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Geometry > Chapter 4 Master Deck > Flashcards

Chapter 4 Master Deck Flashcards

1
Q

Dilations are rigid transformations. True or False?

A

False. Dilations are non rigid transformations. This means that they don’t always produce a congruent figure.

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2
Q

Dilations preserve
a) Lengths of Line Segments
b) Slopes of Line Segments

A

b)
Line Segments change length by the scale factor.

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3
Q

What is the rule about line segments going through the same center of dilation?

A

If a line segment goes through the same center of dilation as the copy, then both of them are collinear.

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4
Q

What is the Slope Formula?

A

(yb - ya)/(xb - xa)

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5
Q

What are the three different types of Dilations Centered at the Origin?

A
  1. n > 1
  2. 0 < n < 1
  3. n = 1
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6
Q

What happens when the scale factor is greater than one and the dilation is centered at the origin?

A

Then the image is dilated further from the origin and it increases in size.

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7
Q

What happens when the scale factor is less than one and the dilation is centered at the origin?

A

The image then shrinks in size and gets closer to the origin.

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8
Q

What happens if the scale factor is 1?

A

The image stays the same and does not change position on the coordinate plane.
(Image is mapped on top of the pre-image and lengths of sides stay the same.)

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9
Q

What is the relationship between the center of dilation the location of the pre-image, the scale factor and any point on the image?

A

The distance between the center of dilation and any specified point on the image is equal to the scale factor multiplied by the distance between the center of dilation and the point on the pre-image.

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10
Q

What is the formula used to find the Center of Dilation?

A

(x1,y1) = (n(x - a)) + a , (n(y - b) + b

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11
Q

A dilation changes the lengths of all lines by
a) the same factor
b) by half the factor
c) no change

A

a) the same factor
That way the shape of the figure stays the same!

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12
Q

A dilation of a line is __________ to the original

A

Parallel. Them lines should not be crossing.

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13
Q

the ratio of the length of any line segment in the image to the length of the corresponding line segment in the pre-image is equal to the _________

A

scale factor

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14
Q

What is the equation for a dilation centered at the origin by scale factor n?

A

(x1 , y1) = (nx , ny)

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15
Q

What does a dilation do to a figure’s slopes?

A

Absolutely nothing!

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16
Q

What are similar figures?

A

Similar figures have congruent corresponding angle and proportional sides to the preimage.

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17
Q

If only one dimension of a shape is stretched, is the shape similar?

A

No.
A stretch in only one side leads to uneven sides and the angles will not be congruent anyone.

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18
Q

What is the order of Determining a Preimage?

A
  1. Dilate the figure first,
  2. Then Translate it
  3. Rotate the figure first,
  4. Then Dilate it.
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19
Q

How do you calculate the ratio of two corresponding sides?

A

Use Ratio Formula: DE/AB

20
Q

What are the three different types of Angle Similarity?

A
  1. AA Angle Angle Similarity
  2. SAS Side Angle Side Similarity
  3. SSS Side Side Side Angle Similarity
21
Q

What are similar figures?

A

Similar figures have proportional sides and have congruent angles with the preimage.

22
Q

What are similar figures?

A

Similar figures have proportional sides and have congruent angles with the preimage.

23
Q

What does AA Angle Similarity mean?

A

Angle Angle Similarity means that if two angles of a triangle are congruent to another triangles’ corresponding angles then the two triangles are similar.

24
Q

What does SAS Angle Similarity mean?

A

Side Angle Side Similarity means that if two sides in one triangle are proportional to the other triangles’s corresponding sides and the angle between the two of those sides is congruent to the other triangle then both triangles are similar.

25
Q

What does SSS Angle Similarity Mean?

A

Side Side Side Angle Similarity means that if the corresponding sides of both triangles are proportional to each other then the corresponding angles of the triangles will be congruent.

26
Q

If two triangles are congruent, their area will be congruent as well.
True or False

A

True duh

27
Q

What is the Perpendicular Bisector Theorem?

A

If a point lies on the perpendicular bisector of a line segment then the point is equidistant from the endpoints of the line segment.

28
Q

What is the Pythagorean Theorem?

A

a2 + b2 = c2

29
Q

What the two properties of Similar Triangle?

A
  1. The corresponding angles of both triangles are congruent.
  2. The corresponding sides of both triangles are proportional.
30
Q

What does CASTC mean in terms of Similar Triangles?

A

CASTC: Corresponding Angles of Similar Triangles are Congruent.

31
Q

What does CSSTP mean in terms of similar triangles?

A

CSSTP: Corresponding Sides of Similar Triangles are Proportional.

32
Q

How do you figure out if two sides in a figure are proportional?

A

Line up sides in a fraction:
Length of Side A/Length of Side B = Length of Corresponding Side A/ Length of Corresponding Side B

33
Q

How do you find the Ratio of Similar Triangles?

A

r = scale factor2 or (r = n2)

34
Q

What is the relationship between the ratio of perimeters in similar triangles and the scale factor?

A

The ratio of perimeters in similar triangles is the same to the scale factor.

35
Q

What is the relationship between the ratio of areas and the scale factor between two similar figures?

A

The ratio of areas is equal to the square of the scale factor.

36
Q

When a regular shape is rotated from its center how many times can it be mapped onto itself.

A

The number of sides basically

37
Q

What is the amount of times a figure can be mapped onto itself with a rotation called?

A

The number of times that a figure maps onto itself is called the Order of Rotational Symmetry.

38
Q

What is the Angle of Symmetry in a shape?

A

The Angle of Symmetry is the smallest angle an image can be rotated by so that it maps onto itself.

39
Q

How do you calculate the Angle of Symmetry?

A

360/n

40
Q

What is the Order of Symmetry and the Angle of Symmetry of a Pentagon?

A

OOS = 5 (Has 5 sides)
AOS = 72 Degrees (360/5)

41
Q

What is the Angle of Symmetry of a Square?

A

AOS = 90 degrees (360/4)

42
Q

What is Point Symmetry?

A

When a figure can be mapped onto itself by a rotation of 180 degrees

43
Q

What is the AOS of Rectangles?

A

Since Rectangles have have half symmetry (n = 2) the Angle of Symmetry is 180 degrees

44
Q

A regular polygon has how many lines of reflection?

A

N (number of sides)

45
Q

If n is even, how many perpendicular bisectors are there?

A

If n is even, then the number of perpendicular bisectors will be n/2

46
Q

If n is odd, how many perpendicular bisectors will there be?

A

n = n 😅

Geometry (10 decks)

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