corresponding parts G.CO.7 (ES&K) Knowledge of vocabulary corresponding parts and the connection to the given triangles Given two figures of the same shape, the corresponding parts are the angles and sides that are in the same position. e.g. shortest side corresponds to the shortest side, the longest side corresponds to the longest side etc.
Previous Math Courses Geometry Unit 1 Future Mathematics Concepts developed in previous mathematics course/units which serve as a foundation for the development of the “Key Concept” Key Concept(s) Concepts that a student will study either later in Geometry or in future mathematics courses for which this “Key Concept” will be a foundation. In 8th grade, students: verify experimentally the properties of rotations, translations and reflections. describe effects of transformations in the coordinate plane. In Algebra I, students: study linear, exponential and quadratic functions. describe how the graph of the parent function f(x) is transformed algebraically to create a new function. Examples Experiment with transformations in the plane. In Algebra II and further mathematics, students will: study additional functions. As each function is explored, students will be required to describe how the graph of the parent function f(x) is transformed algebraically to create a new function. Examples In 8th grade, students: develop an understanding that figures created by a series of reflections, translations and rotations are in fact congruent. Understand congruence in terms of rigid motions. In further mathematics students will: apply their knowledge of rigid motion to the study of application problems which deal with volume of three dimensional shapes. In 8th grade, students: develop informal arguments regarding the angles in a triangle as well as angles formed by parallel lines cut by a transversal. In 8th grade students : explain a proof of the Pythagorean Theorem but they were not actually required to prove the theorem. In Algebra I, students: Develop and use the practice of formal proof as a means of reasoning Throughout the geometry course, students will : continue to prove geometric theorems. In later introductory statistics classes, students will: be asked to defend their answers in a similar fashion to geometric proof. Later in college, some students develop Euclidean and non-Euclidean geometries carefully from a small set of axioms. In all other contents, students must defend their answers
use informal proofs to describe numerical relationships in when working with polynomials, linear equations and systems of equations. and this provides a discipline of structuring the defense. In 7th grade, students: construct triangles with three given measures. draw geometric figures with given conditions. Make geometric constructions In future studies, students must understand concepts of congruence and how they are used by electronic tools to create congruent figures. (Engineering courses, construction courses etc.) Common Misconceptions This list includes general misunderstandings and issues that frequently hinder student mastery of concepts regarding the content of this unit. Topic/Standard/Concept Misconception Strategies to Address Misconception
Understand Congruence in Terms of Rigid Motions/G.CO.7 and G.CO.8 It is often difficult for students to identify the correct combination of corresponding sides and angles required to establish that two triangles are congruent. The following activity provides a hands on method for having students investigate what combination of corresponding sides and angles will create two congruent triangles. Activity Materials Needed Straws – each pair of students will need: two 3 inch straws; two 4 inch straws and two 5 inch straws Angle templates- each pair of students should receive 6 index cards with angles drawn on them in the following manor: two right angles, two 36.8 degree angles and two 53.2 degree angles. Have students use the angles and straws to determine the fewest number of parts needed to construct identical triangles. Discuss how those parts need to be organized – SSS, SAS, ASA, etc.