Este documento describe cómo aplicar el teorema de Tales para dividir los lados de un triángulo equilátero en partes iguales y trazar líneas paralelas utilizando la escuadra y el cartabón. Presenta varias opciones de diseño de una figura tridimensional y proporciona un enlace a la obra del artista José María Yturralde.
This document discusses different types of transformations in mathematics. It defines a transformation as a change in position or orientation of a figure that results in an image of the original. Translations move a figure along a straight line without turning. Reflections flip a figure across a line. Rotations turn a figure around a point. Dilations change the size of a figure. The document provides examples of identifying transformations and graphing translations and reflections on a coordinate plane.
This document discusses parallel lines and their properties. It defines parallel lines as lines that do not intersect and always have the same distance between them. It then covers different types of angles formed when parallel lines are intersected by a transversal line, including corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive exterior angles. It states properties of these angles, such as corresponding angles being congruent and alternate interior angles and exterior angles being congruent. Examples are given of finding missing angle measures using these properties.
The document provides definitions and examples for key mathematical terms related to profit/loss, discounts, interest, and weight measurements. It defines terms like cost, selling price, profit, loss, marked price, discount, interest, interest rate, simple interest, compound interest, bruto, netto, and tarra. Examples show how to calculate profit/loss when given buying and selling prices, determine discounts based on marked prices, and calculate simple interest given principal, rate, and time. It also demonstrates using bruto, netto, and tarra to determine total, net, and packaging weights.
This document contains a mathematics test for 7th grade students on the topic of sets. The test has 10 questions and provides 3 different types of questions for each number - Type A questions are worth 80 points, Type B questions are worth 90 points, and Type C questions are worth 100 points. Students must choose one type of question for each number and show their work. The questions cover topics like examples of sets in daily life, set notation, Venn diagrams, subsets, and relationships between sets. Students are given 60 minutes to complete the test and must sign the answer sheet along with their teacher and parent.
This document contains a mathematics test for 7th grade students on the topic of sets. The test has 10 multiple choice questions covering concepts like Venn diagrams, set operations, and set notation. It also includes one bonus question asking students to calculate the number of people who liked products A and B but not C based on survey data. The test instructions specify that students must choose one of three given question types (A, B, or C), show their work clearly, and cannot change question types once selected.
Este documento describe cómo aplicar el teorema de Tales para dividir los lados de un triángulo equilátero en partes iguales y trazar líneas paralelas utilizando la escuadra y el cartabón. Presenta varias opciones de diseño de una figura tridimensional y proporciona un enlace a la obra del artista José María Yturralde.
This document discusses different types of transformations in mathematics. It defines a transformation as a change in position or orientation of a figure that results in an image of the original. Translations move a figure along a straight line without turning. Reflections flip a figure across a line. Rotations turn a figure around a point. Dilations change the size of a figure. The document provides examples of identifying transformations and graphing translations and reflections on a coordinate plane.
This document discusses parallel lines and their properties. It defines parallel lines as lines that do not intersect and always have the same distance between them. It then covers different types of angles formed when parallel lines are intersected by a transversal line, including corresponding angles, alternate interior angles, alternate exterior angles, consecutive interior angles, and consecutive exterior angles. It states properties of these angles, such as corresponding angles being congruent and alternate interior angles and exterior angles being congruent. Examples are given of finding missing angle measures using these properties.
The document provides definitions and examples for key mathematical terms related to profit/loss, discounts, interest, and weight measurements. It defines terms like cost, selling price, profit, loss, marked price, discount, interest, interest rate, simple interest, compound interest, bruto, netto, and tarra. Examples show how to calculate profit/loss when given buying and selling prices, determine discounts based on marked prices, and calculate simple interest given principal, rate, and time. It also demonstrates using bruto, netto, and tarra to determine total, net, and packaging weights.
This document contains a mathematics test for 7th grade students on the topic of sets. The test has 10 questions and provides 3 different types of questions for each number - Type A questions are worth 80 points, Type B questions are worth 90 points, and Type C questions are worth 100 points. Students must choose one type of question for each number and show their work. The questions cover topics like examples of sets in daily life, set notation, Venn diagrams, subsets, and relationships between sets. Students are given 60 minutes to complete the test and must sign the answer sheet along with their teacher and parent.
This document contains a mathematics test for 7th grade students on the topic of sets. The test has 10 multiple choice questions covering concepts like Venn diagrams, set operations, and set notation. It also includes one bonus question asking students to calculate the number of people who liked products A and B but not C based on survey data. The test instructions specify that students must choose one of three given question types (A, B, or C), show their work clearly, and cannot change question types once selected.
