L2.1 - Congruent Parts, Part 1
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Determine whether or not figures are congruent by reasoning about rigid transformations (in writing).[/*][*]Generate and comprehend congruence statements (orally and in writing) that establish corresponding parts.[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Identify corresponding parts from a congruence statement.[/*][*]Use rigid transformations to figure out if figures are congruent.[/*][*]Write a congruence statement.[/*][/list]
1.1: Notice and Wonder: Transformed Rectangles
What do you notice? What do you wonder?
1.2: If We Know This, Then We Know That...
Triangle ABC is congruent to triangle DEF.
[math]\bigtriangleup[/math]ABC [math]\cong[/math] [math]\bigtriangleup[/math]DEF[br][br]1. Find a sequence of rigid motions that takes triangle [i]ABC[/i] to triangle [i]DEF[/i].
2. What is the image of segment [i]BC[/i] after that transformation?
3. Explain how you know those segments are congruent.
4. Justify that angle [i]ABC[/i] is congruent to angle [i]DEF[/i].
1.2: Are You Ready For More?
For each figure, draw additional line segments to divide the figure into 2 congruent polygons. Label any new vertices and identify the corresponding vertices of the congruent polygons.
1.3: Making Quadrilaterals
1. Draw a triangle.[br]2. Find the midpoint of the longest side of your triangle.[br]3. Rotate your triangle 180[math]^\circ[/math] using the midpoint of the longest side as the center of the rotation.[br]4. Label the corresponding parts and mark what must be congruent.[br]5. Make a conjecture and justify it.[br] a. What type of quadrilateral have you formed?
b. What is the definition of that quadrilateral type?
c. Why must the quadrilateral you have fit the definition?
Lesson Synthesis: Congruent Parts, Part 1
Write down your reason for why corresponding parts of congruent figures must be congruent.
Learning Intentions and Success Criteria
[color=#ff0000]We are learning to:[/color][br][list][*]Determine whether or not figures are congruent by reasoning about rigid transformations (in writing).[/*][*]Generate and comprehend congruence statements (orally and in writing) that establish corresponding parts.[/*][/list][color=#ff0000]We are successful when we can:[/color][br][list][*]Identify corresponding parts from a congruence statement.[/*][*]Use rigid transformations to figure out if figures are congruent.[/*][*]Write a congruence statement.[/*][/list]
Cool-Down: Making Angle Bisectors
Triangle [i]A’B’C’[/i] is a reflection of triangle ABC across line [i]BC[/i]. Prove that ray [i]BC[/i] is the angle bisector of angle [i]ABA’[/i].
