TechMathI - 4.5 - Altitudes, Medians, and Bisectors
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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.
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Final review 1
This geometry review document contains questions about various geometry topics including:
1. Finding measures of angles and classifying angle relationships
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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.
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The document contains instructions for five math centers focused on polynomial operations: adding, subtracting, distributing, and multiplying polynomials. Students are directed to copy problems from each center and show their work. Solution banks with ordered terms are provided for students to write their answers.
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.
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 - 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.
TechMathI - Rate of change and slope
The document contains information about rates of change, slope, and lines. It includes examples of calculating rates of change from tables of data and slope from ordered pairs using the slope formula. It discusses horizontal and vertical lines having slopes of 0 and undefined, and positive and negative slopes indicating the direction a line slants.
TechMathI - Ch6 Test
This document contains a 36 question multiple choice test on various math concepts including:
- 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.
TechMathI - Ch6 Review
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.
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.
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TechMathI - 4.5 - Altitudes, Medians, and Bisectors
- 1. Bell Ringer 1. List the three things you need to use the HL Theorem. 2. In your own words, describe the isosceles triangle theorem. 3. List the four congruence theorems that will prove two triangles congruent.
- 2. Medians
- 4. How many medians can a triangle have? Median vertex to midpoint
- 6. M D P N C 1. What is NC if NP = 18? 9 2. If DP = 7.5, find MP. 15
- 7. A B C E D 1.What is ED if DC = 14? 2.What Is AC is BC is 9? 14 3.If BC = 3, find AC. 6 You Try the Following:
- 8. A E B C D If CD = 2x + 5, BD = 4x – 1, and AE = 5x –2, find BE. BD = CD 4x – 1= 2x + 5 2x = 6 x = 3 AE = BE BE = 5x – 2 BE = 5( 3 ) – 2 BE = 13
- 9. The intersection of the medians is called the CENTROID. How many medians does a triangle have? Draw the Picture:
- 12. Altitude Altitude vertex to opposite side and perpendicular Picture:
- 13. Altitude 08/31/10 EQ: What are the differences between medians, altitudes, and perpendicular bisectors? The altitude is the “true height” of the triangle.
- 14. Tell whether each red segment is an altitude of the triangle. NO YES YES The altitude is the “true height” of the triangle.
- 15. Perpendicular Bisector Perpendicular Bisector midpoint and perpendicular Picture: Both sides are congruent- make sure you see this or it is NOT a perpendicular bisector
- 16. Tell whether each red segment is an perpendicular bisector of the triangle. NO NO YES