Name
Date
Notes Formal Geometry
Chapter 7 Similar Polygons
Period
7.1 Ratios and Proportions
A. Opener:
What is the best approximate perimeter of this isosceles trapezoid?
A.
19 𝑢𝑛𝑖𝑡𝑠
B.
21 𝑢𝑛𝑖𝑡𝑠
C.
31 𝑢𝑛𝑖𝑡𝑠
D.
33 𝑢𝑛𝑖𝑡𝑠
What is the best approximate area of the triangle?
A.
24.1 𝑢𝑛𝑖𝑡𝑠 2
B.
27.4 𝑢𝑛𝑖𝑡𝑠 2
C.
32.0 𝑢𝑛𝑖𝑡𝑠 2
D.
36.0 𝑢𝑛𝑖𝑡𝑠 2
B. Definitions:
1. Ratio:
2. Proportion:
3. Cross Products Property:
4. Equivalent Proportions:
C. Examples:
1. At NVHS, there are 104 teachers and 2204 students. What is the approximate teacher to student
ratio?
2. Kjk
1
3. Solve each proportion:
4. Fg
D. Guided Practice:
1.
2. Solve each proportion.
3. Lk
Date:
Assignment: p 460 #12-32 (x2)
2
7.2 Similar Polygons
A. Opener: Factor
1. 𝑥 2 + 4𝑥 − 5
2. 𝑥 2 − 49
3. 𝑥 2 + 22𝑥 + 21
B. Definitions:
1. Similar Polygons:
2. Similarity ratios:
3. Scale Factor: the ratio of the lengths of the corresponding sides of two similar polygons. The order
of comparison matters.
4. Theorem 7.1: Perimeters of Similar Polygons:
C. Examples:
1. fg
2. Fg
3
3. fg
4. Df
D. Guided Practice:
1. Df
2. Df
a. x
Date:
b. y
Assignment: p 468 #10-24 (x2), 67-71
7.3 Similar Triangles
A. Opener:
1. What do you know about the angles of similar triangles?
2. If you know that two angles of one triangle are congruent to two angles of another triangle, are the
triangles congruent? Are the triangles similar? Explain your reasoning.
4
B. Definitions:
1. Postulate 7.1:
2. Theorem 7.2: Side-Side-Side (SSS) Similarity: If the corresponding side
lengths of two triangles are ______________________, then the triangles
are _________________.
3. Theorem 7.3: Side-Angle-Side (SAS) Similarity: If the lengths of two sides
of one triangle are proportional to the lengths of two corresponding sides of
another triangle and the included angles are congruent, then the triangles are
__________________.
4. Properties of Similarity between Triangles:
C. Examples:
1.
5
2.
3.
4. Find BE and AD.
5. kl
6
Date:
Assignment: p 479 # 9-14, 16-22 (x2), 27, 32
7.4 Parallel Lines and Proportional Parts
A. Opener:
B. Definitions:
1. Theorem 7.5: Triangle Proportionality Theorem: If a line is parallel to one side og a triangle and
_____________ the other two sides, then it divides the sides into segments of __________________
lengths.
2. Theorem 7.6: Converse of Triangle Proportionality Theorem:
3. Midsegment of a triangle:
4. Theorem 7.7: Triangle Midsegment Theorem: a midsegment of a triangle is
parallel to one side of the triangle, and its length is ___________ the length of that
side.
5. Corollary 7.1: Proportional Parts of Parallel Lines: If three or more parallel
lines intersect two transversals, then they cut off the transversals
proportionally.
6. Corollary 7.2: Congruent Parts of Parallel Lines: If three or more parallel
lines cut off ______________________________________________, then
they cut off congruent segments on every transversal.
7
C. Examples:
1. kl
2. Kl
3.
4. df
5. Find x and y.
8
Date:
Assignment: p 489 # 10-26 (x2), 36-40 (x2)
7.5 Parts of Similar Triangles
A. Opener:
1. Find DE, DB and the measure of angle FED.
B. Definitions:
1. Theorem 7.8: If two triangles are similar, the lengths of corresponding _____________ are
proportional to the lengths of the corresponding sides.
2. Theorem 7.9: If two triangles are similar, the lengths of corresponding _____________ are
proportional to the lengths of the corresponding sides.
3. Theorem 7.10: If two triangles are similar, the lengths of corresponding _____________ are
proportional to the lengths of the corresponding sides.
4. Theorem 7.11: Triangle Angle Bisector:
C. Examples:
1. fg
9
2. Fgf
Solve for x.
Date:
Assignment: p 499 #6-24 (x2), omit #18, then do either #26 OR #28
10