Geometry B unit 9

___ polygons are polygons whose corresponding angles are congruent and whose corresponding sides are proportional.

Similar

2) ___ are polygons whose corresponding angles are congruent and whose corresponding sides are proportional.

Similar polygons

3) The ___ is the original figure before a transformation.

preimage

8) Choose the correct word. The number of oranges compared to the total number of fruits in a fruit basket.

ratio

A _____ is a relationship between two similar quantities.

ratio

4) Theorem 9.8.B states that the composition of two reflections across two intersecting lines is equivalent to a ___.

rotation

15) Given the scale factor `k=2` , find `B'C'` .

12

13) Given the scale factor `R=4` , if `DE=12` cm, how long is `D'E'` ?

15 cm

3) ___ means having the same shape, but not necessarily the same size.

Similar

Find the scale factor.

`2`

What is the scale factor?

`7.5`

Determine whether the tessellation is regular, semi-regular, or neither.

neither

Angle of rotational symmetry is the smallest angle through which a _____ can be rotated to coincide with its image.

preimage

10) Choose the property represented by the picture.

reflexive Property

17) Determine whether the tessellation is regular, semi-regular, or neither.

regular

10) Point of ___ is the point around which a figure that demonstrates rotational symmetry is rotated.

rotation

17) Determine if the composition of transformations is equivalent to a translation or a rotation.

rotation

16) Which type of symmetry is illustrated?

rotational symmetry

18) Determine whether the tessellation is regular, semi-regular, or neither.

semi-regular

19) Determine whether the tessellation is regular, semi-regular, or neither.

semi-regular

11) A composition of ___ is the resulting transformation when one transformation is followed by another transformation.

transformations

8) A quantity that has both length and direction is called a(n) ___.

vector

______ of rotational symmetry is the number of times an image can coincide with its preimage as it rotates through 360°.

vector

From 1957 to 1999, the Atlas rocket was launched 301 times. The number of launch failures was 44. At that rate, if it were launched 903 times, how many failures could be expected?

132

12) Given the scale factor `R=1/3` , if `AB=12` cm, how long is `A'B'` ?

4 cm

3) Match the description with the term. If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

AA Similarity Postulate

4) Match the description with the term. If the similarity ratio of two similar figures is a:b, then the ratio of their areas is a2:b2.

Area Proportionality Theorem

5) The axis of ___ is a line that divides a figure into two symmetrical parts.

Line

Choose the correct term. In a proportion, the product of the means is equal to the product of the extremes.

Means-Extremes

12) ___ of rotational symmetry is the number of times an image can coincide with its preimage as it rotates through 360°.

Order

1) Match the description with the term. If the similarity ratio of two similar figures is a:b, then the ratio of their perimeters is also a:b.

Perimeter Proportionality Theorem

6) The ___ Property of Similarity is a geometric property of similarity that states that a polygon is similar to itself.

Reflexive

3) ___ tessellation is a tessellation formed by congruent regular polygons.

Regular

11) ___ symmetry is the symmetry of a figure such that, when it is rotated about a point by an angle greater than 0° and less than 360°, the image coincides with the preimage.

Rotational

1) Given: `bar(BE)∥bar(CD)` Prove: `(BC)/(AB)=(ED)/(AE)`

SAS Similarity Corresponding Alternate Interior

2) Match the description with the term. If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

SAS Similarity Theorem

2) ___ tessellation is a tessellation formed by two or more different regular polygons with the same number of each polygon occurring in the same order at each vertex.

Semi-regular

1) ___ is a repeating pattern that completely covers a plane with no gaps or overlaps.

Tessellation

11) Choose the property represented by the picture.

Transitive Property

6) ___ symmetry is a symmetry of a figure such that, when the figure is reflected across a line, the image coincides with the preimage.

Translation

Match the description with the term. If a line parallel to one side of a triangle intersects the other two sides, then it divides those two sides proportionally.

