Download Similarity – Notes and Problems

Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
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Similarity – Notes and Problems Isometry: a transformation is an isometry if it preserves distance. Transformations that are isometries include: ______________________, _______________________, and _______________________. Uniform Scaling: is a linear transformation that __________________________ (increases) or __________________(diminishes) objects by a scale factor that is the same in all directions. Uniform Scaling of a figure creates ______________________________ figures. Similar Figures: geometric figures that have congruent corresponding _______________________ and proportional corresponding _________________________________. Scale Factor/Similarity Ratio: the _________________ between the side lengths of two __________________ polygons. Ex 1: In the figure below ∆𝐴𝐵𝐶~∆𝐷𝐸𝐹. List the 3 pairs of congruent corresponding angles and the three pairs of proportional corresponding sides. Find the scale factor for the two triangles. Congruent
Corresponding
Angles
Proportional
Corresponding
Sides
Scale Factor/Similarity Ratio
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Ex 2: A triangle has coordinates A (−9, −1), B (−7, 6), and C (−4, 2). A second triangle
has coordinates A’ (10, −4), B’ (6, 10) and C’ (0, 2). Graph the triangles and use
coordinate geometry to show that the corresponding sides of each triangle are
proportional.
10
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6
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– 10
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Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
Homework 66: Similar Polygons Directions: Are the polygons similar? If they are, write a similarity statement, and give the similarity ratio. If they are not, explain why not. 1.
2.
3.
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5.
6.
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
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Directions: LMNO ~ HIJK. Complete the congruence statements and proportions.
7.
10.
∠𝑀 ≅ ∠ ____
!"
!"
=
!"
8. ∠𝐾 ≅ ∠ _____
11.
!"
=
!"
!"
9. ∠𝑁 ≅ ∠ _______
12.
Directions: Use the similarity statements to find the value of x.
13. ∆𝐴𝐵𝐶~∆𝐸𝐹𝐺
x=
14. SPQR ~ OLMN
x=
15. WXYZ ~ EFGH
x=
16. JKLM ~ PQRS
x=
!"
!"
=
!"
Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
17. Quadrilateral DFEG has coordinates D (2, −2), F (−4, 6), E (−8, 3), and G (−2, −5). A
transformed figure has coordinates D’ (2, −2), F’ 423, 0 , E’ 323, 1
1
3
, and G’ 1, −
2
3
.
Determine whether these figures are similar or not. Don’t forget to attend to angles.
Prove your conclusion using coordinate geometry.
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Math 2: Algebra 2, Geometry and Statistics
Ms. Sheppard-Brick 617.596.4133
http://lps.lexingtonma.org/Page/2434
Name:
Date:
18. Triangle KJI has coordinates J (6, −2), K (12, 4) and (I (2, 2), and m∠𝐾 = 34°. It is
transformed such that the new coordinates are J’ (−4, 0), K’ (−7, −3) and I’ (−2, −2) and
𝑚∠𝐼 ! = 56°. Determine whether these figures are similar or not. Don’t forget to attend
to angles. Prove your conclusion using coordinate geometry.
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– 10
–5
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–2
–4
–6
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