Poly centers answer sheet
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TechMathI - Slope intercept form
This document discusses linear equations and slope-intercept form. It provides examples of:
1) Finding the slope and y-intercept of linear equations in slope-intercept form like y = 4x + 2.
2) Writing equations of lines given the slope and y-intercept, such as an equation with m = 3 and y-intercept of 7.
3) Finding the slope and y-intercept from two points on a line, then writing the equation in slope-intercept form.
Final review 1
This geometry review document contains questions about various geometry topics including:
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TechMathI - Standard form
The document discusses finding the x-intercept and y-intercept of linear equations by setting either x or y equal to 0 and solving for the other variable. It provides examples of finding the intercepts of equations and graphing the resulting point coordinates. Students are asked to practice finding and graphing intercepts for several equations.
TechMathI - Rate of change and slope
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TechMathI - Slope intercept form
This document discusses linear equations and slope-intercept form. It provides examples of:
1) Finding the slope and y-intercept of linear equations in slope-intercept form like y = 4x + 2.
2) Writing equations of lines given the slope and y-intercept, such as an equation with m = 3 and y-intercept of 7.
3) Finding the slope and y-intercept from two points on a line, then writing the equation in slope-intercept form.
Final review 1
This geometry review document contains questions about various geometry topics including:
1. Finding measures of angles and classifying angle relationships
2. Solving equations involving geometric variables
3. Applying properties of triangles including the Pythagorean theorem and triangle classification
4. Finding sums of interior and exterior angles of polygons
5. Identifying and applying properties of similar, congruent, and special right triangles
The questions range in difficulty from basic skills to applying multiple concepts and theorems.
TechMathI - Point slope form
The document provides examples and explanations of finding the rate of change and linear equations from tables of data points and given slopes and points. It includes examples of using the point-slope formula to write linear equations from a given point and slope, as well as examples of writing linear equations from two given points. Students are prompted to write linear equations for several examples.
5.1 writing linear equations in slope intercept form
You can use this presentation to introduce students in how to write linear equations given the slope and the y-intercept. This is the first case in writing linear equations.
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TechMathI - Standard form
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TechMathI - Rate of change and slope
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TechMathI - Ch6 Review
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TechMathI - Ch6 Quiz
This document contains a 15 question quiz on math concepts like proportions, ratios, rates, similar triangles, and unit conversions. The questions require setting up and solving proportions, finding unit rates, calculating rates per hour, and using similar triangles to determine unknown lengths.
TechMathI - 6.2 - Similarity examples
Similar figures are two-dimensional shapes that have the same shape but can differ in size. To be similar, the corresponding sides of the figures must be proportional, meaning they differ by a constant scale factor. Similar figures have the same angle measures but different side lengths. Problems involving similar figures can be solved by identifying the scale factor between corresponding sides and using proportional reasoning.
TechMathI - 6.2 - Similarity
This document contains 4 math word problems involving similar triangles and scaling factors to determine unknown side lengths or heights. It also provides examples of finding the height of objects like trees using the similarity of triangles formed by shadows of objects of known height.
TechMathI - 6.1 - Ratio and Proportion
1. The document provides examples of ratios, proportions, rates, unit rates, and examples of setting up and solving proportions using cross multiplication.
2. It includes multi-step proportion examples involving fractions with variables in both the numerator and denominator.
3. Additional practice problems are provided for readers to try setting up and solving different types of proportions.
TechMathI - Ch5 Test
This document contains a 33 question test on polygons and their properties. The test covers identifying polygons by name and type, finding missing side lengths and angle measures of polygons, calculating sums of interior and exterior angles, determining which statements about polygon properties are true or false, and identifying polygons based on given properties. The test includes multiple choice, true/false, and short answer questions.
TechMathI - Ch5 Vocab Quiz
This document is a vocabulary quiz that tests knowledge of polygon terms. It contains 17 multiple choice questions that ask the learner to match polygon names like triangle, square, pentagon, and hexagon with their definitions relating to number of sides, side properties, angles, and geometric shapes. The word bank at the bottom provides additional polygon shape names as potential answers.
