Unit 1 Class Packet - Weebly



Day 2: Translations & Reflections

Congruent figures _______________________________________________________________ .

Transformation of a geometric figure: change in its ______________________________________.

Pre-image: ____________ Notation: __________

Image: ___________ or ________________ Notation: __________

Isometry: transformation in which pre-image and image are the _____________________________.

aka: ___________________________

Warm-Up:

[pic]

Activity 2: Dot Paper Translations

1) Use the dots to help you draw the image of the first figure so that A maps to A’.

2) Use the dots to help you draw the image of the second figure so that B maps to B’.

3) Use the dots to help you draw the image of the third figure so that C maps to C’.

4) Complete each of the following translation rules using your mappings from 1 – 3 above.

a) For A, the translation rule is: T:(x, y) ( ( _______, _______ ) or

b) For B, the translation rule is: T:(x, y) ( ( _______, _______ ) or

c) For C, the translation rule is: T:(x, y) ( ( _______, _______ ) or

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

. . . . . . . . . . . . . .

Checkpoint: (GEO has coordinates G(-2, 5), E(-4, 1) O(0, -2). A translation maps G to G’ (3, 1).

1. Find the coordinates of: a) E’ ( _____, _____) b) O’ ( _____, _____)

2. The translation rule is T: (x, y) ( ( _______, _______ )

3. The vector is

4. Specifically describe the transformation: ________________________________________

Reflections with Polygons

Part 3 – Reflection Symmetry

1. Given triangle ABC.

a. What is the equation of the line of reflection that maps angle A onto angle B? _________________

b. If we reflect triangle ABC over the line of reflection found in part a, [pic] maps to ______________.

c. What can we conclude about the measure of angle A and B?

d. What can we conclude about the lengths of [pic] and [pic]?

e. What kind of triangle is ABC?

2. Given regular hexagon ABCDEF,

a. List the three lines of symmetry drawn on the diagram at right: ______, ______, ______

b. What is the image of point D when reflected across[pic]?

c. What is the image of [pic]when reflected across[pic]? What conclusions can you make about these angles?

d. Draw the other 3 lines of symmetry not already shown on the diagram.

3. Given quadrilateral ABCD,

a. The slope of [pic]is _____. The slope of [pic]is _____.

What kind of quadrilateral is ABCD? Explain how you know.

b. Let line m be the equation of the reflection line mapping [pic] to [pic]. Write the equation of line m.

c. Reflect quadrilateral ABCD over line m.

Angle A maps to __________

Angle B maps to __________

d. Look back at part a – was your description of the type of quadrilateral as specific as it should be (does it include details related to part c)? What is the more specific name of the quadrilateral? Explain how you know.

Reflections

Reflection Exploration

1) (ABC and (XYZ are reflections of each other. While holding the paper towards the light, fold the paper so that the triangles coincide (line up on top of each other). Crease the fold. Then open your paper back up and trace over this fold line using a straightedge to keep it neat.

2) Using a straightedge, draw [pic], [pic], and [pic]. Look at each segment in relationship to the reflection line. What appears to be true about the reflection line? Discuss lengths of segments and angles created in relationship to the reflection line.

Patty Paper Reflections

Use patty paper to reflect each figure across the dashed line. Transfer the image from the patty paper onto the paper below. Label the image points with proper notation.

| | |

|[pic] |[pic] |

3) Points A and B are on the line of reflection. How are A’ and B’ related to the reflection line?

4) Using a straightedge, draw CC ’. How is the reflection line related to CC ’?

Activity: Reflections in the coordinate plane. Given ∆REF: R(-3, 1), E(0, 4), F(2, -5)

1) On the first grid, draw the reflection of ∆REF in the x-axis. Notation: R x-axis

Record the new coordinates: R’( _____ , _____ ), E’( _____ , _____ ), F’( _____ , _____ )

2) On the second grid, draw the reflection of ∆REF in the y-axis. Notation: __________

Record the new coordinates: R’( _____ , _____ ), E’( _____ , _____ ), F’( _____ , _____ )

[pic] [pic]

3) Graph the line y = x on the third coordinate grid. Trace ∆REF, both axes, and the line y = x on patty paper. Then flip the patty paper over and line it up again to see where the triangle’s image would be if you reflected it in the line y = x. Record the new coordinates: R’( ___ , ___ ), E’( ___ , ___ ), F’( ___ , ___ )

