Proportions and Similar Polygons

Question 1

A common fraction

Answer 1

Ratio

Question 2

The numerator of the first term of a ratio

The denominator?

Answer 2

Antecedent

Consequent

Question 3

What are the two definitions for ratio

Answer 3

A common fraction

Comparison between 2 values

Question 4

What is a proportion

Answer 4

A statement of equality between two ratios

Question 5

The first and fourth terms of a proportion

The second and third

Answer 5

Extremes

Means

Question 6

Fourth Proportional

Answer 6

The forth term of the proportion whose first three terms are the three quantities taken in order

Question 7

Mean proportional

Answer 7

The two means equal in a proportion

Question 8

Third proportional

Answer 8

When the two means of a proportion are equal then the last term is said to be the third proportional to the first and second terms

Question 9

Property 1

Answer 9

The product of the means = product of the extremes

Fundamental Property of Proportions FPP

Question 10

Property 1 Corollary 1

Answer 10

If three terms are equal to three terms of another proportion respectively then the fourth terms are equal

Question 11

Property 2

Answer 11

If the product of two quantities is equal to the product of two other quantities either pair may be used as the means and the other pair as the extremes of a proportion

Question 12

Axiom 14

Answer 12

Like powers or like roots of equal quantities are equal

Question 13

Property 3

Answer 13

The mean proportional between two quantities is equal to the square root of their product

Question 14

Property 4

Answer 14

The products of the corresponding terms of two or more proportions are in proportion

a:b = c:d ; m:n= p:q
Therefore:
(a)(m): (b)(n) = (c)(p): (d)(q)

Question 15

Property 5

Answer 15

In a series of equal ratios the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent

Question 16

Transformation 1

Answer 16

Alternation

Question 17

Transformation 2

Answer 17

Inversion

Question 18

Transformation 3

Answer 18

Addition consequent

Question 19

Transformation 3 Corollary 1

Answer 19

Addition antecedent

Question 20

Transformation 4

Answer 20

subtraction consequent

Question 21

Transformation 4 Corollary 1

Answer 21

Subtraction Antecedent

Question 22

Transformation 5

Answer 22

If four quantities are in proportion then like powers or like roots of these quantities are in proportion

Question 23

If a line is drawn through two sides of a triangle parallel to the third side then it

Answer 23

divides the two sides proportionally

Question 24

If a parallel is drawn through two sides of a triangle (parallel to the third side) then

Answer 24

either side is to one of its segments as the other side is to the corresponding segment

Question 25

Corresponding segments cut off on two transversals by a series of parallels...

Answer 25

are proportional

Question 26

If a line divides two sides of a triangle proportionally,

Answer 26

then it is parallel to the third side

Question 27

In Triangle ABC with DE as a line in the triangle, AC: DC equals BC: EC or AC: AD equals BC: BE Then...

Answer 27

DC is parallel to AB

Question 28

The bisector of an interior angle of a triangle divides the

Answer 28

opposite side internally into segments which have the same ratio as the other two sides (at the end of the angle bisector are the letters that will be used... left to right in the proportion)

Question 29

The bisector of an exterior angle of a triangle divides the opposite side

Answer 29

externally into segments which have the same ratio as the other two sides (Remember that the point of division is the point that will be used in both segments [In triangle TRS with TM as bisector of angle PTR{ P being an extension of ST} MR:MS=RT:TS)

Question 30

If two polygons are similar , then

Answer 30

their corresponding angles are equal | their corresponding sides are proportional

Question 31

What are 4 ways to prove that triangles are similar (not Rt triangles )

Answer 31

a. a.a. s. a.s. a. a. s. s.s.

Question 32

What are 2 ways of proving that two right triangles are similar

Answer 32

If one ACUTE angle of one triangle is equal respectively to the other acute angle l.l.

Question 33

What is the usual means of proving that lines are proportional?

Answer 33

Similar Triangles

Question 34

What does C.S.S.T.P. stand for?

Answer 34

Corresponding Sides of Similar Triangles are Proportional

Question 35

What does C.A.S.T.E. stand for ?

Answer 35

Corresponding Angles of Similar Triangles are Equal

Question 36

If two parallels are cut by three or more transversals passing through a common point then

Answer 36

the corresponding segments of the parallels are proportional (Higher is to Lower)

Question 37

In a right triangle the perpendicular is drawn from the vertex of the right angle to the hypotenuse:

Answer 37

One: the two triangles thus formed are similar to the given triangle and to each other Two: the perpendicular is the mean proportional between the segments of the hypotenuse Three: each leg of the given triangle is the mean proportional between the hypotenuse and the adjacent segment of the hypotenuse

Question 38

If a perpendicular is dropped from any point on a circle upon a diameter then

Answer 38

The perpendicular is the mean proportional between the segments of the diameter