TechMathI - 5.6 - Trapezoids
This document discusses properties and definitions related to trapezoids. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines an isosceles trapezoid as one where the non-parallel sides are congruent. It states that the diagonals of an isosceles trapezoid are congruent and that the median of any trapezoid is parallel to the bases and has a length that is half the sum of the base lengths. It includes examples of finding missing side lengths using the median property.
TechMathI - 5.5 - Special Parallelograms
1. The document discusses different types of quadrilaterals including trapezoids, parallelograms, rectangles, squares, and rhombuses.
2. It provides steps to identify these shapes based on their properties like the number of parallel sides and whether the angles are right angles or the sides are congruent.
3. Tests are described to determine if a quadrilateral is a parallelogram based on properties like opposite sides being parallel and congruent.
TechMathI - 5.4 - Parallelograms
This document provides examples and practice problems for identifying angle measures in parallelograms. It gives the side lengths of parallelogram ABCD and asks to find the three other angle measures. It also provides a practice problem to find missing angle measures for an additional parallelogram.
TechMathI - 5.3 - Properties of Quadrilaterals
This document provides information about different types of quadrilaterals (four-sided polygons) through a foldable activity. It defines and lists properties of parallelograms, rectangles, rhombuses, squares, and trapezoids. Key quadrilaterals are distinguished by their parallel sides, right angles, and congruent sides or angles. The foldable allows students to draw and label examples of each quadrilateral type.
TechMathI - 5.2 - Angles of Polygons
This document contains information about polygons, including:
1. Formulas for calculating the sum of interior angles and exterior angles of polygons. The interior angle sum is (n-2)×180° and the exterior angle sum is 360°.
2. Examples of calculating interior and exterior angles for regular polygons with specific numbers of sides. Interior angles decrease and exterior angles increase as the number of sides increases.
3. Practice problems involving calculating unknown interior and exterior angles of polygons using the angle sum properties.
TechMathI - 5.1 - Polygons
The document introduces polygons, which are two-dimensional shapes with three or more straight sides. It defines key terms like vertex, diagonal, and regular polygons. Examples of specific polygons are given, including triangles, quadrilaterals like squares and rectangles, and polygons with 5+ sides like pentagons and hexagons. Real-world examples of each polygon type are also provided.
TechMathI - 4.5 - Altitudes, Medians, and Bisectors
This document provides information about medians, altitudes, and perpendicular bisectors of triangles:
1) A median is a line segment connecting a vertex to the midpoint of the opposite side. A triangle has 3 medians. The point where the 3 medians intersect is called the centroid.
2) An altitude is a line segment from a vertex perpendicular to the opposite side. It represents the "true height" of the triangle.
3) A perpendicular bisector is a line segment through the midpoint of a side, perpendicular to that side. The two segments formed on either side are congruent.
TechMathI - 4.2 - Proving Triangles Congruent
The document discusses three postulates for triangle congruence:
1) Angle-Side-Angle (ASA) postulate - If two angles and the included side of one triangle are congruent to another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS) postulate - If two angles and a non-included side of one triangle are congruent to another, then the triangles are congruent.
3) Side-Side-Side (SSS) postulate - If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
TechMathI - 4.3 - Using Congruent Triangles
The document discusses three triangle congruence postulates:
1) Angle-Side-Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS) postulate states that if two angles and a non-included side of one triangle are congruent to another, then the triangles are congruent.
3) Side-Side-Side (SSS) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
TechMathI - 4.4 - Isosceles and Right Triangle Theorems
The document is a math lesson on isosceles triangles that includes definitions, theorems, examples and practice problems. It defines isosceles triangles as triangles with two congruent sides and base angles as the two angles adjacent to the base. It presents the Isosceles Triangle Theorem stating that if two sides are congruent, the angles opposite are also congruent. Examples show applying the theorem to find missing angle measures and side lengths. The Hypotenuse-Leg Congruence Theorem is introduced for right triangles. Practice problems have students identify if triangles can be proven congruent.
