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This page intentionally left blank, SECONDARY MATH 1 MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF, MODULE 7 TABLE OF CONTENTS. CONGRUENCE CONSTRUCTION AND PROOF, 7 1 Under Construction A Develop Understanding Task Page 1. Exploring compass and straightedge constructions to construct rhombuses and squares. NC M2 G CO 9 Math Practice 5, READY SET GO Homework Congruence Construction and Proof 7 1. 7 2 More Things Under Construction A Develop Understanding Task Page 11. Exploring compass and straightedge constructions to construct parallelograms equilateral triangles. and inscribed hexagons NC M2 G CO 9 Math Practice 5. READY SET GO Homework Congruence Construction and Proof 7 2. 7 3 Can You Get There From Here A Develop Understanding Task Page 17. Describing a sequence of transformations that will carry congruent images onto each other. NC M2 G CO 5, READY SET GO Homework Congruence Construction and Proof 7 3.

7 4 Congruent Triangles A Solidify Understanding Task Page 21. Establishing the ASA SAS and SSS criteria for congruent triangles. NC M2 G CO 6 NC M2 G CO 7 NC M2 G CO 8, READY SET GO Homework Congruence Construction and Proof 7 4. 7 5 Congruent Triangles to the Rescue A Practice Understanding Task Page 29. Identifying congruent triangles and using them to justify claims. NC M2 G CO 7 NC M2 G CO 8, READY SET GO Homework Congruence Construction and Proof 7 5. Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, This page intentionally left blank. CC BY UK Department for International Development, SECONDARY MATH I MODULE 7.

CONGRUENCE CONSTRUCTION AND PROOF 7 1, https flic kr p ekUmnG. 7 1 Under Construction, A Develop Understanding Task. Anciently one of the only tools builders and surveyors had for laying out a plot of land or the. foundation of a building was a piece of rope, There are two geometric figures you can create with a piece of rope you can pull it tight to. create a line segment or you can fix one end and while extending the rope to its full length trace. out a circle with the other end Geometric constructions have traditionally mimicked these two. processes using an unmarked straightedge to create a line segment and a compass to trace out a. circle or sometimes a portion of a circle called an arc Using only these two tools you can. construct all kinds of geometric shapes, Suppose you want to construct a rhombus using only a compass and straightedge You. might begin by drawing a line segment to define the length of a side and drawing another ray from. one of the endpoints of the line segment to define an angle as in the following sketch. Now the hard work begins We can t just keep drawing line segments because we have to. be sure that all four sides of the rhombus are the same length We have to stop drawing and start. constructing, Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0.

mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 1, Constructing a rhombus. Knowing what you know about circles and line segments how might you locate point C on the ray. in the diagram above so the distance from B to C is the same as the distance from B to A. 1 Describe how you will locate point C and how you know BC BA then construct point C. on the diagram above, Now that we have three of the four vertices of the rhombus we need to locate point D the fourth. 2 Describe how you will locate point D and how you know CD DA AB then construct. point D on the diagram above, Constructing a Square A rhombus with right angles. The only difference between constructing a rhombus and constructing a square is that a. square contains right angles Therefore we need a way to construct perpendicular lines using only. a compass and straightedge, We will begin by inventing a way to construct a perpendicular bisector of a line segment.

3 Given below fold and crease the paper so that point R is reflected onto point S Based on. the definition of reflection what do you know about this crease line. Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 1, You have constructed a perpendicular bisector of by using a paper folding strategy Is. there a way to construct this line using a compass and straightedge. 4 Experiment with the compass to see if you can develop a strategy to locate points on the. crease line When you have located at least two points on the crease line use the. straightedge to finish your construction of the perpendicular bisector Describe your. strategy for locating points on the perpendicular bisector of. Now that you have created a line perpendicular to we will use the right angle formed to. construct a square, 5 Label the midpoint of on the diagram above as point M Using segment as one side of. the square and the right angle formed by segment and the perpendicular line drawn. through point M as the beginning of a square Finish constructing this square on the. diagram above Hint Remember that a square is also a rhombus and you have already. constructed a rhombus in the first part of this task. Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0.

mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 1 7 1, READY SET GO Name Period Date. Topic Tools for construction and geometric work, 1 Using your compass draw several concentric circles that have point A as a center and then draw those. same sized concentric circles that have B as a center What do you notice about where all the circles with. center A intersect all the corresponding circles with center B. 2 In the problem above you have demonstrated one way to find the midpoint of a line segment Explain. another way that a line segment can be bisected without the use of circles. Topic Constructions with compass and straight edge. 3 Bisect the angle below do it with compass and straight edge as well as with paper folding. Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7.