4) Graph the line y = -x on the fourth coordinate grid. Trace ∆REF, both axes, and the line y = -x on patty paper. Then flip the patty paper over and line it up again to see where the triangle’s image would be if you reflected it in the line y = -x. Record the new coordinates: R’( ___ , ___ ), E’( ___ , ___ ), F’( ___ , ___ )

[pic] [pic]

Translations Practice Name: ___________________________

|Graph and label [pic] with vertices |Graph and label quadrilateral DUCK with vertices D(2,2), U(4, 1), C(3, -2), |

|L(-3, -1), I(-1, 4), and P(2, 2) |and K(0,-1) Graph and label the image of Quadrilateral DUCK when the |

|Graph and label the image of [pic] under the translation [pic]. |Quadrilateral is shifted left 4 and up 3. |

| |D’ _____ |

|L’ _____ |U’ _____ |

|I’ _____ |C’ _____ |

|P’ _____ |K’ _____ |

| | |

| | |

| | |

| | |

| | |

|Write the rule in vector notation: ________ | |

|Write the shift using words: | |

| |Write the rule in vector notation: ________ |

| | |

| |Write the rule in algebraic notation: ________ |

|Graph and label quadrilateral MATH with vertices M(4, 1), A(2, 4), T(0,6), |Write the rule mapping the pre-image to the image. |

|and H(1,2). Graph and label the image of Quadrilateral MATH when the |[pic] |

|Quadrilateral is shifted according to the vector | |

| |Write the rule in vector notation: _____ |

|M’ _____ |Write the rule in algebraic notation: ________ |

|A’ _____ | |

|T’ _____ |Describe in words the shift: |

|H’ _____ | |

| | |

| | |

| | |

| | |

| | |

| | |

| | |

|Write the rule in algebraic notation: ________ | |

|Describe in words the shift: | |

|Gerald is rearranging the furniture in his living room. He has to leave before he is finished, so he draws the diagram at right for his wife to place the |

|end table. Draw the new position of the end table. Include the answers to the following questions in your explanation. Use complete sentences! |

| |

|What method did you use? Is there only one possible answer? |

| |

|What does the arrow tell you? What do you call this motion? |

| |

|What could you call the table before it moved? After? |

Practice with Translations using Algebra

Given the translation from ABC to A’B’C’, find the specified values.

1. Find x, y, AB, and B’C’ given the diagram .

[pic]

Use the following diagram for questions 2 – 4:

[pic]

2. Find x, y, m(C, and m(A’ given m(A = y, m(A’ = 2x + 5, m(C = 3x - y, m(C’ = 4 .

3. Find x, y, BC, and AC given BC = 3x - 2y, B’C’ = 11, AC = 3x - y, and A’C’ = 7 .

4. Find r, s, m(C, and m(A given m(A = r + 4s + 40, m(C = 3r + 2s, m(A’ = 32, and m(C’ = 6.

Practice: Reflections

Graph the image using the transformation given, and give the algebraic rule as requested

|ΔEFG if E(-1, 2), F(2, 4) and G(2, -4) reflected over the y-axis. |ΔPQR if P(-3, 4), Q(4, 4) and R(2, -3) reflected over the x-axis. |

| | |

|E’ _____ |P’ _____ |

|F’ _____ |Q’ _____ |

|G’ _____ |R’ _____ |

| | |

| | |

|Notation: |Notation: |

| | |

|Rule: |Rule: |

| | |

|Quadrilateral VWXY if V(0, -1), W(1, 1), X(4, -1), and Y(1, -5) reflected |ΔBEL if B(-2, 3), E(2, 4), and L(3, 1) reflected over the line [pic]. |

|over the line y = x. | |

| |B’ _____ |

|V’ _____ |E’ _____ |

|W’ _____ |L’ _____ |

|X’ _____ | |

|Y’ ______ | |

| |Notation: |

|Notation: | |

| |Rule: |

|Rule: | |

| | |

|Square SQUR if S(1, 2), Q(2, 0), U(0, -1), and R(-1, 1) reflected over the |Quadrilateral MATH if M(1, 4), A(-1, 2), T(2, 0) and H(4, 0) reflected over |

|line [pic]. |[pic]. |

|S’ _____ | |

|Q’ _____ |M’ _____ |

|U’ _____ |A’ _____ |

|R’ _____ |T’ _____ |

|Notation: |H’ _____ |

| | |

| |Notation: |

| | |

| | |

Write a specific description of each transformation and give the algebraic rule, as requested.