The document contains a series of math word problems and geometry exercises involving angles, triangles, trapezoids, and algebraic expressions. Students are asked to identify geometric features of shapes, calculate unknown angle measures, and solve for unknown variables in expressions. They must apply properties of angles, triangles, parallel lines, and algebraic operations to determine the requested values.
This document contains 10 problems about relationships between angles including complementary, supplementary, and ratio relationships. It asks the reader to find missing angle measures based on information provided about other angles. For each problem it provides space for the answer but no worked solutions are shown. Overall it focuses on developing understanding of complementary, supplementary, and ratio relationships between angles.
The document contains 9 problems involving finding unknown angles or their measures given relationships between complements, supplements, and measures of various angles. It provides equations relating angles to their complements and supplements to be solved for the unknown value or measure of an angle.
There are several word problems presented involving sets and counting principles. They can be summarized as follows:
1) The problems involve counting elements in sets based on given information such as the number of elements in overlapping and separate sets.
2) Questions ask how many elements are in the intersection or union of sets, or how many elements satisfy single or multiple criteria.
3) The context of the problems involves surveys, students, products, newspapers, and other everyday scenarios to count people or items in categories.
1) The document discusses linear equations with one variable (LEOV). It defines key terms like statements, open and closed sentences, equations, and the components of a linear equation with one variable.
2) Examples are provided to illustrate open sentences that can be made into closed sentences or equations by replacing variables with values. Exercises ask the reader to write open sentences as equations and solve simple equations.
3) The final section directs the reader to solve two sample linear equations with one variable, tying together the concepts discussed in the document.
The document provides instructions to prove the Pythagorean theorem using origami. It instructs the reader to cut origami paper into rectangles and then into right triangles. It then tells them to arrange 4 right triangles into a larger right triangle to demonstrate that the hypotenuse of the larger triangle is equal to the sum of the squares of the other two sides.
The document defines and describes properties of different types of quadrilaterals. It provides a chart showing the relationships between quadrilaterals and their defining characteristics. Formulas for calculating the area and perimeter of parallelograms, rectangles, squares, rhombuses, and kites are also presented. Key terms related to quadrilaterals such as parallel, perpendicular, diagonal, and symmetry are defined in a glossary.
This document discusses different types of quadrilaterals: trapezium, parallelogram, rhombus, rectangle, square, and kite. It provides the key properties of each shape, including that a trapezium has one pair of parallel sides, a parallelogram has opposite sides that are equal and parallel, and a rhombus has all four sides of equal length. It also defines geometric attributes like diagonals, angles, areas, and perimeters.
The document discusses proportional line segments formed when a line parallel to one side of a triangle intersects the other two sides. It states that if a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally. An example problem demonstrates finding the value of x given lengths of line segments intercepted by parallel lines intersecting two transversals. The document concludes by thanking the reader and providing attribution for the material.
The document is a daily mathematics test for 7th grade students consisting of 20 multiple choice questions and 10 short answer questions related to sets. It tests concepts such as subsets, unions, intersections, complements and Venn diagrams. The test has a time limit of 80 minutes.
1) The document is a mathematics quiz on angles that contains 11 questions testing students' knowledge of rewriting angles in degrees and hexadecimal, calculating angles, finding complements, supplements, and unknown angles based on relationships between angles.
2) It asks students to rewrite angles in degrees and hexadecimal, calculate angle sums and differences, find named angles based on a diagram, determine angles formed by clock hands, find complements and supplements of given angles, and solve for unknown angles based on relationships between complements, supplements and the unknown angle.
3) The quiz contains a variety of angle problems to assess students' understanding of the key concepts of angles, units of measurement, relationships between complementary/supplementary angles, and solving for
This document contains a 10 question quiz on angle relationships in mathematics. It asks the student to find missing angle measures based on given information about angles being supplementary, complementary, ratios of angles, and relationships between an angle and its complement or supplement. The student must show their work and arrive at the exact angle measure.
Basic geometrical constuctions is how to construct angle by using compass and ruler.
this slide can help students or teachers to construct any angles especially for special angles they are 90 degree, 60 degree, 45 degree and 30 degree.
