Lesson 5 Menu 1.Determine whether a regular quadrilateral tessellates the plane. Explain. 2.Determine whether a regular octagon tessellates the plane.

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Presentation transcript:

Lesson 5 Menu 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.

Lesson 5 MI/Vocab dilation similarity transformation Determine whether a dilation is an enlargement, a reduction, or a congruence transformation. Determine the scale factor for a given dilation.

Lesson 5 KC1

Lesson 5 TH1

Lesson 5 Ex1 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.

Lesson 5 Ex1 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 Lesson 5 CYP1 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 Lesson 5 CYP1 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 =.

Lesson 5 KC2

Lesson 5 Ex2 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.

Lesson 5 Ex2 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

Lesson 5 Ex2 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.

Lesson 5 CYP2 1.A 2.B 3.C 4.D Which diagram shows the dilation image of ΔLMN with center C and ? A.B. C.D.

Lesson 5 TH2

Lesson 5 Ex3 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.

Lesson 5 Ex3 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 Lesson 5 CYP3 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

Lesson 5 Ex4 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

Lesson 5 Ex4 Identify Scale Factor  image length  preimage length Simplify. Since the scale factor is less than 1, the dilation is a reduction. Answer:

Lesson 5 Ex4 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.

Lesson 5 Ex4 Identify Scale Factor Answer: –1; congruence transformation  image length  preimage 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 Lesson 5 CYP4 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 Lesson 5 CYP4 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

Lesson 5 Ex5 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

Lesson 5 Ex5 Step 2Find the scale factor.  frame length  photo length Simplify. Step 1Convert 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 Lesson 5 CYP5 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?