1. Congruence and Similarity pg. 87
Unit 1 Chapter 2
Congruence and Similarity
pg. 87

2. Congruence and Transformations pg. 95
Lesson 1
Congruence and Transformations
pg. 95

3. Vocabulary Composition of Transformations Corresponding Parts
The resulting transformation when a transformation is applied to a figure and then another transformation is applied to its image
Corresponding Parts
Parts of congruent or similar figures that match
Indirect Measurement
A technique using properties of similar polygons to find distances or lengths that are difficult to measure directly

4. Vocabulary Scale Factor Similar Similar Polygons
The ratio of the lengths of two corresponding sides of two similar polygons
Similar
If one image can be obtained from another by a sequence of transformations and dilations
Similar Polygons
Polygons that have the same shape

5. Identifying Congruence
Example
Determine if the two figures are congruent by using transformations
Reflection over vertical line
Translation
Triangles are congruent

6. Identifying Congruence
Example
Determine if the two figures are congruent by using transformations
Reflection then Translation
Figures are not congruent

7. Determine the Transformations
You can determine the transformations by analyzing the orientation or relative position of the figures
Translation
Reflection
Rotation
Length is the same
Orientation is the same
Orientation is reversed
Orientation is changed B B' B' B B B' A' A A A' A' A

8. Homework
Group 1: pg (1-3, 5,9)

9. Unit 1 Chapter 2 Lesson 2
Congruence
Pg. 107

10. Learn to use properties of congruent figures to solve problems.
Vocabulary
correspondence
A correspondence is a way of matching up two sets of objects.
If two polygons are congruent, all of their corresponding sides and angles are congruent.

11. Marks on the sides of a figure can be used to show congruence.
QR (1 mark)
PR (2 mark)
PQ (3 mark)
Helpful Hint __

12. Writing Congruent Statements
Write a congruence statement for each pair of polygons. 55
The first triangle can be named triangle ABC. To complete the congruence statement, the vertices in the second triangle have to be written in order of the correspondence.
The congruence statement is triangle triangle QRP.

13. Write a congruence statement for each pair of polygons.
Try this!
Write a congruence statement for each pair of polygons.
The first trapezoid can be named trapezoid ABCD. To complete the congruence statement, the vertices in the second trapezoid have to be written in order of the correspondence. A B |
60°
60° ||
||||
120°
120° D
||| C Q R
|||
120°
120° ||
||||
60°
60° | T S
The congruence statement is trapezoid trapezoid STQR.

14. Write a congruence statement for each pair of polygons.
Try this!
Write a congruence statement for each pair of polygons. A B C D E F N O P Q L M
140°
110°
The vertices in the first pentagon are written in order around the pentagon starting at any vertex.
The congruence statement is
hexagon hexagon MNOPQL.

15. Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral quadrilateral JKLM.
Find a.
a + 8 = 24 KL
a = 16
–8 –8
Subtract 8 from both sides.

16. In the figure, quadrilateral VWXY @ quadrilateral JKLM.
Using Congruence Relationships to Find Unknown Values
In the figure, quadrilateral quadrilateral JKLM.
Find b.
6b = 30 YX
6b = 30
Divide both sides by 6.
b = 5

17. quadrilateral JIHK @ quadrilateral QRST.
Try This!
In the figure,
quadrilateral quadrilateral QRST. 3a
4b° 6
30° Q
120° R S H I J K
c + 10° T
Find a.

18. NOT THE OTHER TWO…. SSS ASA SAS AAS AAA SSA
We have learned about Congruent Polygons
Congruency Statements lead to corresponding angles and sides
Congruent simply means the same size and shape
We will now expand this to study Congruent Triangles
We will use four acronyms……….
SSS
ASA
SAS
AAS
NOT THE OTHER TWO….
AAA
SSA

19. Congruent Triangles
If two figures are exactly the same size and shape, they are congruent.
Two triangles are congruent if the following corresponding parts of two triangles are congruent.
Three Sides (SSS)
Two angles and the included side (ASA)
Two sides and the included angle (SAS)
Two angles then a side (AAS)
Video below if to show why SSA and AAA do not work

20. Homework
CC: pg (1-5, 7)

21. Similarity and Transformations
Ch. 2 Lesson 3
Pg. 123

22. Identify Similarity
Two figures are similar if the second can be obtained from the first by a sequence of transformations and dilations

23. Examples
Determine if the two triangles are similar by using transformations.
Since the orientation of the figures is the same, one of the transformations is a Translation.
Notation?
( x , y )
Write ratios comparing the lengths of each side. (corresponding sides)

24. Examples
Determine if the two rectangles are similar by using transformations.
The orientation of the figures is different, so one of the transformations is a Rotation.
Make “W” the origin and rotate 90° clockwise.
Write ratios comparing the lengths of the sides.

25. Example
Ken enlarges a photo by a scale factor of 2 for his webpage. He then enlarges the webpage photo by a scale factor of 1.5 to print. If the original photo is 2 in. by 3 in., what are the dimensions of the print?
Are the enlarged photos similar to the original?

26. Homework
Pg (1-3, 5, 10)