4.1 Congruence and Transformations Target: Draw, identify, and describe transformations in the coordinate plane.

Warm-Up: Identify the transformation and then use arrow notation to describe the transformation.

1. 2. 3.

transformation: transformation: transformation:

arrow notation: arrow notation: arrow notation:

Apply the transformation to the given vertices. Identify and describe the transformation.

Example 1: : ( , ) ( 2, 5)M x y x y Example 2: : ( , ) ( , )M x y x y

P(1, 2), Q(4, 4), R(4, 2) A(1, 1), B(4, 3), C(3, 5)

Transformation: ____________________ Transformation: ____________________

Example 3: The graph shows the following Example 4: The graph shows the following

transformation: : ( , ) ( , )M x y y x . transformation: : ( , ) (2 ,2 )M x y x y

Describe the transformation: Describe the transformation:

Big Idea: Translations, reflections, rotations produce images that are _________ to their pre-images.

Enlarging or Shrinking a pre-image produce images that are _______________ to their pre-images.

Example 5: Determine whether the Example 6: Determine whether the

polygons with the given vertices are polygons with the given vertices are

congruent. congruent.

A(1, 1), B(4, 1), C(4, 3) A(2, 2), B(-4, 4), C(2, 4)

P(-4, 2), Q(-1, 2), R(-1, 4) P(3, 3), Q(-6, 6), R(3, 6)

Partner Practice

Example 7: Apply the transformation. Example 8: Determine if the polygons are

Identify and describe the transformation. congruent. Support your answer by describing

the transformation.

: ( , ) ( , )M x y y x P(-2, -2), Q(-4, -1), R(-1, -1)

X(2, 2), Y(4, 1), Z(1, 1)

L(3, 1), M(3, 4), N(4, 4), O(4, 1) Congruent?

Transformation: ____________________ Transformation: ____________________

4.2 Classify Triangles Target: Classify triangles by their angle measures and side lengths.

______, ________, and ________ are the ________ of ∆ABC.

______, ________, and ________ are the triangle’s ___________.

Classifying Triangles by Angle Measures

Acute Triangle Equiangular Triangle Right Triangle Obtuse Triangle

Example 1:

Classify each triangle by its angle measures.

a. ∆ABD ______________________________________

b. ∆ADC ______________________________________

c. ∆BDC ______________________________________

Classifying Triangles by Side Lengths

Equilateral Triangle Isosceles Triangle Scalene Triangle

*Remember: When you look at a figure, you cannot assume segments are congruent based on

appearance. They must be marked congruent.

Example 2:

Classify each triangle by its side lengths.

a. ∆ABD ______________________________________

b. ∆ADC ______________________________________

c. ∆ABC ______________________________________