TechMathI - 4.1 - Congruent Triangles
This document discusses different ways to prove that two triangles are congruent, including:
1. Side-Side-Side (SSS) - If all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
2. Side-Angle-Side (SAS) - If one angle and the sides that form it in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.
3. Angle-Side-Angle (ASA) - If two angles and the included side in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.
TechMathI - Ch3 TOD2
1) <7 and all angles corresponding to <7 are <1, <2, <3, <4, <5, <6, <7, <8, <9, <10, <11, <12, <13, <14, <15, <16.
2) A matching pair of alternate interior angles is <5 and <8.
3) A matching pair of alternate exterior angles is <13 and <16.
4) A set of consecutive interior angles is <1, <2, <7, <8.
5) The measure of <1 is 60°. The measure of <2 is 110°.
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- Calculating unit rates
- Solving proportions
- Finding percentages of quantities
- Calculating percent increases and decreases
The questions require skills like setting up and solving proportions, unit conversion, percent calculation, and percent change.
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This document contains 30 math word problems testing foundations concepts like rates, proportions, percentages, and percent change. The problems can be solved by setting up and solving proportions, finding unit rates, calculating percentages, or determining percent change between two amounts. Key information includes rates, costs, percentages, initial and final amounts, and measurements involved in rate and percent problems.
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TechMathI - 6.2 - Similarity examples
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1. The document provides examples of ratios, proportions, rates, unit rates, and examples of setting up and solving proportions using cross multiplication.
2. It includes multi-step proportion examples involving fractions with variables in both the numerator and denominator.
3. Additional practice problems are provided for readers to try setting up and solving different types of proportions.
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TechMathI - Ch5 Vocab Quiz
This document is a vocabulary quiz that tests knowledge of polygon terms. It contains 17 multiple choice questions that ask the learner to match polygon names like triangle, square, pentagon, and hexagon with their definitions relating to number of sides, side properties, angles, and geometric shapes. The word bank at the bottom provides additional polygon shape names as potential answers.
TechMathI - 5.6 - Trapezoids
This document discusses properties and definitions related to trapezoids. It defines a trapezoid as a quadrilateral with one pair of parallel sides, and defines an isosceles trapezoid as one where the non-parallel sides are congruent. It states that the diagonals of an isosceles trapezoid are congruent and that the median of any trapezoid is parallel to the bases and has a length that is half the sum of the base lengths. It includes examples of finding missing side lengths using the median property.
TechMathI - 5.5 - Special Parallelograms
1. The document discusses different types of quadrilaterals including trapezoids, parallelograms, rectangles, squares, and rhombuses.
2. It provides steps to identify these shapes based on their properties like the number of parallel sides and whether the angles are right angles or the sides are congruent.
3. Tests are described to determine if a quadrilateral is a parallelogram based on properties like opposite sides being parallel and congruent.
TechMathI - 5.4 - Parallelograms
This document provides examples and practice problems for identifying angle measures in parallelograms. It gives the side lengths of parallelogram ABCD and asks to find the three other angle measures. It also provides a practice problem to find missing angle measures for an additional parallelogram.
TechMathI - 5.3 - Properties of Quadrilaterals
This document provides information about different types of quadrilaterals (four-sided polygons) through a foldable activity. It defines and lists properties of parallelograms, rectangles, rhombuses, squares, and trapezoids. Key quadrilaterals are distinguished by their parallel sides, right angles, and congruent sides or angles. The foldable allows students to draw and label examples of each quadrilateral type.
TechMathI - 5.2 - Angles of Polygons
This document contains information about polygons, including:
1. Formulas for calculating the sum of interior angles and exterior angles of polygons. The interior angle sum is (n-2)×180° and the exterior angle sum is 360°.
2. Examples of calculating interior and exterior angles for regular polygons with specific numbers of sides. Interior angles decrease and exterior angles increase as the number of sides increases.
