geometry unit 3 lesson 4 homework

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Welcome to the Math Medic Geometry course! Here you will find a ready-to-be-taught lesson for every day of the school year, along with expert tips and questioning techniques to help the lesson be successful. Each lesson is designed to be taught in an Experience First, Formalize Later (EFFL) approach, in which students work in small groups on an engaging activity before the teacher formalizes the learning.

Our Geometry course develops reasoning, justification, and proof skills through an in-depth study of shapes and their properties, rigid transformations and congruence, and the relationship between similarity and right triangle trigonometry. Rich opportunities for problem solving culminate in the unit on surface area and volume. This course was created using the Common Core State Standards as a guide. The standards taught in each Math Medic Geometry lesson can be found here . Additionally, we've chosen to include a unit on Statistics and Probability that can be used as a stand-alone unit at any time during high school course work. The unit overviews and learning targets for the Math Medic Geometry course can be found here .

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Unit 3: Linear relationships

Lesson 3: representing proportional relationships.

• Graphing proportional relationships: unit rate (Opens a modal)
• Graphing proportional relationships from a table (Opens a modal)
• Graphing proportional relationships from an equation (Opens a modal)
• Graphing proportional relationships Get 3 of 4 questions to level up!

Lesson 4: Comparing proportional relationships

• Rates & proportional relationships example (Opens a modal)
• Rates & proportional relationships: gas mileage (Opens a modal)
• Rates & proportional relationships Get 5 of 7 questions to level up!

Lesson 7: Representations of linear relationships

• Linear & nonlinear functions: missing value (Opens a modal)

Lesson 8: Translating to y=mx+b

• Intro to slope-intercept form (Opens a modal)
• Graph from slope-intercept equation (Opens a modal)

Lesson 9: Slopes don't have to be positive

• Intro to intercepts (Opens a modal)
• Slope-intercept equation from slope & point (Opens a modal)
• Linear & nonlinear functions: word problem (Opens a modal)
• Intercepts from a graph Get 3 of 4 questions to level up!
• Slope from graph Get 3 of 4 questions to level up!
• Slope-intercept intro Get 3 of 4 questions to level up!
• Graph from slope-intercept form Get 3 of 4 questions to level up!
• Slope-intercept equation from graph Get 3 of 4 questions to level up!

Lesson 10: Calculating slope

• No videos or articles available in this lesson
• Slope from two points Get 3 of 4 questions to level up!

Lesson 11: Equations of all kinds of lines

• Converting to slope-intercept form (Opens a modal)

Extra practice: Slope

• Intro to slope (Opens a modal)
• Worked examples: slope-intercept intro (Opens a modal)
• Graphing slope-intercept form (Opens a modal)
• Writing slope-intercept equations (Opens a modal)
• Slope-intercept form review (Opens a modal)
• Slope-intercept from two points Get 3 of 4 questions to level up!

Lesson 12: Solutions to linear equations

• Solutions to 2-variable equations (Opens a modal)
• Worked example: solutions to 2-variable equations (Opens a modal)
• Solutions to 2-variable equations Get 3 of 4 questions to level up!

Lesson 13: More solutions to linear equations

• Completing solutions to 2-variable equations (Opens a modal)
• Complete solutions to 2-variable equations Get 3 of 4 questions to level up!

Extra practice: Intercepts

• x-intercept of a line (Opens a modal)
• Intercepts from an equation (Opens a modal)
• Worked example: intercepts from an equation (Opens a modal)
• Intercepts of lines review (x-intercepts and y-intercepts) (Opens a modal)
• Intercepts from an equation Get 3 of 4 questions to level up!

Unit 4 Similarity and Right Triangle Trigonometry

Learning focus.

Describe the essential features of a dilation transformation.

Lesson Summary

In this lesson, we observed the key features of a dilation transformation while figuring out how a photocopy machine enlarges an image. We learned how to locate points on a dilated image by using the center and scale factor that define a specific dilation. We observed that “the same shape, different size” relationship between the pre-image and image figures are a consequence of the way dilations are defined.

Create similar figures by dilation given the scale factor.

Prove a theorem about the midlines of a triangle using dilations.

In this lesson, we extended our understanding of similar figures. Since corresponding segments of similar figures are proportional, and dilations produce similar figures, corresponding parts of an image and its pre-image after a dilation are proportional. We also learned that corresponding line segments in a dilation are parallel. These two observations provided a tool for proving a theorem about the midlines of a triangle, a segment connecting the midpoints of two sides of a triangle.

Determine criteria for triangle similarity.

In this lesson, we examined what it means to say that two figures are similar geometrically, and we examined conditions under which two triangles will be similar. We wrote and justified several theorems for triangle similarity criteria.

Prove that a line drawn parallel to one side of a triangle that intersects the other two sides divides the other two sides proportionally.

In a previous lesson, we learned that a midline of a triangle, a line that passes through the midpoints of two of the sides, is parallel to the third side and half its length. In this lesson, we extended this theorem to include other segments that cut the sides of a triangle proportionally. We also proved a non-intuitive “side-splitting” theorem about the multiple segments formed when multiple lines parallel to a side of a triangle cut the other two sides of the triangle.

Practice using geometric reasoning in computational work.

In this lesson, we drew upon a variety of theorems to support the computational work of finding missing sides and angles. To identify which theorems to use, we had to examine the available features of the diagram. For many measurements, multiple strategies could be used. We also used the diagram, along with our computed measurements, to develop and justify a conjecture for the sum of the interior angles of any polygon, similar to the theorem we proved previously about the sum of the interior angles in a triangle.

