UNIT 2 DAY 5CONGRUENCE

TRANSFORMATIONSMR. KUGLER

FRANK H. PETERSON ACADEMIES OF TECHNOLOGY

MATCHING

1. Translation

2. Rotation

3. Reflection

A. This transformation creates points that are equidistant from a single point.

B. This transformation does not change orientation of the figure.

C. This transformation creates points that are equidistant from a line.

Objective:• The student will be able to identify

congruence transformations.• Students will show mastery of

transformation concepts.

Essential Question:

• What do you need to show to prove that the triangles are congruent?

KFC – KNOWLEDGE FOR COLLEGEDefinition:

A single or composition of rigid motions that moves a congruent geometric figure onto another one.

Characteristics and Tendencies:

The sides must be congruent and the angles must be congruent to know that the transformation is a perfect mapping onto the other.

Example:

(T<1, 5> ∘ r(90°, O))( ∆PQR) = ∆STU

Congruence Transformations

IDENTIFYING CONGRUENCE TRANSFORMATIONS

Based on the naming rules of congruency, the name will always tell us which parts must be corresponding. It gives us our starting point.

Focusing on a set of corresponding sides is typically easier to figure out if a rotation OR reflection is needed. It is very rare that both would be used in a test question.

MATCHING

1. Translation

2. Rotation

3. Reflection

4. Glide Reflection

A.

B.

C.

D.

Find the coordinates of

the vertex M’.

Rx-axis(MATH)

Find the coordinates of

the vertex H’.

T<–1, 2>(MATH)

Find the coordinates of

the vertex A’.

r(90°, O)(MATH)

Find the coordinates of

the vertex T’.

(Ry-axis ○ T<0, 2>)(MATH)

• The point (1, 1) is the image under the translationT<5, 5> (x, y). What is its preimage?

The point (a, b) is rotated about the origin -90° and then reflected in the y-axis. Which pair of coordinates best describes the resulting transformation of the point?

(a, -b), (b, -a), (b, a), (-b, -a), (-a, -b), (-a, b), (-b, a)

The point (a, b) is rotated about the origin 180° and then reflected in the y-axis. Which pair of coordinates best describes the resulting transformation of the point?

(a, -b), (b, -a), (b, a), (-b, -a), (-a, -b), (-a, b), (-b, a)

•Write down all of the Rigid Motions.

Write down the Congruency

Transformation.

Write down the Congruency

Transformation.

•Point R(x, y) moves 13 units West and 14 units South. What is a rule thatdescribes this translation?

What is the degree measurement after a Clockwise rotations around point O from point B to C?

O

A

H

G

F E

D

C

B

What is the degree measurement after a Counter-Clockwise rotations around point O from point C to H?

O

A

H

G

F E

D

C

B

What is the degree measurement after a Clockwise rotations around point O from point A to G?

O

A

H

G

F E

D

C

B

What is the degree measurement after a Counter-Clockwise rotations around point O from point B to C?

O

A

H

G

F E

D

C

B

•What is the image of (6, 6) after a reflection across the y-axis?

Write a single transformation rule that has the same effect as the composition of transformation listed below.

T<–3, 4> ○ T<1, –2>

Write a single transformation rule that has the same effect as the composition of transformation listed below.

Ry = –2 ○ Ry = 2

Write a single transformation rule that has the same effect as the composition of transformation listed below.

Rx = 1 ○ Ry = –1

HOME LEARNINGTonight

• Make sure I have your Construction Portfolio Review

Over the Weekend• Review all of the notes and home learning• Re-watch the videos on Pearson Realize

• Make Flashcards to memorize the Rotation Rules