The document discusses ratios, proportions, and scale drawings. It begins by defining a ratio as a comparison of two or more quantities without units. Ratios can be written in different forms such as a:b or a to b. A proportion is an equation stating that one ratio is equal to another. Direct proportion means that as one quantity increases, the other also increases by the same factor. Inverse proportion means that as one quantity increases, the other decreases. Scale drawings use a scale ratio to show the relationship between an object's depicted size and its actual size. Examples are provided to demonstrate calculating ratios, proportions, direct and inverse proportions, and using scale ratios.
Here are the key steps to solve word problems involving linear equations:
1. Read the problem carefully and identify the important details.
2. Define variables to represent unknown quantities.
3. Write a mathematical expression relating the variables based on the context of the problem.
4. Form an equation and solve it using proper order of operations.
5. Check that the solution makes sense in the context of the original problem.
1. This document discusses multiplication and division of polynomials.
2. It provides examples of multiplying and dividing terms with variables and exponents, using the distributive property and dividing polynomials.
3. The key steps shown are multiplying similar terms, distributing multiplication over addition, and dividing the first polynomial by the second to obtain the quotient.
Michael went to the library for the first time on September 3rd. Andi went every 2 days, Nathan every 3 days, and Michael every 4 days. They ask how many times each person went alone and together during September. Bondan and Samantha play badminton every 4 and 5 days respectively and played together for the first time on August 7th. They are asked when they will play together again. The test questions involve calculating scores based on multiple choice answers and operations with fractions, exponents, and algebraic expressions.
The document contains 500 questions and answers organized into 5 categories. Each category covers mathematical and numerical problems, including standard form, percentages, fractions, and word problems. The questions test various calculation skills and the ability to simplify numerical expressions in different forms. Pictures may be included between questions and answers using custom animations.
The document contains a series of math word problems and geometry exercises involving angles, triangles, trapezoids, and algebraic expressions. Students are asked to identify geometric features of shapes, calculate unknown angle measures, and solve for unknown variables in expressions. They must apply properties of angles, triangles, parallel lines, and algebraic operations to determine the requested values.
This document contains 10 problems about relationships between angles including complementary, supplementary, and ratio relationships. It asks the reader to find missing angle measures based on information provided about other angles. For each problem it provides space for the answer but no worked solutions are shown. Overall it focuses on developing understanding of complementary, supplementary, and ratio relationships between angles.
The document contains 9 problems involving finding unknown angles or their measures given relationships between complements, supplements, and measures of various angles. It provides equations relating angles to their complements and supplements to be solved for the unknown value or measure of an angle.
There are several word problems presented involving sets and counting principles. They can be summarized as follows:
1) The problems involve counting elements in sets based on given information such as the number of elements in overlapping and separate sets.
2) Questions ask how many elements are in the intersection or union of sets, or how many elements satisfy single or multiple criteria.
3) The context of the problems involves surveys, students, products, newspapers, and other everyday scenarios to count people or items in categories.
1) The document discusses linear equations with one variable (LEOV). It defines key terms like statements, open and closed sentences, equations, and the components of a linear equation with one variable.
2) Examples are provided to illustrate open sentences that can be made into closed sentences or equations by replacing variables with values. Exercises ask the reader to write open sentences as equations and solve simple equations.
3) The final section directs the reader to solve two sample linear equations with one variable, tying together the concepts discussed in the document.
The document provides instructions to prove the Pythagorean theorem using origami. It instructs the reader to cut origami paper into rectangles and then into right triangles. It then tells them to arrange 4 right triangles into a larger right triangle to demonstrate that the hypotenuse of the larger triangle is equal to the sum of the squares of the other two sides.
The document defines and describes properties of different types of quadrilaterals. It provides a chart showing the relationships between quadrilaterals and their defining characteristics. Formulas for calculating the area and perimeter of parallelograms, rectangles, squares, rhombuses, and kites are also presented. Key terms related to quadrilaterals such as parallel, perpendicular, diagonal, and symmetry are defined in a glossary.
This document discusses different types of quadrilaterals: trapezium, parallelogram, rhombus, rectangle, square, and kite. It provides the key properties of each shape, including that a trapezium has one pair of parallel sides, a parallelogram has opposite sides that are equal and parallel, and a rhombus has all four sides of equal length. It also defines geometric attributes like diagonals, angles, areas, and perimeters.
The document discusses proportional line segments formed when a line parallel to one side of a triangle intersects the other two sides. It states that if a line parallel to one side of a triangle intersects the other two sides, it divides those sides proportionally. An example problem demonstrates finding the value of x given lengths of line segments intercepted by parallel lines intersecting two transversals. The document concludes by thanking the reader and providing attribution for the material.
