Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 5
Math
Unit 5
10th Grade
Lesson 5 of 15
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Describe and apply the slope criteria for parallel lines.
The core standards covered in this lesson
G.GPE.B.5 — Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
The foundational standards covered in this lesson
8.EE.B.6 — Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.
8.EE.C.8 — Analyze and solve pairs of simultaneous linear equations.
8.G.A.1 — Verify experimentally the properties of rotations, reflections, and translations:
A.REI.C.6 — Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
In the diagram below, $${m\parallel p}$$.
a. Write three equations that are perpendicular to line $$m$$.
b. What is the relationship between your three equations and line $$p$$?
c. Find the distance between line $$m$$ and $$p$$ using your three equations. What do you notice?
Distance between Parallel Lines is made available by CK-12 under the CC BY-NC 3.0 license. © CK-12 Foundation 2017. Visit them at ck12.org. Accessed June 1, 2018, 4:27 p.m..
In the diagram below, $${\overleftrightarrow {AI} \parallel {\overleftrightarrow {CK}}}$$ and $${\overleftrightarrow{IC} \perp \overleftrightarrow {AK}}$$. How can you use the triangles $${AHI}$$ and $${KHC}$$ to prove that the slopes for $${\overleftrightarrow{AI}}$$ and $${\overleftrightarrow {CK}}$$ are the same?
Write three equations that are parellel to $${\overleftrightarrow{AB}}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Write the equation of the line that passes through point $${ (6,8)}$$ and is parallel to the line $${3x+2y=8}$$.
The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.
Lesson 4
Lesson 6
Topic A: Distance on the Coordinate Plane
Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
G.GPE.B.7
Partition horizontal and vertical line segments into equal proportions on a number line.
G.GPE.B.6
Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.
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Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments
Algebraically and using the Pythagorean Theorem, determine the slope criteria for perpendicular lines.
G.GPE.B.5 G.SRT.C.8
G.GPE.B.5
Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.
G.GPE.B.4
Algebraically verify midsegment, median, and parallel line relationships in triangles.
G.CO.C.10 G.SRT.B.4
Algebraically verify diagonal relationships in quadrilaterals and parallelograms.
G.CO.C.11 G.GPE.B.4
Topic C: Area and Perimeter On and Off the Coordinate Plane
Calculate and justify the area and perimeter of polygons and composite shapes off the coordinate plane.
Calculate and justify the area and perimeter of parallelograms and triangles on the coordinate plane.
Calculate and justify composite and irregular areas on the coordinate plane.
G.GPE.B.7 N.Q.A.3
Describe how the area changes when a figure is scaled.
Solve area applications by creating and solving quadratic equations.
A.CED.A.1
Describe a polygon on the coordinate plane using a system of inequalities.
A.CED.A.3 G.CO.A.2
Calculate and justify the area and perimeter of polygons on the coordinate plane given a system of inequalities.
A.REI.D.12 G.GPE.B.4 G.GPE.B.7
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