Curriculum / Math / 8th Grade / Unit 3: Transformations and Angle Relationships / Lesson 19
Math
Unit 3
8th Grade
Lesson 19 of 22
Jump To
Solve for missing angle measures in parallel line diagrams using equations.
The core standards covered in this lesson
8.G.A.5 — Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so.
The foundational standards covered in this lesson
8.EE.C.7 — Solve linear equations in one variable.
7.G.B.5 — Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
A common error is to set up an equation that inaccurately represents the relationship between the angles, for example, setting the expressions equal to each other in a supplementary relationship rather than adding up to 180$$^\circ$$. Have students start by looking at the structure of the diagram and understanding the relationship between the angles before they set up an equation (MP.7).
Unlock features to optimize your prep time, plan engaging lessons, and monitor student progress.
Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Lines $${L_1 }$$ and $${L_2}$$ are parallel and cut by transversal $$p$$.
What are the measures of the angles shown by the algebraic expressions?
Determine the values of $$x$$ and $$y$$ in the diagram below, and use them to determine the measures of the eight angles formed by the parallel lines and transversal.
A set of suggested resources or problem types that teachers can turn into a problem set
Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Lines $$b$$ and $$c$$ are parallel cut by transversal line $$a$$. Determine all of the angle measures.
An example response to the Target Task at the level of detail expected of the students.
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 18
Lesson 20
Topic A: Congruence and Rigid Transformations
Understand the rigid transformations that move figures in the plane (translation, reflection, rotation).
8.G.A.1.A 8.G.A.1.B 8.G.A.1.C 8.G.A.2
Describe and perform translations between congruent figures. Use translations to determine if figures are congruent.
Describe and apply properties of translations. Use coordinate points to represent relationships between translated figures.
8.G.A.1.A 8.G.A.1.B 8.G.A.1.C 8.G.A.2 8.G.A.3
Describe and perform reflections between congruent figures. Use reflections to determine if figures are congruent.
Describe sequences of transformations between figures using reflections and translations. Use coordinate points to represent relationships between reflected figures.
Describe and perform rotations between congruent figures.
Describe sequences of transformations between figures using rotations and other transformations.
Describe a sequence of rigid transformations that will map one figure onto another.
Describe multiple rigid transformations using coordinate points.
8.G.A.2 8.G.A.3
Review rigid transformations and congruence between two figures.
Create a free account to access thousands of lesson plans.
Already have an account? Sign In
Topic B: Similarity and Dilations
Define a dilation as a non-rigid transformation, and understand the impact of scale factor.
8.G.A.4
Describe and perform dilations.
Describe a sequence of dilations and rigid motions between two figures. Use coordinate points to represent relationships between similar figures.
8.G.A.3 8.G.A.4
Determine and informally prove or disprove if two figures are similar or congruent using transformations.
8.G.A.2 8.G.A.4
Find missing side lengths in similar figures. Find scale factor between similar figures.
Use properties of similar triangles to model and solve real-world problems.
Topic C: Angle Relationships
Define and identify corresponding angles in parallel line diagrams. Review vertical, supplementary, and complementary angle relationships.
8.G.A.2 8.G.A.5
Define and identify alternate interior and alternate exterior angles in parallel line diagrams. Find missing angles in parallel line diagrams.
8.G.A.5
Define and use the interior angle sum theorem for triangles.
Define and use the exterior angle theorem for triangles.
Define and use the angle-angle criterion for similar triangles.
See all of the features of Fishtank in action and begin the conversation about adoption.
Learn more about Fishtank Learning School Adoption.
Yes
No
Access rigorous, relevant, and adaptable math lesson plans for free