3. Practice problems involving calculating unknown interior and exterior angles of polygons using the angle sum properties.
TechMathI - 5.1 - Polygons
The document introduces polygons, which are two-dimensional shapes with three or more straight sides. It defines key terms like vertex, diagonal, and regular polygons. Examples of specific polygons are given, including triangles, quadrilaterals like squares and rectangles, and polygons with 5+ sides like pentagons and hexagons. Real-world examples of each polygon type are also provided.
TechMathI - 4.5 - Altitudes, Medians, and Bisectors
This document provides information about medians, altitudes, and perpendicular bisectors of triangles:
1) A median is a line segment connecting a vertex to the midpoint of the opposite side. A triangle has 3 medians. The point where the 3 medians intersect is called the centroid.
2) An altitude is a line segment from a vertex perpendicular to the opposite side. It represents the "true height" of the triangle.
3) A perpendicular bisector is a line segment through the midpoint of a side, perpendicular to that side. The two segments formed on either side are congruent.
TechMathI - 4.2 - Proving Triangles Congruent
The document discusses three postulates for triangle congruence:
1) Angle-Side-Angle (ASA) postulate - If two angles and the included side of one triangle are congruent to another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS) postulate - If two angles and a non-included side of one triangle are congruent to another, then the triangles are congruent.
3) Side-Side-Side (SSS) postulate - If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
TechMathI - 4.3 - Using Congruent Triangles
The document discusses three triangle congruence postulates:
1) Angle-Side-Angle (ASA) postulate states that if two angles and the included side of one triangle are congruent to another triangle, then the triangles are congruent.
2) Angle-Angle-Side (AAS) postulate states that if two angles and a non-included side of one triangle are congruent to another, then the triangles are congruent.
3) Side-Side-Side (SSS) postulate states that if three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
TechMathI - 4.4 - Isosceles and Right Triangle Theorems
The document is a math lesson on isosceles triangles that includes definitions, theorems, examples and practice problems. It defines isosceles triangles as triangles with two congruent sides and base angles as the two angles adjacent to the base. It presents the Isosceles Triangle Theorem stating that if two sides are congruent, the angles opposite are also congruent. Examples show applying the theorem to find missing angle measures and side lengths. The Hypotenuse-Leg Congruence Theorem is introduced for right triangles. Practice problems have students identify if triangles can be proven congruent.
TechMathI - 4.1 - Congruent Triangles
This document discusses different ways to prove that two triangles are congruent, including:
1. Side-Side-Side (SSS) - If all three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.
2. Side-Angle-Side (SAS) - If one angle and the sides that form it in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.
3. Angle-Side-Angle (ASA) - If two angles and the included side in one triangle are congruent to the corresponding parts in another triangle, then the triangles are congruent.
TechMathI - Ch3 TOD2
1) <7 and all angles corresponding to <7 are <1, <2, <3, <4, <5, <6, <7, <8, <9, <10, <11, <12, <13, <14, <15, <16.
2) A matching pair of alternate interior angles is <5 and <8.
3) A matching pair of alternate exterior angles is <13 and <16.
4) A set of consecutive interior angles is <1, <2, <7, <8.
5) The measure of <1 is 60°. The measure of <2 is 110°.
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TechMathI - 4.5 - Altitudes, Medians, and Bisectors
TechMathI - 4.4 - Isosceles and Right Triangle Theorems
TechMathI - 4.4 - Isosceles and Right Triangle Theorems
Poly centers answer sheet
- 1. Polynomial Centers – Answer Sheet Name: _____________ Center 1 1. Center 2 1. 2. 2. 3. 4. 3. 5. 4. 6. Center 3 5. 1. 6. 2. 3. 7. 4. 8. 5. 9. 6.
- 2. Center 4 1. Center 5 1. 2. 2. 3. 3. 4. 5. 4. 6. 5. 7. 8. 6. 9. ANSWER: