1) The student can identify and prove congruent triangles using three criteria: side-side-side (SSS), side-angle-side (SAS), and hypotenuse-leg (HL).
2) For SSS, if three sides of one triangle are congruent to three sides of another, the triangles are congruent.
3) For SAS, if two sides and the included angle of one triangle are congruent to those of another, the triangles are congruent.
4) For HL, if the hypotenuse and one leg are congruent between two right triangles, the triangles are congruent.
Identify congruent parts based on a congruence relationship statement
Identify and prove congruent triangles given
Three pairs of congruent sides (Side-Side-Side)
Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)
Identify congruent parts based on a congruence relationship statement
Identify and prove congruent triangles given
Three pairs of congruent sides (Side-Side-Side)
Two pairs of congruent sides and a pair of congruent included angles (Side-Angle-Side)
* Name polygons based on their number of sides
* Classify polygons based on concave/convex and equilateral/equiangular/regular
* Calculate and use the measures of interior and exterior angles of polygons
* Name polygons based on their number of sides
* Classify polygons based on concave/convex and equilateral/equiangular/regular
* Calculate and use the measures of interior and exterior angles of polygons
Identify isosceles and equilateral triangles by side length and angle measure
Use the Isosceles Triangle Theorem to solve problems
Use the Equilateral Triangle Corollary to solve problems
* Classify triangles by sides and by angles
* Find the measures of missing angles of right and equiangular triangles
* Find the measures of missing remote interior and exterior angles
Classify triangles by sides and by angles
Find the measures of missing angles of right and equiangular triangles
Find the measures of missing remote interior and exterior angles
* Construct perpendicular and angle bisectors
* Use bisectors to solve problems
* Identify the circumcenter and incenter of a triangle
* Use triangle segments to solve problems
* Model exponential growth and decay
* Use Newton's Law of Cooling
* Use logistic-growth models
* Choose an appropriate model for data
* Express an exponential model in base e
* Identify, write, and analyze conditional statements
* Write the inverse, converse, and contrapositive of a conditional statement
* Write a counterexample to a fake conjecture
* Find the distance between two points
* Find the midpoint of two given points
* Find the coordinates of an endpoint given one endpoint and a midpoint
* Find the coordinates of a point a fractional distance from one end of a segment
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
* Connect functions to their graphs
* Graph piecewise-defined functions
* Graph absolute value functions
* Graph greatest-integer functions
* Interpret graphs
* Use the vertical line test to determine a function
* Introduce functions and function notation
* Develop skills in constructing and interpreting the graphs of functions
* Learn to apply this knowledge in a variety of situations
* Recognize graphs of common functions.
* Graph functions using vertical and horizontal shifts.
* Graph functions using reflections about the x-axis and the y-axis.
* Graph functions using compressions and stretches.
* Combine transformations.
* Identify intervals on which a function increases, decreases, or is constant
* Use graphs to locate relative maxima or minima
* Test for symmetry
* Identify even or odd functions and recognize their symmetries
* Understand and use piecewise functions
* Solve polynomial equations by factoring
* Solve equations with radicals and check the solutions
* Solve equations with rational exponents
* Solve equations that are quadratic in form
* Solve absolute value equations
* Determine whether a relation or an equation represents a function.
* Evaluate a function.
* Use the vertical line test to identify functions.
* Identify the domain and range of a function from its graph
* Identify intercepts from a function’s graph
* Solve counting problems using the Addition Principle.
* Solve counting problems using the Multiplication Principle.
* Solve counting problems using permutations involving n distinct objects.
* Solve counting problems using combinations.
* Find the number of subsets of a given set.
* Solve counting problems using permutations involving n non-distinct objects.
* Use summation notation.
* Use the formula for the sum of the first n terms of an arithmetic series.
* Use the formula for the sum of the first n terms of a geometric series.
* Use the formula for the sum of an infinite geometric series.
* Solve annuity problems.
* Find the common ratio for a geometric sequence.
* List the terms of a geometric sequence.
* Use a recursive formula for a geometric sequence.
* Use an explicit formula for a geometric sequence.
* Find the common difference for an arithmetic sequence.
* Write terms of an arithmetic sequence.
* Use a recursive formula for an arithmetic sequence.
* Use an explicit formula for an arithmetic sequence.
How to Split Bills in the Odoo 17 POS ModuleCeline George
Bills have a main role in point of sale procedure. It will help to track sales, handling payments and giving receipts to customers. Bill splitting also has an important role in POS. For example, If some friends come together for dinner and if they want to divide the bill then it is possible by POS bill splitting. This slide will show how to split bills in odoo 17 POS.
The Roman Empire A Historical Colossus.pdfkaushalkr1407
The Roman Empire, a vast and enduring power, stands as one of history's most remarkable civilizations, leaving an indelible imprint on the world. It emerged from the Roman Republic, transitioning into an imperial powerhouse under the leadership of Augustus Caesar in 27 BCE. This transformation marked the beginning of an era defined by unprecedented territorial expansion, architectural marvels, and profound cultural influence.
The empire's roots lie in the city of Rome, founded, according to legend, by Romulus in 753 BCE. Over centuries, Rome evolved from a small settlement to a formidable republic, characterized by a complex political system with elected officials and checks on power. However, internal strife, class conflicts, and military ambitions paved the way for the end of the Republic. Julius Caesar’s dictatorship and subsequent assassination in 44 BCE created a power vacuum, leading to a civil war. Octavian, later Augustus, emerged victorious, heralding the Roman Empire’s birth.
Under Augustus, the empire experienced the Pax Romana, a 200-year period of relative peace and stability. Augustus reformed the military, established efficient administrative systems, and initiated grand construction projects. The empire's borders expanded, encompassing territories from Britain to Egypt and from Spain to the Euphrates. Roman legions, renowned for their discipline and engineering prowess, secured and maintained these vast territories, building roads, fortifications, and cities that facilitated control and integration.
The Roman Empire’s society was hierarchical, with a rigid class system. At the top were the patricians, wealthy elites who held significant political power. Below them were the plebeians, free citizens with limited political influence, and the vast numbers of slaves who formed the backbone of the economy. The family unit was central, governed by the paterfamilias, the male head who held absolute authority.
Culturally, the Romans were eclectic, absorbing and adapting elements from the civilizations they encountered, particularly the Greeks. Roman art, literature, and philosophy reflected this synthesis, creating a rich cultural tapestry. Latin, the Roman language, became the lingua franca of the Western world, influencing numerous modern languages.
Roman architecture and engineering achievements were monumental. They perfected the arch, vault, and dome, constructing enduring structures like the Colosseum, Pantheon, and aqueducts. These engineering marvels not only showcased Roman ingenuity but also served practical purposes, from public entertainment to water supply.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Students, digital devices and success - Andreas Schleicher - 27 May 2024..pptxEduSkills OECD
Andreas Schleicher presents at the OECD webinar ‘Digital devices in schools: detrimental distraction or secret to success?’ on 27 May 2024. The presentation was based on findings from PISA 2022 results and the webinar helped launch the PISA in Focus ‘Managing screen time: How to protect and equip students against distraction’ https://www.oecd-ilibrary.org/education/managing-screen-time_7c225af4-en and the OECD Education Policy Perspective ‘Students, digital devices and success’ can be found here - https://oe.cd/il/5yV
Palestine last event orientationfvgnh .pptxRaedMohamed3
An EFL lesson about the current events in Palestine. It is intended to be for intermediate students who wish to increase their listening skills through a short lesson in power point.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
How to Create Map Views in the Odoo 17 ERPCeline George
The map views are useful for providing a geographical representation of data. They allow users to visualize and analyze the data in a more intuitive manner.
The French Revolution, which began in 1789, was a period of radical social and political upheaval in France. It marked the decline of absolute monarchies, the rise of secular and democratic republics, and the eventual rise of Napoleon Bonaparte. This revolutionary period is crucial in understanding the transition from feudalism to modernity in Europe.
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1. Congruent Triangles
The student is able to (I can):
• Identify and prove congruent triangles given
— Three pairs of congruent sides (Side-Side-Side)
— Two pairs of congruent sides and a pair of congruent— Two pairs of congruent sides and a pair of congruent
included angles (Side-Angle-Side)
— A Hypotenuse and a Leg of a right triangle
2. SSS – Side-Side-Side
If three sides of one triangle are congruent
to three sides of another triangle, then the
triangles are congruent.
I C P6
T N U
4
6
7 4 7
ΔTIN ≅ ΔCUP
3. Example Given: , D is the midpoint of
Prove: ΔFRD ≅ ΔERD
F
R
ED
FR ER≅ FE
StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasonsStatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons
1. 1. Given
2. D is midpt of 2. Given
3. 3. Def. of midpoint
4. 4. Refl. prop. ≅
5. ΔFRD ≅ ΔERD 5. SSS
FR ER≅
FE
FD ED≅
RD RD≅
4. SAS – Side-Angle-Side
If two sides and the included angle of one
triangle are congruent to two sides and the
included angle of another triangle, then the
triangles are congruent.
H U
L
S
T
A
ΔLHS ≅ ΔUTA
5. Example Given: , A is the midpoint of
Prove: ΔFAR ≅ ΔEAM F
R
A
M
E
FA EA≅ RM
E
StatementsStatementsStatementsStatements ReasonsReasonsReasonsReasons
1. 1. Given
2. ∠FAR ≅ ∠EAM 2. Vertical ∠s
3. A is midpt of 3. Given
4. 4. Def. of midpoint
5. ΔFAR ≅ ΔEAM 5. SAS
FA EA≅
RM
RA MA≅
6. HL – hypotenuse-leg
If the hypotenuse and leg of one right
triangle are congruent to the hypotenuse
and leg of another right triangle, then the
two triangles are congruent.
J
E
M
O
E
AC
∆JOE ≅ ∆MAC
