Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 9
Math
Unit 2
10th Grade
Lesson 9 of 18
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Develop the Side Angle Side criteria for congruent triangles through rigid motions.
The core standards covered in this lesson
G.CO.B.7 — Use the definition of congruence in terms of rigid motions to show that two triangles are congruent if and only if corresponding pairs of sides and corresponding pairs of angles are congruent.
G.CO.B.8 — Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions.
The foundational standards covered in this lesson
8.G.A.2 — Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.
The essential concepts students need to demonstrate or understand to achieve the lesson objective
Suggestions for teachers to help them teach this lesson
This lesson marks the beginning of congruence criteria in triangles. Students should record all congruence criteria in notes in an organized way so they can refer to the criteria when necessary. Â We will compare the congruence criteria to similarity criteria in the next unit.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Using patty paper, trace the sides and the included angle below. How many different triangles can you make, starting with these two sides and the included angle?
How can you use rigid motions to prove that if two triangles meet the side-angle-side criteria, the triangles are congruent?
Given: $${\overline{AB} \parallel \overline{CD}}$$ and $${\overline{AB} \cong \overline{CD}}$$
Do $${\triangle ABD}$$ and $${\triangle CDB}$$ meet the SAS criteria?
Geometry > Module 1 > Topic D > Lesson 22 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
In the diagram, $${\overline{AB} \cong \overline{DE}}$$, $${\angle B \cong \angle E}$$, and $${\overline{BC} \cong \overline{EF}}$$. Using rigid motion(s), explain in detail why triangle ABC must be congruent to triangle DEF by the Side Angle Side criteria.
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 8
Lesson 10
Topic A: Introduction to Polygons
Define polygon and identify properties of polygons.
G.CO.A.1 G.CO.C.11
Prove interior and exterior angle relationships in triangles.
G.CO.C.10
Describe and apply the sum of interior and exterior angles of polygons.
G.CO.C.11
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Topic B: Rigid Motion Congruence of Two-Dimensional Figures
Determine congruence of two dimensional figures by translation.
G.CO.A.2 G.CO.A.4 G.CO.A.5 G.CO.B.7
Reflect two dimensional figures on and off the coordinate plane.
G.CO.A.2 G.CO.A.3 G.CO.A.5 G.CO.B.7
Rotate two dimensional figures on and off the coordinate plane.
Describe a sequence of rigid motions that map a pre-image to an image (specifically triangles, rectangles, parallelograms, and regular polygons).
G.CO.A.5 G.CO.B.6
Describe single rigid motions, or sequences of rigid motions that have the same effect on a figure.
G.CO.A.3 G.CO.A.5 G.CO.B.6
Topic C: Triangle Congruence
G.CO.B.7 G.CO.B.8
Prove angle relationships using the Side Angle Side criteria.
G.SRT.B.5
Prove and apply that the points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
G.CO.A.2 G.CO.C.10 G.CO.C.9
Develop Angle, Side, Angle (ASA) and Side, Side, Side (SSS) congruence criteria. Describe how the criteria develop from rigid motions.
Use triangle congruence criteria, rigid motions, and other properties of lines and angles to prove congruence between different triangles.
Prove triangles congruent using Angle, Angle, Side (AAS), and describe why AAA is not a congruency criteria.
G.CO.B.7 G.CO.B.8 G.CO.C.10
Develop the Hypotenuse- Leg (HL) criteria, and describe the features of a triangle that are necessary to use the HL criteria.
G.CO.B.7 G.CO.C.10
Use criteria for triangle congruence to prove relationships among angles and sides in geometric problems.
G.CO.C.9 G.SRT.B.5
Topic D: Parallelogram Properties from Triangle Congruence
Prove that the opposite sides and opposite angles of a parallelogram are congruent.
Prove theorems about the diagonals of parallelograms.
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