Name: ___________________________ Period: ___________ 8.1 Drawing Dilations by Hand Need more? Try searching Khan Academy for “Dilations or scaling around a point” 1. Draw the image of the figure under a dilation with a scale factor of 2, using point A as the center of dilation. 2. Draw the image of the figure under a dilation with a scale factor of 3, using point P as the center of dilation. 3. Draw the image of the figure under a dilation with a scale factor of ½ using point A as the center of dilation.
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Name: ___________________________ Period: ___________ 8.1 Drawing Dilations by Hand
Need more? Try searching Khan Academy for “Dilations or scaling around a point”
1. Draw the image of the figure under a dilation with a scale factor of 2, using point A as the center of dilation.
2. Draw the image of the figure under a dilation with a scale factor of 3, using point P as the center of dilation.
3. Draw the image of the figure under a dilation with a scale factor of ½ using point A as the center of dilation.
For the dilations in the coordinate plane assume the center of dilation is always the origin. Draw the image under a
dilation using the indicated scale factor.
4. Scale factor: 2 5. Scale factor: 1/2
6. Scale factor: -1 7. The coordinates of the pre-image are:
A(1,-6), B(-4,4) and C(-1,-3)
Using a scale factor of 6.6, what would the coordinates
of the image be?
A __________ B__________ C _________
8. Investigate it: If you were to dilate a line segment would the image be parallel to the pre-image? Try dilating a line
around a point not on the line, or a point on the line. What happens?
Name: __________________________ Similarity Investigation 8.2a AA,SSS, SAS Similarity
Similar Triangle Investigation 1
Is AA (angle-angle) enough to say 2 triangles are similar?
You need rulers, protractors, pencils and graph paper will probably help
Step 1: Draw any triangle ABC
Step 2: Construct a 2nd triangle DEF with ∠𝐷 ≅ ∠𝐴 and ∠𝐸 ≅ ∠𝐵
Question: What must automatically be true about ∠𝐶 and ∠𝐹? _______________________
How do you know? _________________________________________________________
Step 3: Carefully measure the lengths of the sides of both triangles. Compare the ratios of the
corresponding sides. Is 𝐴𝐵
𝐷𝐸≈
𝐴𝐶
𝐷𝐹≈
𝐵𝐶
𝐸𝐹 ?
Step 4: Compare your results with others at your same table. You should be able to state a conjecture.
AA similarity conjecture:
If ________ angles of one triangle are congruent to __________ angles of another triangle
then _______________________________________________
Drawings:
Similar Triangle Investigation 2
Is SSS Sufficient to say two triangles are similar?
You need rulers, protractors, pencils and graph paper will probably help
Step 1: Draw any triangle ABC.
Step 2: Construct a second triangle, DEF, whose side lengths are a multiple of the original triangle. (Your
second triangle can be larger or smaller) – Recall how to make an SSS construction which can be found in
your notes from last semester. If all else fails, by all means you can use a phone too look up how to make
an SSS triangle.
Step 3: Compare the corresponding angles of the two triangles, and also compare the results of your
peers. Do their findings match yours?
SSS similarity conjecture:
If three sides of one triangle are proportional to the three sides of another triangle then the two triangles
are __________________.
Drawings:
Similar Triangle Investigation 3
Is SAS Sufficient to say two triangles are similar?
You need rulers, protractors, pencils and graph paper will probably help
Step 1: Construct two different triangles that are not similar but have two pairs of sides proportional and
the included angles congruent. (For a hint I made this in geogebra to sort of illustrate how you should
start this process. But it would be totally unoriginal if you copied my work…)
Step 2: Compare the measures of the corresponding sides and angles. Share you results with your peers,
and finish the conjecture.
SAS similarity conjecture –
If the sides of one triangle are proportional to the two sides of another triangle and ___________, then the