Curriculum / Math / 10th Grade / Unit 2: Congruence in Two Dimensions / Lesson 2
Math
Unit 2
10th Grade
Lesson 2 of 18
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Prove interior and exterior angle relationships in triangles.
The core standards covered in this lesson
G.CO.C.10 — Prove theorems about triangles. Theorems include: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
The foundational 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 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
Given that $${\overleftrightarrow{AB} \parallel \overleftrightarrow{ED}}$$ in the diagram below, prove that $${a^{\circ}+b^{\circ}+c^{\circ}=180^{\circ}}$$
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A Triangle's Interior Angles, accessed on Aug. 10, 2017, 9:48 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.
Prove that $${\angle1 + \angle2 = \angle 4}$$.
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
What is the value of $$y$$?
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 1
Lesson 3
Topic A: Introduction to Polygons
Define polygon and identify properties of polygons.
G.CO.A.1 G.CO.C.11
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
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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