7. 8.

[pic] [pic]

Find the image of the following transformations and give a specific description.

Hint: If you get stuck, look at the notes in your Interactive Notebook. (

9. The points (2,4), (3,1), (5,2) are reflected with the rule [pic]

[pic]

10. The points (2,4), (3,1), (5,2) are reflected with the rule [pic]

[pic]

Day 3:Rotations

Warm-Up: Given triangle ABC with A(-1, 4), B(4, 3) and C(1, -5), graph the image points after the following transformations, identify the coordinates of the image, and write the Algebraic Rule for each.

1) Translate triangle ABC left 3, up 2

Points: Algebraic Rule:

2) Translate triangle ABC right 2, down 1

Points: Algebraic Rule:

3) Solve the following system 4m + 18n = 80

Exploration. Trace Triangle ABC and point O on patty paper. Put your pencil point on top of the patty paper on point O and turn the patty paper around and around in both directions (keeping the O on your patty paper on top of the O on this sheet.) What do you notice about the triangle as it rotates around in either direction?

Rotations with a Coordinate Plane and with Polygons

Rotations on the Coordinate Plane Exploration

1) Triangle ABC has coordinates A(2, 0), B(3, 4), C(6, 4). Trace the triangle and the x- and y-axes on patty paper.

2) Rotate Triangle ABC 90(, using the axes you traced to help you line it back up. Record the new coordinates. A’( _____ , _____ ), B’( _____ , _____ ), C’( _____ , _____ )

3) Rotate Triangle ABC 270(, using the axes you traced to help you line it up. Record the new coordinates. A’( _____ , _____ ), B’( _____ , _____ ), C’( _____ , _____ )

4) Rotate Triangle ABC 180(, using the axes you traced to help you line it back up correctly. Record the new coordinates. A’( _____ , _____ ), B’( _____ , _____ ), C’( _____ , _____ )

Rotations with Polygons

Part 1 – Regular Polygons and rotation symmetry

A few definitions to support you as you work:

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). In the case of regular polygons the center is the point that is equidistant from each vertex.

4. Given regular triangle EFG with center O.

a. F is rotated about O. If the image of F is G, what is the angle of rotation?

b. [pic]is rotated 120° about O. What is the image of [pic]?

General Rule: The regular triangle has rotation symmetry with respect to the center of the polygon

and angles of rotation that measure _____ and _____.

Side note: A regular triangle is also called an ______________ triangle or an _______________ triangle.

5. Given regular quadrilateral EFGH with center O.

a. F is rotated about O. If the image of F is G, what is the angle of rotation?

b. F is rotated about O. If the image of F is H, what is the angle of rotation?

c. [pic]is rotated 270° about O. What is the image of [pic]?

General Rule: The regular quadrilateral has rotation symmetry with respect to the center of the polygon

and angles of rotation that measure _____, _____,______ and _____.

Side note: A regular quadrilateral is often called a _______________.

6. Given regular pentagon ABCDE with center O,

a. C is rotated about O. If the image of C is D, what is the angle of rotation?

b. C is rotated about O. If the image of C is E, what is the angle of rotation?

c. C is rotated about O. If the image of C is A, what is the angle of rotation?

d. [pic]is rotated 288° about O, what is the image of [pic]?

e. Pentagon ABCDE is rotated 72° about O, what is the image of pentagon ABCDE (in terms of the original points’ labels – do not use A’B’C’D’E’)?

f. Explain the significance of the multiples of 72°.

General Rule: The regular pentagon has rotation symmetry with respect to the center of the polygon

and angles of rotation that measure _____, _____,_____, ______ and _____.

7. Given regular hexagon ABCDEF with center O,

a. C is rotated 60° about O, what is the image of C?

b. C is rotated 120° about O, what is the image of C?

c. C is rotated 180° about O, what is the image of C?

d. [pic]is rotated 240° about O, what is the image of [pic]?

e. Explain the significance of the multiples of 60°.

General Rule: The regular hexagon has rotation symmetry with respect to the center of the polygon

and angles of rotation that measure _____, _____, _____, _____, ______ and _____.

