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22 Cards in this Set
- Front
- Back
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ratio
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comparison of 2 numbers by division
a/b a:b a to b |
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Porportion
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an equation with 2 equal rations
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a/b=c/d
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A and D are the extrems
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a/b=c/d
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b and c are the means
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product of ratios
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product of the means = the product of the extremes
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What are similar figures
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They have the same shape, but not always the same size
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conditions of similar figures
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1. corresponding angles are congruent
2. corresponding sides are proportional |
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similarity ratio
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is reduced ration for any corresponding sides
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AA
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if 2 triangles have 2 pairs of congruent angles, the triangle is similar
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SSS
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if all 3 sides of 2 triangles are proportional. triangles are similar
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SAS
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if 2 sides of one triangle are proportional to 2 sides of a 2nd triangle, and their included angles are congruent, the triangles are similar
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to verify
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1. Write the similar ratio
2. Write the statement |
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triangle proportionality theorem
1st |
if a line parallel to one side of a triangle intersects the other 2 sides, it divides those 2 sides proportionaly
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triangle proportionality theorem
2nd |
If a line divides 2 sides of a triangle proportionally, its parallel to the 3rd side.
*it has to be ll |
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triangle proportionality theorem
3rd |
If ( 3 or more ) ll lines are cut by 2 traversals the traversal are divided proportionally
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triangle proportionality theorem
4th |
An angle bisector of a triangle divides the opposite side into 2 segments which are proportional to the segments. ADJACENT SIDES
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Indirect measurement
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using formulas, similar figures, and/or proportions to measure objects
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scale
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scale drawing= measure of model/measure of actual object
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perimeter and area
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Ex. 5/2 ration. 35 perim and 75 area
5/2=35/x : x=14 5^2/2^2=25/4 25/4=75/x : x=12 perim=14 area=12 |
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slopes
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rise/run
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product of ratios
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a/b=c/d equal product
b/c=a/d |
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example
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Three siblings are to share an inheritance of
$750,000 in the ratio 4 : 5 : 6. What is the amount of the greatest share? 4x+5x+6x=750,000, then solve |
