Curriculum / Math / 10th Grade / Unit 5: Polygons and Algebraic Relationships / Lesson 7
Math
Unit 5
10th Grade
Lesson 7 of 15
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Algebraically verify midsegment, median, and parallel line 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.
G.SRT.B.4 — Prove theorems about triangles. Theorems include: a line parallel to one side of a triangle divides the other two proportionally, and conversely; the Pythagorean Theorem proved using triangle similarity.
The foundational 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.
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 connects to Unit 3 Lesson 6 because it deals with properties of triangles that were developed off the coordinate plane using proof. This lesson will expand the knowledge of these properties and work with them on the coordinate plane.
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Problems designed to teach key points of the lesson and guiding questions to help draw out student understanding
Given triangle $${JKL}$$,
Given triangle $${DEF}$$,
Below is triangle $${ABC}$$ with midpoints $$D$$, $$E$$, and $$F$$.
Draw a line segment from each midpoint to the opposite vertex. Mark a point that is $${{2\over3}}$$ of the distance between the midpoint and the opposite vertex, closer to the midpoint. What do you notice?
Explorations of Medians & Centroid of a Triangle by Kim Kembitzky and Tim Brzezinski is made available by GeoGebra under the CC BY-NC-SA 3.0 license. Copyright © International GeoGebra Institute, 2013. Accessed June 1, 2018, 4:48 p.m..
A task that represents the peak thinking of the lesson - mastery will indicate whether or not objective was achieved
Triangle $${ABC}$$ has vertices $${A(3,3)}$$, $${B(7,9)}$$, and $${C(11,3)}$$. Determine the point of intersection of the medians and state its coordinates.
G.CO.C.10: Centroid, Orthocenter, Incenter and Circumcenter is made available on JMAP by Steve Sibol and Steve Watson. Copyright © 2017 JMAP, Inc. - All rights reserved. Accessed May 31, 2018, 2:29 p.m..
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 6
Lesson 8
Topic A: Distance on the Coordinate Plane
Use the Pythagorean Theorem to calculate distance on a coordinate plane. Develop a formula for calculating distances.
G.GPE.B.7
Partition horizontal and vertical line segments into equal proportions on a number line.
G.GPE.B.6
Divide a line segment on a coordinate plane proportionally and identify the point that divides the segment proportionally.
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Topic B: Classify Polygons using Slope Criteria and Proportional Line Segments
Algebraically and using the Pythagorean Theorem, determine the slope criteria for perpendicular lines.
G.GPE.B.5 G.SRT.C.8
Describe and apply the slope criteria for parallel lines.
G.GPE.B.5
Identify and create parallelograms, rectangles, rhombuses, and squares on the coordinate plane.
G.GPE.B.4
G.CO.C.10 G.SRT.B.4
Algebraically verify diagonal relationships in quadrilaterals and parallelograms.
G.CO.C.11 G.GPE.B.4
Topic C: Area and Perimeter On and Off the Coordinate Plane
Calculate and justify the area and perimeter of polygons and composite shapes off the coordinate plane.
Calculate and justify the area and perimeter of parallelograms and triangles on the coordinate plane.
Calculate and justify composite and irregular areas on the coordinate plane.
G.GPE.B.7 N.Q.A.3
Describe how the area changes when a figure is scaled.
Solve area applications by creating and solving quadratic equations.
A.CED.A.1
Describe a polygon on the coordinate plane using a system of inequalities.
A.CED.A.3 G.CO.A.2
Calculate and justify the area and perimeter of polygons on the coordinate plane given a system of inequalities.
A.REI.D.12 G.GPE.B.4 G.GPE.B.7
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