8. Given regular octagon ABCDEFGH with center O,

a. When point C is rotated about O, the image of point C is point D. Describe the rotation (be sure to include degree).

b. When point C is rotated about O, the image of point C is point F. Describe the rotation (be sure to include degree).

A regular polygon can be mapped onto itself if we rotate in multiples of the central angle measure.

The central angle of a regular polygon is found by ______________________________

Part 2 – Parallelograms and rotation symmetry

9. Given parallelogram ABCD, there is a center of rotation, O, that will map point A onto point C.

a. What are the coordinates of O?

b. What degree of rotation mapped C onto A using the center O?

c. If we rotate the parallelogram around center O using the degree measure found in part b, angle D maps to angle _________.

d. If angle A maps to angle C, then angle A and angle C are _________.

e. If angle D maps to angle ____, then angle D and angle _____ are _________.

Rotations Practice

Graph the preimage and image. List the coordinates of the image. Then write the rule and proper notation.

1) ΔRST: R(2, -1), S(4, 0), and T(1, 3) 2) ΔFUN: F(-4, -1), U(-1, 3), and N(-1, 1)

90° counter clockwise about the origin. 180° clockwise about the origin.

Rule: Rule:

Notation: Notation:

R’ ( ___ , ___ ) S’ ( ___ , ___ ) T’ ( ___ , ___ ) F’ ( ___ , ___ ) U’ ( ___ , ___ ) N’( ___ , ___ )

3) ΔTRL: T(2, -1), R(4, 0), and L(1, 3) 4) ΔCDY: C(-4, 2), D(-1, 2), and Y(-1, -1)

90° clockwise about the origin. 180° counter clockwise about the origin.

Rule: Rule:

Notation: Notation:

T’ ( ___ , ___ ) R’( ___ , ___ ) L’( ___ , ___ ) C’ ( ___ , ___ ) D’ ( ___ , ___ ) Y’ ( ___ , ___ )

5) Application

|ABCDE is a regular pentagon with center X. | |

| | |

|a. Name the image of point E for a | |

|counterclockwise 72° rotation about X. | |

| | |

|b. Given the image for a clockwise 216° rotation about X is [pic]. What | |

|was its preimage? | |

| | |

|c. Describe 2 rotations with a preimage of point D and image of B. | |

| | |

Practice: Rotations with Coordinates

For each problem graph the image points. Specifically describe in words the rotation that occurred. Then, write the Algebraic Rule and the proper notation for the rotation.

|1) The coordinates of ABC are A(3, 1), B(6, 5) | |

|and C(2, 4). The coordinates of A’B’C’ are | |

|A’(-1, 3), B’(-5, 6), and C’(-4, 2). | |

| | |

|Description: | |

| | |

|Algebraic Rule: | |

| | |

|Notation: | |

|2) The coordinates of ABC are A(3, 1), | |

|B(6, 5) and C(2, 4). The coordinates of | |

|A’B’C’ are A’(1, -3), B’(5, -6), and C’(4, -2). | |

| | |

|Description: | |

| | |

|Algebraic Rule: | |

| | |

|Notation: | |

|3) The coordinates of ABC are A(3, 1), | |

|B(6, 5) and C(2, 4). The coordinates of | |

|A’B’C’ are A’( -3, -1), B’(-6, -5), and C’(-2, -4). | |

| | |

|Description: | |

| | |

|Algebraic Rule: | |

| | |

|Notation: | |

|4) The coordinates of ABC are A(2, -1), | |

|B(6, 4) and C(-3, 2). The coordinates of | |

|A’B’C’ are A’(-1, -2), B’(4, -6), and C’(2, 3). | |

| | |

|Description: | |

| | |

|Algebraic Rule: | |

| | |

|Notation: | |

Day 4: Compositions

Warm-Up: Given triangle GHI with G(-2, 1), H(3, 4), and I(1, 5), find the points of the image under the following transformations and write the Algebraic Rule. Start from the preimage GHI each time.

1) Translate right 2, down 3

2) Reflect over the x-axis

3) Rotate 90 degrees, counter-clockwise

Practice 1: Compositions of Transformations with Coordinates

All rectangles in the grid below are congruent. Follow the instructions and then write the number of the rectangle that matches the location of the final image.

Which rectangle is the final image of each transformation?