Locate the midpoint of a segment and a point that divides the segment in a given ratio.

In this lesson, we examined strategies for dividing a line segment into two parts that fit a given ratio. One common application of this concept is to find the coordinates of the midpoint of a segment, given the coordinates of the endpoints.

Prove the Pythagorean theorem algebraically.

In today’s lesson, we learned that drawing the altitude of a right triangle from the vertex at the right angle to the hypotenuse divides the right triangle into two smaller triangles that are similar to each other and to the original right triangle. We were able to prove the Pythagorean theorem using proportionality statements about the three similar triangles.

Investigate corresponding ratios of right triangles with the same acute angle.

In this lesson, we learned about some special ratios, called trigonometric ratios, that occur in right triangles. If two right triangles have a pair of corresponding acute angles that are congruent, the right triangles will be similar. Therefore, corresponding ratios of the sides of these two right triangles will be equal. This observation is so useful when working with right triangles that have the same acute angle that values of these ratios were recorded in tables for each acute angle between 0 ° and 90 ° .

Examine properties of trigonometric expressions.

In this lesson, we examined some relationships between trigonometric ratios, such as a relationship between the sine and cosine of complementary angles. We were able to use the properties of a right triangle, including the Pythagorean theorem that describes a relationship between the lengths of the sides, to justify the observations we made today.

Solve for the missing side and angle measures in a right triangle.

In this lesson, we extended our strategies for finding unknown sides and angles in a right triangle beyond using the Pythagorean theorem and the angle sum theorem for triangles, since sometimes we don’t have enough information in terms of side lengths or angle measures to use these theorems. We found that trigonometric ratios are useful in solving for unknown sides and that inverse trigonometric relationships are useful for finding unknown angles in a right triangle. Adding these tools allows us to find all of the missing sides and angles in a right triangle given two pieces of information: two sides of the triangle or one side and an angle.

Solve application problems using trigonometry.

In this lesson, we learned about the modeling process and how to use right triangle trigonometry to model many different types of applications, even applications that didn’t naturally include right triangles. A right triangle became a tool for representing a situation so we could draw upon trigonometric ratios and inverse trigonometric relationships to answer important problems in construction, aviation, transportation, and other contexts.

Geo.4 Right Triangle Trigonometry

In this unit students build an understanding of ratios in right triangles which leads to naming cosine, sine, and tangent as trigonometric ratios. Practicing without naming the ratios allows students to connect similarity, proportional reasoning, and scale factors to right triangles with a congruent acute angle before the calculator takes over some of the computation. Students encounter several contexts to both make sense of and apply right triangle measurement.

Angles and Steepness

• 1 Angles and Steepness
• 2 Half a Square
• 3 Half an Equilateral Triangle
• 4 Ratios in Right Triangles
• 5 Working with Ratios in Right Triangles

Defining Trigonometric Ratios

• 6 Working with Trigonometric Ratios
• 7 Applying Ratios in Right Triangles
• 8 Sine and Cosine in the Same Right Triangle
• 9 Using Trigonometric Ratios to Find Angles
• 10 Solving Problems with Trigonometry
• 11 Approximating Pi

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Classifying Triangles

15.1k plays, 6th -  8th  , 4th -  5th  , special right triangles, triangle inequality theorem.

Geometry Unit 4 Homework #3

Mathematics.

25 questions

Introducing new   Paper mode

No student devices needed.   Know more

An acute triangle has __________ angles that each measure less than 90°.

An isosceles triangle has _________ equal sides.

A right triangle has one angle that measures _______ and two acute angles.

less than 90°

more than 90°

An ____________ triangle has three equal sides.

equilateral

An obtuse triangle has one angle that measures _____________ 90°.

A _________ triangle has no equal sides.

• 7. Multiple Choice Edit 5 minutes 1 pt If a triangle has all angles less than 90° and two equal sides, what type of triangle is it? Acute Isosceles Acute Scalene Obtuse Scalene Obtuse Isosceles
• 8. Multiple Choice Edit 5 minutes 1 pt If a triangle has one angle greater than 90° and no equal sides, what type of triangle is it? Acute Isosceles Acute Scalene Obtuse Scalene Obtuse Isosceles
• 9. Multiple Choice Edit 5 minutes 1 pt If a triangle has one angle exactly 90° and two equal sides, what type of triangle is it? Right Isosceles Acute Scalene Obtuse Scalene Obtuse Isosceles
• 10. Multiple Choice Edit 5 minutes 1 pt If a triangle has all three angles equivalent and all three sides equivalent, what type of triangle is it? Acute Isosceles Equilateral Obtuse Scalene Obtuse Isosceles

Find the measure of the angle indicated.

Find the value of x?

What is the value

Use the distance formula to find the measure of the sides of LMN and classify it by its sides:

L(2,7) M(-4,2) N(3,-6)

5, 6.1, 2.8: Scalene

5, 10.2, 10.2: Isosceles

7.8, 10.6, 13.0: Scalene

6.4, 9.2, 6.4: Isosceles

Use the figure to find the measure of angle P.

Solve for x in the figure

In △ QRS, if m ∠ Q is two less than six times x,

m ∠ R is sixteen less than seven times x,

and m ∠ S is three times x plus 6.

What is the value of x?

What is the measure of ∠R?

What is the measure of ∠S?

What is the measure of ∠Q?

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