lesson 5 menu 1.determine whether a regular quadrilateral tessellates the plane. explain....

1. Determine whether a regular quadrilateral tessellates the plane. Explain.

2. Determine whether a regular octagon tessellates the plane. Explain.

3. Determine whether a semi-regular tessellation can be created from a triangle and a square. Assume each figure has a side length of 1 unit.

4. Determine whether a semi-regular tessellation can be created from a pentagon and a square. Assume each figure has a side length of 1 unit.

• dilation

• similarity transformation

• Determine whether a dilation is an enlargement, a reduction, or a congruence transformation.

• Determine the scale factor for a given dilation.

Determine Measures Under Dilations

Answer: 45

Theorem 9.1

Multiply.

A. Find the measure of the dilation image C′D′ using the given scale factor for CD = 15, r = 3.

Determine Measures Under Dilations

Answer: 10.5

Theorem 9.1

Multiply each side by

B. Find the measure of the preimage using the

given scale factor for

A. A

B. B

C. C

D. D

A. 2

B. 4

C. 8

D. 32

A. Find the measure of the dilation image A′B′ using the given scale factor for AB = 16, r = –2.

A. A

B. B

C. C

D. D

A. 16

B. 36

C. 48

D. 18

B. Find the measure of the preimage using the

given scale factor for A′B′ = 24, r = .

Draw a Dilation

Draw the dilation image of trapezoid PQRS with center C and r = –3.Since the dilation is an enlargement of trapezoid PQRS.

Draw . Since r is negative, P', Q', R', and S' will lie on the opposite side of point C.

Draw a Dilation

Draw the dilation image of trapezoid PQRS with center C and r = –3.Since the dilation is an enlargement of trapezoid PQRS.

Locate P', Q', R', and S' so that

Draw a Dilation

Answer: Draw trapezoid P'Q'R'S'.

Draw the dilation image of trapezoid PQRS with center C and r = –3.Since the dilation is an enlargement of trapezoid PQRS.

1. A

2. B

3. C

4. D

Which diagram shows the dilation image of ΔLMN

with center C and ?

A. B.

C. D.

Dilations in the Coordinate Plane

COORDINATE GEOMETRY Trapezoid EFGH has vertices E(–8, 4), F(–4, 8), G(8, 4) and H(–4, –8). Find the image of trapezoid EFGH after a dilation centered at the origin with a scale factor of Sketch the preimage and the image.

Dilations in the Coordinate Plane

Answer: E'(–2, 1), F'(–1, 2), G'(2, 1), H'(–1, –2)

1. A

2. B

3. C

4. D

COORDINATE GEOMETRY Triangle ABC has vertices A(–1, 1), B(2, –2), and C(–1, –2). Find the image of ΔABC after a dilation centered at the origin with a scale factor of 2. Sketch the preimage and the image. A. B.

C. D. none of the above

A. Determine the scale factor used for the dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

Identify Scale Factor

Identify Scale Factor

image lengthpreimage length

Simplify.

Since the scale factor is less than 1, the dilation is a reduction.

Answer:

Identify Scale Factor

B. Determine the scale factor used for the dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

Identify Scale Factor

Answer: –1; congruence transformation

image lengthpreimage length

Simplify.

Since the image falls on the opposite side of the center, C, than the preimage, the scale factor is negative. So the scale factor is –1. The absolute value of the scale factor equals 1, so the dilation is a congruence transformation.

A. A

B. B

C. C

D. D

A. For the green preimage, determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

A. 2; enlargement

B.

C.

D. 1; congruence transformation

A. A

B. B

C. C

D. D

B. For the green preimage, determine the scale factor used for each dilation with center C. Determine whether the dilation is an enlargement, reduction, or congruence transformation.

A. 2; enlargement

B.

C.

D. 3; enlargement

The photograph’s dimensions are given in centimeters, and the frame’s dimensions are in millimeters. You need to convert from millimeters to centimeters in the problem.

Sharetta built a frame for a photograph that is 20 centimeters by 25 centimeters. The frame measures 400 millimeters by 500 millimeters. Which scale factor did she use?

Scale Drawing

Step 2 Find the scale factor.

frame lengthphoto length

Simplify.

Step 1 Convert from millimeters to centimeters.

or 40 centimeters

Answer: Sharetta used a scale factor of 2 to build the frame.

Scale Drawing

A. A

B. B

C. C

D. D

A. 19 in. by 26 in.

B. 22 in. by 30 in.

C. 20.5 in. by 28 in.

D. 16 in. by 29 in.

Ruben is making a scale drawing of the front of his

house. His house is 48 feet wide and 30 feet high at

its highest point. Ruben decides on a dilation

reduction factor of What size poster board will

he need to make a complete drawing?