Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 16
Math
Unit 2
10th Grade
Lesson 16 of 18
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Use criteria for triangle congruence to prove relationships among angles and sides in geometric problems.
The core standards covered in this lesson
G.CO.C.9 — Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
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.
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
Triangle A has a side that is one inch long, and has angles with measures of $${90^{\circ}}$$ and $${20^{\circ}}$$.
If Triangle B is drawn with the same properties as Triangle A, will it be congruent to Triangle A? Explain your reasoning.
Evaluating Conditions for Congruency from the Classroom Challenges by the MARS Shell Center team at the University of Nottingham is made available by the Mathematics Assessment Project under the CC BY-NC-ND 3.0 license. Copyright © 2007-2015 Mathematics Assessment Resource Service, University of Nottingham. Accessed Aug. 10, 2017, 4:08 p.m..
Given: $${AB=AC}$$, $${RB=RC}$$
Prove: $${SB=SC}$$
Geometry > Module 1 > Topic D > Lesson 27 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
Given: $$M$$ is the midpoint of $${\overline {GR}}$$, $${\angle G \cong \angle R}$$
Prove:Â $$\triangle GHM \cong \triangle RPM$$
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 15
Lesson 17
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
Develop the Side Angle Side criteria for congruent triangles through rigid motions.
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
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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