Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 10
Math
Unit 2
10th Grade
Lesson 10 of 18
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Lesson Notes
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Prove angle relationships using the Side Angle Side criteria.
The core standards covered in this lesson
G.SRT.B.5 — Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
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.
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 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
25-30 minutes
Given: $${\overline{AB} \parallel \overline{CD}}$$ and $${\overline{AB} \cong \overline{CD}}$$
Prove: $${\triangle ABD \cong \triangle CDB}$$
Prove that $${\triangle BEC \cong \triangle ADC}$$ given that $$C$$ is the midpoint of $${\overline{DE}}$$ and $${\overline {AB}}$$.
The proof below is incorrect. Identify the statement and reason that are incorrect, and correct the reasoning. Given: $${\overline{BD} \cong \overline{EC}}$$, $${\overline {BA} \cong \overline{EA}}$$, $${\angle BCE \cong \angle EDB}$$. Prove: $${\triangle ABD \cong \triangle AEC}$$
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
5-10 minutes
Given: $${AC \perp BC}$$, $$D$$ is the midpoint of $${\overline{AC}}$$
Prove:Â $$\triangle ABC \cong \triangle CBD$$
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.
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Prove and apply that the points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Topic A: Introduction to Polygons
Define polygon and identify properties of polygons.
Standards
G.CO.A.1G.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.2G.CO.A.4G.CO.A.5G.CO.B.7
Reflect two dimensional figures on and off the coordinate plane.
G.CO.A.2G.CO.A.3G.CO.A.5G.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.5G.CO.B.6
Describe single rigid motions, or sequences of rigid motions that have the same effect on a figure.
G.CO.A.3G.CO.A.5G.CO.B.6
Topic C: Triangle Congruence
Develop the Side Angle Side criteria for congruent triangles through rigid motions.
G.CO.B.7G.CO.B.8
G.SRT.B.5
G.CO.A.2G.CO.C.10G.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.7G.CO.B.8G.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.7G.CO.C.10
Use criteria for triangle congruence to prove relationships among angles and sides in geometric problems.
G.CO.C.9G.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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