1. Reflect Rectangle 1 over the y-axis. Then translate down three units and rotate 90° counterclockwise around the point (3, 1). (Hint: redraw the axes so that the origin corresponds to (3, 1). )

2. Translate Rectangle 2 down one unit and reflect over the x-axis. Then reflect over the line x = 4.

3. Reflect Rectangle 3 over the y-axis and then rotate 90° clockwise around the point (-2, 0). Finally, glide five units to the right.

4. Rotate Rectangle 4 90° clockwise around the point (-3, 0). Reflect over the line y = 2 and then translate one unit left.

5. Translate Rectangle 5 left five units. Rotate 90° clockwise around the point (-2, 2) and glide up two spaces.

6. Rotate Rectangle 6 90° clockwise around the point (4, 4) and translate down three units.

7. Rotate Rectangle 7 90° clockwise around (-4, 4) and reflect over the line x = -4.

8. Reflect Rectangle 8 over the x-axis. Translate four units left and reflect over the line y = 1.5.

Practice 2: Composition of Motions with Algebraic Rules

For #1 – 4, there is a composition of motions. Using your algebraic rules, write a new rule after both transformations have taken place. (Hint: Write algebraic rules for each transformation. Then, determine a single algebraic rule that would accomplish the same motion with a single transformation.)

1) Translate a triangle 4 units right and 2 units up, and then reflect the triangle over the line y = x.

2) Translate a triangle 4 units left and 2 units down, and then reflect the triangle over the y-axis.

3) Translate a triangle 4 units right and 2 units down, and then reflect the triangle over the x-axis.

4) Translate a triangle 4 units left and 2 units up, and then reflect the triangle over the line y = x.

9) 9) a. On a coordinate grid, draw a triangle using A(-9, -2), B(-6, -1), C(-6, -3) to represent a duck foot.

b. Transform [pic]ABC using [pic], followed by [pic]. Label the final image [pic]A’B’C’.

c. Write a coordinate rule for this composite transformation.

d. Does the order in which you apply the translation and reflection matter in this case? Why or why not?

e. Now apply the coordinate rule you gave in Part c at least three more times to [pic]A’B’C’. Describe how alternate images such as images one and three, or two and four, are related.

Day 5: Dilations

Warm-Up/Quiz Review

Given the points C(3,2), A(-5, 4), and T(-1, 6), name the new points after the following transformations. Then write a specific description for the new transformation. For #1 and 2, give the proper notation for the transformation. For #3, give the translation vector.

1. (x,y)→(-x,-y)

2. (x,y) →(y,x)

3. (x,y) →(x-3, y+1)

Practice 1: Dilations Activity

1. Graph and connect these points: (2, 2) (3, 4) (5, 2) (5, 4).

[pic]

2. Graph the image on the same coordinate plane by applying a scale factor of 2.

What is the Algebraic Rule for this transformation? ___________________________

How do the preimage and image compare? What are the coordinate pairs of the image?

3. Graph the image on the same coordinate plane by applying a scale factor of 1/2.

What is the Algebraic Rule for this transformation? ___________________________

How do the preimage and image compare? What are the coordinate pairs of the image?

4. What happens when you apply a scale factor greater than 1 to a set of coordinates?

5. What happens when you apply a scale factor less than 1 to a set of coordinates?

6. Circle the appropriate choice for the following characteristic/property:

A dilation is SOMETIMES / ALWAYS / NEVER an ‘Isometry’.

Practice 2: Dilations with Coordinates

For each problem, graph the image points, and describe the transformation that occurred. Specify if the transformation is an enlargement or reduction and by what scale factor. Then, examine the coordinates to create an Algebraic Rule.

|The coordinates of ABC are | |

|A(2, -1), B(3, 2) and C(-3, 1). The coordinates of A’B’C’ are A’(1, | |

|-1/2), | |

|B’(3/2, 1), and C’(-3/2, 1/2). | |

| | |

|Transformation: | |

| | |

| | |

|Algebraic Rule: | |

| The coordinates of ABC are | |

|A(2, -1), B(3, 2) and C(-3, 1). The coordinates of A’B’C’ are A’(4, -2),| |

| | |

|B’(6, 4), and C’(-6, 2). | |

| | |

|Transformation: | |

| | |

| | |

|Algebraic Rule: | |

|The coordinates of ABC are A(2, -1), | |

|B(3, 2) and C(-3, 1). The coordinates of A’B’C’ are A’(3, -3/2), B’(9/2, | |

|3), and | |

|C’(-9/2, 3/2). | |

| | |

|Transformation: | |

| | |

| | |

|Algebraic Rule: | |

| | |

For #4-7, there is a composition of motions. Using your algebraic rules, write a new rule after both transformations have taken place.