The document is a daily mathematics test for 7th grade students consisting of 20 multiple choice questions and 10 short answer questions related to sets. It tests concepts such as subsets, unions, intersections, complements and Venn diagrams. The test has a time limit of 80 minutes.
1) The document is a mathematics quiz on angles that contains 11 questions testing students' knowledge of rewriting angles in degrees and hexadecimal, calculating angles, finding complements, supplements, and unknown angles based on relationships between angles.
2) It asks students to rewrite angles in degrees and hexadecimal, calculate angle sums and differences, find named angles based on a diagram, determine angles formed by clock hands, find complements and supplements of given angles, and solve for unknown angles based on relationships between complements, supplements and the unknown angle.
3) The quiz contains a variety of angle problems to assess students' understanding of the key concepts of angles, units of measurement, relationships between complementary/supplementary angles, and solving for
This document contains a 10 question quiz on angle relationships in mathematics. It asks the student to find missing angle measures based on given information about angles being supplementary, complementary, ratios of angles, and relationships between an angle and its complement or supplement. The student must show their work and arrive at the exact angle measure.
Basic geometrical constuctions is how to construct angle by using compass and ruler.
this slide can help students or teachers to construct any angles especially for special angles they are 90 degree, 60 degree, 45 degree and 30 degree.
The document discusses ratios, proportions, and scale drawings. It begins by defining a ratio as a comparison of two or more quantities without units. Ratios can be written in different forms such as a:b or a to b. A proportion is an equation stating that one ratio is equal to another. Direct proportion means that as one quantity increases, the other also increases by the same factor. Inverse proportion means that as one quantity increases, the other decreases. Scale drawings use a scale ratio to show the relationship between an object's depicted size and its actual size. Examples are provided to demonstrate calculating ratios, proportions, direct and inverse proportions, and using scale ratios.
Here are the key steps to solve word problems involving linear equations:
1. Read the problem carefully and identify the important details.
2. Define variables to represent unknown quantities.
3. Write a mathematical expression relating the variables based on the context of the problem.
4. Form an equation and solve it using proper order of operations.
5. Check that the solution makes sense in the context of the original problem.
1. This document discusses multiplication and division of polynomials.
2. It provides examples of multiplying and dividing terms with variables and exponents, using the distributive property and dividing polynomials.
3. The key steps shown are multiplying similar terms, distributing multiplication over addition, and dividing the first polynomial by the second to obtain the quotient.
Michael went to the library for the first time on September 3rd. Andi went every 2 days, Nathan every 3 days, and Michael every 4 days. They ask how many times each person went alone and together during September. Bondan and Samantha play badminton every 4 and 5 days respectively and played together for the first time on August 7th. They are asked when they will play together again. The test questions involve calculating scores based on multiple choice answers and operations with fractions, exponents, and algebraic expressions.
The document contains 500 questions and answers organized into 5 categories. Each category covers mathematical and numerical problems, including standard form, percentages, fractions, and word problems. The questions test various calculation skills and the ability to simplify numerical expressions in different forms. Pictures may be included between questions and answers using custom animations.
1. EXERCISE POINT
PARALLEL LINES
Name :
Class / No. absent :
QUESTION SOLUTION
1) Find the value of x !
3x
12x
2) Find the value of x !
(6x + 68 )o
(10x - 28 )o
3) Find the value of x !
41o
x
35o
4) Find the value of x !
xo
92o
52o
5) Find the value of x !
(3x + 7)o
(7x - 30)o
41o
2. 6) Find the value of x !
37o
285o
xo
68o
7) Find the value of x !
113o
132o
xo
8) Find the value of y !
132o
118o
yo
9) Find the value of x !
120o
xo
63o
10) Find the value of x !
2xo
110o 125o
xo
3. 6) Find the value of x !
37o
285o
xo
68o
7) Find the value of x !
113o
132o
xo
8) Find the value of y !
132o
118o
yo
9) Find the value of x !
120o
xo
63o
10) Find the value of x !
2xo
110o 125o
xo
4. 6) Find the value of x !
37o
285o
xo
68o
7) Find the value of x !
113o
132o
xo
8) Find the value of y !
132o
118o
yo
9) Find the value of x !
120o
xo
63o
10) Find the value of x !
2xo
110o 125o
xo
5. 6) Find the value of x !
37o
285o
xo
68o
7) Find the value of x !
113o
132o
xo
8) Find the value of y !
132o
118o
yo
9) Find the value of x !
120o
xo
63o
10) Find the value of x !
2xo
110o 125o
xo