Download presentation

Presentation is loading. Please wait.

1
**Rotations California Standards for Geometry**

16: Perform basic constructions 17: Prove theorems using coordinate geometry 22: Know the effect of rigid motions on figures in the coordinate plane.

2
**Properties of a Rotation**

Transformation in which a figure is turned about a fixed point called the CENTER OF ROTATION. Rays drawn from the center of rotation to a point and its image form the ANGLE OF ROTATION. Rotations can be clockwise or counterclockwise.

3
**Properties of a Rotation**

If P is not C (the center of rotation), then PC = P’C P xo P’ C

4
**Properties of a Rotation**

If P is C (the center of rotation), then P = P’ P P’ C

5
**Properties of a Rotation**

Q’ Q P’ R S R’ P T’ T S’ C

6
**identify and use rotations**

Q’ Q P’ R S R’ P T’ T 88o S’ C

7
**theorem Rotation Theorem A rotation is an isometry**

to prove this theorem, you must show that a rotation keeps segment lengths from the preimage to the image this means that AB = A’B’

8
**theorem Three Cases are needed to prove that a rotation is an isometry**

Q P P’ Case 1: P, Q and C are noncollinear C Q’

9
theorem Q Case 2: P, Q, and C are collinear Q’ P’ P C

10
theorem Case 3: P and C are the same point Q P C P’ Q’

11
**Case 1: P, Q and C are noncollinear Prove: PQ = P’Q’**

Definition rotation Definition rotation + prop of =

12
**Case 1: P, Q and C are noncollinear Prove: PQ = P’Q’ C.P.C.T.C. Q P P’**

13
**and name the new coordinates**

Example S R Graph Quad PQRS P(3, 1), Q(4, 0), R(4, 3) S(2, 4) and then rotate PQRS 180o counterclockwise about (0, 0) and name the new coordinates P (-3, -1) P’ Q

14
**and name the new coordinates**

Example S R Graph Quad PQRS P(3, 1), Q(4, 0), R(4, 3) S(2, 4) and then rotate PQRS 180o counterclockwise about (0, 0) and name the new coordinates (-4, 0) Q’ P (-3, -1) P’ Q

15
**and name the new coordinates**

Example S R Graph Quad PQRS P(3, 1), Q(4, 0), R(4, 3) S(2, 4) and then rotate PQRS 180o counterclockwise about (0, 0) and name the new coordinates (-4, 0) Q’ P (-3, -1) P’ Q R’ (-4, -3)

16
**and name the new coordinates**

Example S R Graph Quad PQRS P(3, 1), Q(4, 0), R(4, 3) S(2, 4) and then rotate PQRS 180o counterclockwise about (0, 0) and name the new coordinates (-4, 0) Q’ P (-3, -1) P’ Q R’ (-4, -3) S’ (-2, -4)

17
**and name the new coordinates**

Example S R Graph Quad PQRS P(3, 1), Q(4, 0), R(4, 3) S(2, 4) and then rotate PQRS 180o counterclockwise about (0, 0) and name the new coordinates (-4, 0) Q’ P (-3, -1) P’ Q R’ (-4, -3) S’ (-2, -4)

18
**theorem Reflection-Rotation Theorem**

If two lines intersect, then a reflection in the first line followed by a reflection in the second line is the same as a rotation about the point of intersection. m A B B’ A’ P B’’ A’’

19
**theorem xo 2xo Reflection-Rotation Theorem**

The angle of rotation is 2xo, where xo is the measure of the acute or right angle formed by the two lines. m A 2xo xo B B’ A’ P B’’ A’’

20
**Example is reflected in line k to produce .**

This triangle is the reflected in line m to produce Describe the transformation k J’ J” K’ K” K L’ L” 90o clockwise rotation 45o J P L m

21
**Definition 90o Rotational Symmetry**

A figure that can be mapped onto itself by a rotation of 180o or less. 90o

22
**120o Definition Rotational Symmetry**

A figure that can be mapped onto itself by a rotation of 180o or less. 120o

23
**No rotational symmetry**

Definition Rotational Symmetry A figure that can be mapped onto itself by a rotation of 180o or less. No rotational symmetry

24
**Summary What are the properties of a rotation?**

How are reflections and rotations related? What does it mean when a figure has rotational symmetry?

Similar presentations

OK

This presentation is the intellectual property of Christine Markstrum Chapter 7 Transformations.

This presentation is the intellectual property of Christine Markstrum Chapter 7 Transformations.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on condition based maintenance definition Ppt on media research tools Ppt on remote server monitoring system Ppt on coalition government examples Open ppt on mac Ppt on national congress party Ppt on e-mail spam Ppt on kirchhoff's current and voltage laws Ppt on satellite orbit map Ppt on organisational structure and design