4) Rotate a triangle 90 degrees counter clockwise, and then dilate the figure by a scale factor of 3.

5) Rotate a triangle 90 degrees clockwise, and then dilate the figure by a scale factor of 1/3.

6) Rotate a triangle 180 degrees counter clockwise, and then dilate the figure by a scale factor of 2.

7) Rotate a triangle 180 degrees clockwise, and then dilate the figure by a scale factor of 1/2.

Dilations around a point other than the Origin

Dilate triangle RST using a scale factor of 2 around point T.

[pic]

Day 6: Properties of Dilations and Similarity

Warm-Up: Given triangle CDE with C(2, 2), D(-6, 4) and E(-2, -6), write the points of the image under the following transformations. For #1 and 2, write the specific description and the vertices. For #3, give the algebraic rule and the coordinate pairs.

1) (x, y) → (3x, 3y)

2) (x, y) → (1/4x, 1/4y)

3) Dilation with a scale factor 2

4) 21st Century Skill Check: Triangle ABC and Triangle A’B’C’ are shown on the right. The scale on each axis is 1.

Properties of Dilation Investigation

Dilate [pic] about the origin with a magnitude of 2. Graph the new triangle; label the vertices [pic].

Complete the following using your dilation.

1. Using a protractor, measure the angles of [pic] and [pic]. Write the measurements below and label appropriately. What do you notice?

2. Using the distance formula, calculate the lengths of [pic] What do you notice? (Hint: you may want to round to the tenths place to make the comparison easier)

3. Dilations create similar figures. Based on your observations from 1 and 2, what can we say about similar figures?

4. What do you notice about the placement of [pic] on the coordinate plane? [pic]?

Note that A and A’ lie on the origin. What conclusion can you make about the segments of an image when the corresponding segments of the preimage pass through the center of dilation?

5. Using the slope formula, calculate the slopes of [pic] What do you notice about the slopes? What does that tell you about the relationship of the lines to one another? What conclusion can you make about the segments of an image when the corresponding segments of the preimage do not pass through the center of dilation?

Dilations Practice Name: _____________________

Graph and label each figure and its image under the given reflection. Write the rule using formal notation.

1) Dilate [pic]QRS if Q(-1, 0), R(-1, 2), S(-2, 1) 2) Dilate [pic]TRK if T(-1, -2), R(1, 0), K(0, 1)

by a magnitude of 2 from the origin. by a magnitude of 3 from the origin.

Q’ ______ T’ ______

R’ ______ R’ ______

S’ ______ K’ ______

Rule: _________ Rule: _________

3) Dilate [pic]XYZ if X(-4, 0), Y(-4, 3), Z(-2, -2) 4) Dilate [pic]IBM if I(2, -4), B(1, 2), M(4, 1)

by a magnitude of [pic] from the origin. by a magnitude of [pic] from the origin.

X’ ______ I’ ______

Y’ ______ B’ ______

Z’ ______ M’ ______

Rule: _________ Rule: _________

Determine the scale factor that was used to dilate the following figures.

5) 6) 6)

Scale Factor: ______________ Scale Factor: ______________

-----------------------

Prerequisite Skill:

Solving Systems of Equations

Solve for x and y.

2. x = 8 + 3y

2x – 5y = 8

3. 5x – y = 20

3x + y = 12

4. x + 3y = 7

x + 2y = 4

5. 19 = 5x + 2y

1 = 3x – 4y

1.

B’

B

A

C

A’

C’

What can be concluded about both pairs of base angles?

Description:

Algebraic Rule:

Description:

Description:

Notation:

Description:

1

8

5

4

3

2

7

6

Adapted from Core-Plus Mathematics Course 2, Pg. 224

Since Triangle A’B’C’ is bigger than triangle ABC, Logan thinks that triangle A’B’C’ can be obtained by applying a size transformation centered at the origin to triangle ABC. Do you agree or disagree with Logan? Explain your reasoning.

A

B

C

................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download