/15.jpg)
Skill #5 Segment Addition• Segment Addition: Adding two smaller
segments together to get a larger segment.
• Example: If HI = 2x + 3 and IJ = 4x + 1and HJ = 16, find x.
• It may help to draw a picture
• 2x + 3 + 4x + 1 = 16• 6x + 4 = 16• x = 2
![Page 16: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/16.jpg)
Skill #5 Segment AdditionPractice
• 11) AB = 12; BC = 24; AC = 3x. Find x.• 12) EF = 3x – 1; FG = 2x + 6; EG = 25. Find x.
![Page 17: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/17.jpg)
Skill #6 Distance Formula• Distance Formula: Used to determine the
distance of points in the coordinate plane.
• Distance formula =
• Example: A is at (-2, 3) and B is at (6, 9). Find AB.
• 10
212
212 )()( yyxx
22 )39()26( 22 )6()8(
![Page 18: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/18.jpg)
Skill #6 Distance Formula Practice
• 13) Find CD if C is at (5, 1) and D is at (1, 4)
![Page 19: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/19.jpg)
Skill #7 Simplifying Radicals
• If a perfect square exists inside a radical(square root sign), then we can simplify the radical by creating a factor tree and pulling one of the numbers from each pair outside the square root sign.
• Example: 175
25 7
5 5 75
![Page 20: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/20.jpg)
Skill #7 Simplifying Radicals Practice
• 14) If F is at (7, -2) and G is at (3, 10). Find FG. Remember to simplify any radicals.
16014416
104
![Page 21: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/21.jpg)
Skill #8 Angle Measure and Classification
• There were four different classifications for individual angles: acute, right, obtuse, straight.
• Acute – any angle less than 90°• Right – any angle exactly 90°• Obtuse – any angle greater than 90° but
less than 180°• Straight – any angle exactly 180°
![Page 22: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/22.jpg)
Skill #8 Angle Measure and Classification Practice
• Find the angle measure and classify it• 15) Angle EAD
• 16) Angle CAF
• 17) Angle EAB
![Page 23: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/23.jpg)
Skill #9 Midpoint• Midpoint – The point that cuts a line into
two congruent pieces• Example: If N is the midpoint of MO and
MN = 2x + 3 and NO = x + 7. Find x. It may help to draw a picture.
• 2x + 3 = x + 7• x = 4
![Page 24: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/24.jpg)
Skill #9 Midpoint
• Midpoint Formula – a formula used to find the midpoint when points are in the coordinate plane
• Midpoint Formula = • Example: A is at (-2, 2) and B is at (4, 4).
Find the midpoint
• (1, 3)
2,
22121 yyxx
2
42,
2
42
![Page 25: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/25.jpg)
Skill #9 MidpointPractice
• 18) B is the midpoint of AC. Find x• AB = 4x + 5• BC = x + 14
• 19) Find the midpoint between C and D if:• C(5, 1) and D(1, 8)
![Page 26: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/26.jpg)
Skill #10 Angle Bisector
• Angle Bisector – a ray, line, or segment that cuts an angle into two congruent smaller angles
• Example: EF is an angle bisector, find x.• 42 = 2x + 12• x = 15
![Page 27: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/27.jpg)
Skill #10 Angle Bisector Practice
• 20)
![Page 28: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/28.jpg)
Skill #11 Angle Pair Relationships• There are 4 angle relationships that
involve two lines, rays or segments, intersecting each other.
• Vertical Angles – Two angles that share a vertex, are opposite each other, and made from opposite rays
• Linear Pair – Two angles that form a straight line
• Supplementary – Two angles whose sum is 180°
• Complementary – Two angles whose sum is 90°
![Page 29: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/29.jpg)
Skill #11 Angle Pair Relationships Examples
• Vertical Angles
• Linear Pair
• Supplementary
• Complementary
![Page 30: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/30.jpg)
Skill #11 Angle Pair Relationship Practice
• 21) The two angles below form a linear pair. Find x.
• 22) The two angles below are complementary. Find x.
![Page 31: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/31.jpg)
Skill #12 Conditional Statements
• Conditional Statements: Statements that have a hypothesis and a conclusion.
• To be true, both the hypothesis and the conclusion must be true.
• May be written symbolically, where p is the hypothesis and q is the conclusion.
• Example: If it is sunny, then it is warm.• Hypothesis: it is sunny(p)• Conclusion: it is warm(q)• In symbols: p --> q
![Page 32: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/32.jpg)
Skill #13 Converse Statements
• Converse Statement – Switching the hypothesis and the conclusion of a conditional statement
• Conditional: If it is sunny, then it is warm.• Converse: • If it is warm, then it is sunny.
![Page 33: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/33.jpg)
Skill #14 Inverse Statements
• Inverse Statement – negating both the hypothesis and the conclusion of a conditional statement.
• Conditional: If it is sunny, then it is warm.• Inverse: If it is not sunny, then it is not
warm.
![Page 34: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/34.jpg)
Skill #15 Contrapositive Statements
• Contrapositive Statement – Negating both the hypothesis and the conclusion of a converse statement
• Conditional: If it is sunny, then it is warm.• Converse: If it is warm, then it is sunny.• Contrapositive: If it is not warm, then it is
not sunny.
![Page 35: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/35.jpg)
Skill #’s 12-15 Practice
• Conditional statement:• If it is freezing outside, then there is snow
on the ground.• 23) Write the converse of the statement• 24) Write the inverse of the statement• 25) Write the contrapositive of the
statement
![Page 36: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/36.jpg)
Skill #16 Biconditional Statements• Biconditional Statement – Any statement with
the phrase “if and only if” in it. • To verify if a biconditional is true, break it down
to check the validity of the conditional statement and it’s converse.
• Example: Two triangles are congruent if and only if their corresponding parts are congruent.
• Conditional: If two triangles are congruent, then their corresponding parts are congruent.
• Converse: If their corresponding parts are congruent, then two triangles are congruent.
![Page 37: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/37.jpg)
Skill #16 BiconditionalPractice
• Determine if the following is a biconditional statement. If it is a biconditional, is it true?
• 26) A polygon is a square if and only if it has 4 sides.
![Page 38: Bell Work 1) Name the congruent triangles and the congruence shortcut that verifies their congruence: 2) Use segment addition to find x AB = x + 11; BC](https://reader033.vdocument.in/reader033/viewer/2022051820/56649e405503460f94b3222c/html5/thumbnails/38.jpg)
Study Guide Check Wednesday
• Chapter 1 and 2 of the study guide should be completed