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Review Sheet Chapter Seven
Ratios:
To get a proportion, we must set up a ratio that has the corresponding parts (parts from the same
triangle have to be in either the top or the bottom). Solve using cross-multiplication.
a
b
--- = --ad = cb
a and b must come from same triangle (c and d from other) !
c
d
Triangle Similarity Theorems:
All similar triangles must have their corresponding angles congruent !!
All sides must have the same scaling factor with their corresponding side
AA – (includes ASA and AAS) – if two angles are congruent in a triangle then the third angle must be
congruent
SAS – sides must have the same scaling factor (be in the same ratio); included angle
SSS – all sides must have the same scaling factor
Proofs:
Use similar steps to congruent triangle proofs.
Need to show angles congruent (parallel lines, vertical angles, etc) and sides having the same ratio
(scaling factor)
Similar triangles (or figures) problem solving:
1) Draw a picture of triangles, if you are not given one or if the picture given is too complex
2) Find corresponding parts (angles must be congruent and order still rules!)
3) Set up a proportion; make sure the tops (and bottoms) come from the same triangles!
4) Solve using cross multiplication
5) Check answer to make sure it makes sense
Test Taking Tips:
Check your answer and make sure that it makes sense in the picture
If the figure is smaller, then the corresponding part must be smaller than the given piece of the larger
Similar triangles:
30
36
----- = ----15
x
30 x = 540
SSM:
• Scaling factor is 1/2
• ED matches to 36 (order rules)
• ED = ½(36) = 18
x = 18
And any other triangle option
Triangles and Logic
SSM:
• Read the equations and see
which look right
Which angles match up?
A  T, C  C and B  R
look for ratios that match corresponding sides
and are consistent – all one triangle on top and
the other triangle on the bottom
Coordinate Relations and Transformations
SSM:
• measure the 30 side
• measure the 105 side
• Not to scale!
• Answer closest # to 105
since 28 is close to 30
set up similar triangles:
28
ST
---- = ----30
105
30 ST = 2940
ST = 98
Ch 7
Coordinate Relations and Transformations
SSM:
• isosceles
• Eliminate C
Isosceles triangle with legs bigger than the base. Only triangles A and B satisfy that.
Scaling factor of ¾ only fits triangle A completely.
Coordinate Relations and Transformations
Ch 7
SSM:
• draw figure
• draw lines of symmetry
Similar triangle proofs (AA, SAS and SSS)
CBD and ABE have right angles and a 2:1 ratio between long and short legs
of the right triangle
Ch 7
Coordinate Relations and Transformations
SSM:
• order rules
• shared angle R
Similarity theorems (AA, SAS, SSS) with shared angle R, either another
corresponding angle or the sides on both sides of angle R.
Options A and B do not fit order rules. Option D has the correct sides.
Triangles
Ch 7
SSM:
• no help
A  Q
C  S
Only AA similarity has two relationships for similarity. Order rules!
Triangles
Ch 7
SSM:
• no help
Triangle similarity theorems are AA, SAS and SSS. With no side information
given, the later two are tougher to prove. Hidden feature of “bowtie” gives us
vertical angles and a second angle in choice A.
Triangles
Ch 7
SSM:
• look for scaling factor
Need to find a scaling factor (3) that each of the sides of the given
triangle is multiplied and we get one of the answers
Answer C is another Pythagorean triple, but not in right proportion.
Polygons, Circles, and Three-Dimensional Figures
Ch 7
SSM:
• slightly less than
1 to 1
• less than 55
Need to set up a proportion to solve for model’s width
555.5
--------505
55
= ------x
505(55) = 555.5x
27775 = 555.5x
50 = x
Statement
Reason
AB // CD
Given
A  D
Alt Interior Angles
B  C
Alt Interior Angles
AFB  DFC
Vertical Angles
ABF ~ DCF
AA Similarity