1. Transformations and Congruence
Geometry
Topic 1
Transformations and Congruence

2. Table of Contents
Recommended Instructional Design and Planning Continuum Slide 3
Vocabulary …………………………………………………………………….……………..Slides 4 – 38
Reporting Category Practice Items ………………….…………………………….Slides

4. Vocabulary

5. Mathematically Speaking!
Choose 3-4 vocabulary words for the day. Throughout the lesson, as students respond to your questions or are presenting a problem on the board, mark a tally when a vocabulary word is used accurately. This can be turned into a competition among groups or between periods.
Examples of accuracy
line vs line segment
translation vs slide
midpoint vs the middle

6. Point – a point has no dimension. It is a location on a plane
Point – a point has no dimension. It is a location on a plane. It is represented by a dot.

7. Line – a line has one dimension
Line – a line has one dimension. It is an infinite set of points represented by a line with two arrowheads that extends without end.

8. Plane – a plane has two dimensions extending without end
Plane – a plane has two dimensions extending without end. It is often represented by a parallelogram.

9. Line segment – a line segment consists of two endpoints and all the points between them.

10. Ray – a ray has one endpoint and extends without end in one direction.
Note: Name the endpoint first. BC and CB are different rays.

11. Coplanar – points that lie in the same plane.

12. Collinear – points that lie on the same line.
K, L and M are collinear points.

13. Postulate – a statement that is accepted as true without proof.

14. Midpoint - divides a segment into two congruent segments.

15. Segment bisector – a line, ray or segment that divides a segment into two congruent segments.

16. Angle – a figure forms by two rays with a common endpoint.

17. Vertex – the common endpoint of two or more rays or line segments.

18. Side of an angle – one of the two rays that form an angle.
𝐷𝐸 and 𝐸𝐹 are sides of ∠𝐷𝐸𝐹

19. Angle bisector – a ray that divides an angle into two congruent angles.

20. Transformation – a change in the position, size, or shape of a figure
Transformation – a change in the position, size, or shape of a figure. A transformation maps the preimage to the image.

21. Rigid motion– a transformation of the plane or space, which preserves distance and angles.

22. Conjecture – a statement that is believed to be true.
Theorem – a statement that has been proven.

23. Deductive reasoning - method using logic to draw conclusions based upon definitions, postulates, and theorems.
Inductive reasoning – method of drawing conclusions from a limited set of observations

24. Counterexample - specific case for which a conjecture is false.
One counterexample proves a conjecture false.

25. Conditional Statement - a logical argument consisting of a set of premises, hypothesis (p), and conclusion (q).
Symbolically:
if p, then q p→q

26. Linear pair – a pair of adjacent angles whose non-common sides are opposite rays.
∠1 and ∠2 form a linear pair

27. Translation - a transformation in which all the points of a figure move the same distance in the same direction; the figure is moved along a vector so that all of the segments joining a point and its image are congruent and parallel.
Preimage
Image
A(1,2)
A(-2,-3)
B(3,2)
B(0,-3)
C(4,3)
C(1,-2)
D(3,4)
D(0,-1)
E(1,4)
E(-2,-1)

28. Perpendicular lines – lines that intersect at 90° angles.

29. Perpendicular bisector - a segment, ray, line, or plane that is perpendicular to a segment at its midpoint.

30. Parallel lines – lines in the same plane that do not intersect.

31. Reflection – a transformation across a line, called the line of reflection. The line of reflection is the perpendicular bisector of each segment joining a point and its image.
Preimage
Image
D (1,-2)
D(-1,-2)
E (3,-2)
E(-3,-2)
F (3,2)
F(-3,2)

32. Rotation – a transformation about a point P, also known as the center of rotation, such that each point and its image are the same distance from P. All of the angles with vertex P formed by a point and its image are congruent.
Preimage
Image
A (-3,0)
A(0,3)
B (-3,3)
B(3,3)
C (-1,3)
C(3,1)
D (-1,0)
D(0,1)
Pre-image has been transformed by a 90° clockwise rotation about the origin.

33. Center of rotation – the point around which a figure is rotated.
Pre-image A has been transformed by a 90° clockwise rotation about the point (2, 0) to form image A’.

34. Symmetry – the transformation of a figure such that the image coincides with the preimage, the image and preimage have symmetry.

35. Line of Symmetry – a line that divides a place figure into two congruent reflected halves.

36. Rotational symmetry – a figure that can be rotated about a point by an angle less thank 360° so that the image coincides with the preimage has a rotational symmetry.

37. Complementary angles – two angles whose measures have a sum of 90°.

38. Supplementary angles – two angles whose measures have a sum of 180°.