CONGRUENCE CONSTRUCTION AND PROOF 7 1 7 1, 4 Copy the segment below using construction tools of compass and straight edge label the image D E. 5 Copy the angle below using construction tool of compass and straight edge. 6 Construct a rhombus on the segment AB that is given below and that has point A as a vertex Be sure. to check that your final figure is a rhombus, Mathematics Vision Project. Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 1 7 1, 7 Construct a square on the segment CD that is given below Be sure to check that your final figure is a. 8 Given the equilateral triangle below find the center of rotation of the triangle using compass and. straight edge, Topic Solving systems of equations, Solve each system of equations Utilize substitution elimination graphing or matrices.

11 4 9 9 2 11, 2 19 3 6 4 2, 2 1 3 8 6 2 8, Mathematics Vision Project. Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 2, https flic kr p 7eEbDP. CC BY Brian Negus, 7 2 More Things Under, Construction. A Develop Understanding Task, Like a rhombus an equilateral triangle has three congruent sides Show and describe how.

you might locate the third vertex point on an equilateral triangle given below as one side of the. equilateral triangle, Constructing a Parallelogram. To construct a parallelogram we will need to be able to construct a line parallel to a given. line through a given point For example suppose we want to construct a line parallel to segment. through point C on the diagram below Since we have observed that parallel lines have the same. slope the line through point C will be parallel to only if the angle formed by the line and is. congruent to ABC Can you describe and illustrate a strategy that will construct an angle with. vertex at point C and a side parallel to, Mathematics Vision Project. Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 2, Constructing a Hexagon Inscribed in a Circle. Because regular polygons have rotational symmetry they can be inscribed in a circle The. circumscribed circle has its center at the center of rotation and passes through all of the vertices of. the regular polygon, We might begin constructing a hexagon by noticing that a hexagon can be decomposed into.

six congruent equilateral triangles formed by three of its lines of symmetry. 1 Sketch a diagram of such a decomposition, 2 Based on your sketch where is the center of the circle that would circumscribe the. 3 The six vertices of the hexagon lie on the circle in which the regular hexagon is inscribed. The six sides of the hexagon are chords of the circle How are the lengths of these chords. related to the lengths of the radii from the center of the circle to the vertices of the hexagon. That is how do you know that the six triangles formed by drawing the three lines of. symmetry are equilateral triangles Hint Considering angles of rotation can you convince. yourself that these six triangles are equiangular and therefore equilateral. Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 2, 4 Based on this analysis of the regular hexagon and its circumscribed circle illustrate and. describe a process for constructing a hexagon inscribed in the circle given below. 5 Modify your work with the hexagon to construct an equilateral triangle inscribed in the. circle given below, 6 Describe how you might construct a square inscribed in a circle.

Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 2 7 2, READY SET GO Name Period Date. Topic Transformation of lines connecting geometry and algebra. For each set of lines use the points on the line to determine which line is the image and which is. the pre image write image by the image line and pre image by the original line Then define the. transformation that was used to create the image Finally find the equation for each line. a Description of Transformation a Description of Transformation. b Equation for pre image b Equation for pre image, c Equation for image c Equation for image. a Description of Transformation a Description of Transformation. b Equation for pre image b Equation for pre image, c Equation for image c Equation for image.

Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0. mathematicsvisionproject org, SECONDARY MATH I MODULE 7. CONGRUENCE CONSTRUCTION AND PROOF 7 2 7 2, Topic Geometric constructions with compass and straight edge. 5 Construct a parallelogram given sides and 6 Construct a line parallel to and through. and point R, 7 Given segment AB show all points C such that ABC is an isosceles triangle. 8 Given segment AB show all points C such that ABC is a right triangle. Mathematics Vision Project, Licensed under the Creative Commons Attribution CC BY 4 0.

Mathematics Vision Project Licensed under the Creative Commons Attribution CC BY 4 0 mathematicsvisionproject org 7 1 Under Construction A Develop Understanding Task Anciently one of the only tools builders and surveyors had for laying out a plot of land or the foundation of a building was a piece of rope