Unit 7 – Scale Drawings and Dilations Day Classwork Day Homework Tuesday 12/4 Unit 6 Test Wednesday 12/5 Properties of Scale Drawings Scale Drawings Using Constructions 1 HW 7.1 Thursday 12/6 Dilations and Scale Drawings with Various Centers of Dilation 2 HW 7.2 Friday 12/7 Computer Lab 120 (Periods 1 & 3) Library Lab (Period 6) Monday 12/10 Triangle Side Splitter Theorem Midsegments of Triangles 3 HW 7.3 Tuesday 12/11 Dividing a Line Segment into Equal Segments Unit 7 Quiz 1 4 HW 7.4 Wednesday 12/12 Dilations in the Coordinate Plane 5 HW 7.5 Thursday 12/13 Review Unit 7 Quiz 2 6 Review Sheet Friday 12/14 Review 7 Review Sheet Monday 12/17 Begin Unit 8 HW 8.1 (Due Wednesday) Tuesday 12/18 Unit 7 Test 8
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Unit 7 Scale Drawings and Dilations - Revize€¦ · Day Classwork Day Homework Tuesday 12/4 Unit 6 Test Wednesday Properties of Scale Drawings 12/5 Scale Drawings Using Constructions
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Unit 7 – Scale Drawings and Dilations
Day Classwork Day Homework
Tuesday 12/4
Unit 6 Test
Wednesday 12/5
Properties of Scale Drawings
Scale Drawings Using Constructions 1 HW 7.1
Thursday 12/6
Dilations and Scale Drawings with Various
Centers of Dilation
2 HW 7.2
Friday 12/7
Computer Lab 120 (Periods 1 & 3)
Library Lab (Period 6)
Monday 12/10
Triangle Side Splitter Theorem
Midsegments of Triangles
3 HW 7.3
Tuesday 12/11
Dividing a Line Segment into Equal Segments
Unit 7 Quiz 1 4 HW 7.4
Wednesday 12/12
Dilations in the Coordinate Plane 5 HW 7.5
Thursday 12/13
Review
Unit 7 Quiz 2 6 Review Sheet
Friday 12/14
Review 7 Review Sheet
Monday 12/17
Begin Unit 8 HW 8.1 (Due Wednesday)
Tuesday 12/18
Unit 7 Test 8
SCALE DRAWINGS
The scale factor r is the ratio of any length in a scale drawing relative to its corresponding length in the
original figure. A scale factor r > 1 results in an enlargement of the original figure. A scale factor of 0 < r < 1 results in a reduction of the original figure.
Examples
1. Use construction tools to create a scale drawing of ABC with a scale factor of r =2.
Measure the length of BC and B’C’. What do you notice?
Measure the angles , , ',B C B and 'C . What do you notice?
Steps:
2. Use construction tools to create a scale drawing of DEF with a scale factor of r = 3. What properties does your scale drawing share with the original figure? Explain how you know.
3. Use construction tools to create a scale drawing of XYZ with a scale factor of 1
2r .
4. Use construction tools to create a scale drawing of PQR with a scale factor or 1
4r . What
properties do the scale drawing and the original figure share? Explain how you know.
5. EFG is provided below, and one angle of scale drawing ' ' 'E F G is also provided. Use
construction tools to complete the scale drawing so that the scale factor is 3r . What properties
do the scale drawing and original figure share? Explain how you know.
6. Triangle ABC is provided below, and one side of scale drawing ' ' 'A B C is also provided. Use construction tools to complete the scale drawing and determine the scale factor.
MORE SCALE DRAWINGS
For 𝑟>0, a dilation with center 𝑂 and scale factor 𝑟 is denoted ,O rD
For the center 𝑂, ,O rD (𝑂)=𝑂
For any other point 𝑃, ,O rD (𝑃) is the point 𝑃 on the ray OP so that 'OP r OP
1. Create a scale drawing of the figure below about center O and scale factor 1
2r .
Does A’B’C’D’E’ look like a scale drawing? How can we verify this?
2. Create a scale drawing of the figure below about center O and scale factor 2r . Verify that the
resulting figure is in fact a scale drawing by showing that corresponding side lengths are in constant proportion and the corresponding angles are equal in measurement.
3. Create a scale drawing of the figure below about center O and scale factor 3r .
4. ' ' 'A B C is a scale drawing of ABC . Use your straight edge to determine the location of the
center O used for the scale drawing.
5. Use the figure below, center O, a scale factor of 1
2r to create a scale drawing. Verify that the
resulting figure is in fact a scale drawing by showing that corresponding side lengths are in constant proportion and that the corresponding angles are equal in measurement.
TRIANGLE PROPORTIONS
Triangle Proportionality Theorem (Triangle Side Splitter Theorem) Example Figure
A line segment divides two sides of a triangle into
segments of proportional lengths if and only if it is
M(-4, 2). Graph the image of JKLM after a dilation centered at the origin with a scale factor of 2.5.
2. Find the image of each polygon below with the given
vertices after a dilation centered at the origin with the scale factor.
a. Q (0, 6), R (-6, -3), S (6, -3); r = 1/3
b. A (2, 1), B (0, 3), C (-1, 2), D (0, 1); r = 2
3. A dilation with center O1 and scale factor 1/2 maps figure F onto F’. A dilation with center O2 and scale factor 1/2 maps figure F’ to F’’. Draw figures F’ and F’’, and then find the center O and scale factor r of the dilation that takes F to F’’.
4. If a figure T is dilated from center O1 with a scale factor 1
3
4r to yield image T’, and figure T’ is
then dilated from center O2 with a scale factor 2
4
3r to yield figure T’’. Explain why figure T and T’’