`Delta` Proportionality Theorem

14) Find the scale factor. `DC=6` cm and `D'C'=2` cm.

`R=12`

A ___ is a noncongruent transformation in which the size, but not the shape of a geometric figure is changed.

dilation

10) Theorem 9.8.D states that any translation or rotation is equivalent to a composition of two ___.

enlargement

9) A symmetry of a figure such that, when it is transformed along a glide reflection, the image coincides with the preimage is called ___ reflection symmetry.

glide

9) The composition of transformations that results when a translation is followed by a reflection across a line parallel to the translation vector is called a(n) ___.

glide reflection

A _____ is the composition of transformations that results when a translation is followed by a reflection across a line parallel to the translation vector.

glide reflection

15) Which type of symmetry is illustrated?

glide reflection symmetry

Which type of symmetry is illustrated?

glide reflection symmetry

8) Angle of ___ symmetry is the smallest angle through which a preimage can be rotated to coincide with its image.

glide rotational

Symmetry is the property of a geometric figure such that when the figure is transformed, the _____ coincides with the preimage.

image

A translation is a congruent transformation along a vector such that each segment joining a _____ and its image has the same length as the vector and is parallel to the vector.

point

7) ___ symmetry is symmetry of a figure such that, when it is translated along a vector, the image coincides with the preimage.

rotational

A _____ is the ratio of any linear measurement of the image to the corresponding measurement of the preimage in a dilation.

scale factor

20) Determine whether the tessellation is regular, semi-regular, or neither.

semi-regular

Determine whether the tessellation is regular, semi-regular, or neither.

semi-regular

A ___ transformation is a noncongruent transformation in which the points on a given line in a geometric figure remain fixed while other points of the figure are shifted parallel to the line by a distance proportional to their perpendicular distance from the line.

shear

4) ___ is the property of a geometric figure such that when the figure is transformed, the image coincides with the preimage.

symmetry

A ___ is a repeating pattern that completely covers a plane with no gaps or overlaps.

tessellation

16) Determine if the composition of transformations is equivalent to a translation or a rotation.

translation

13) Which type of symmetry is illustrated?

translation symmetry

14) Which type of symmetry is illustrated?

translation symmetry

Which type of symmetry is illustrated?

translation symmetry

12) As of August, 2011, Russia has had 21 rocket launch failures out of 743 total launches. To the nearest whole number, how many failures can be expected from the next 800 launches?

23

After finding the area from the dimensions of the first polygon, find the area of the similar polygon after finding the similarity ratio.

300 ft2

The scale factor for an airplane model is 5 cm = 7 meters. If the model is 25 cm long, how long is the full size plane?

35 meters

14) Edy filled her small 150 gallon swimming pool. In 45 minutes, the pool had 90 gallons in it. How long did it take Edy to fill the pool?

75

Match the description with the term. If two angles of one triangle are congruent to two angles of another triangle, then the two triangles are similar.

AA Similarity Postulate

7) Choose the theorem or corollary that matches the statement. If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Converse of the `Delta` Proportionality Theorem

Match the description with the term. If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Converse of the `Delta` Proportionality Theorem

Match the description with the term. If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.

Corollary 1 of the `Delta` Proportionality Theorem

8) Choose the theorem or corollary that matches the statement. If one transversal intersects three or more parallel lines so that it is divided into congruent segments, then any transversal that intersects the same parallel lines will be divided into congruent segments.

Corollary 2 of the `Delta` Proportionality Theorem

6) Norman made a scale drawing of his patio located in the back of his house. He used the scale 1 millimeter = 2 feet. If the patio is 12 millimeters long in the drawing, how long is the actual patio?

`24` feet

6) Choose the theorem or corollary that matches the statement. If a line parallel to one side of a triangle intersects the other two sides, then it divides those two sides proportionally.

`Delta` Proportionality Theorem

6) A dilation with a scale factor greater than 1 is a(n) ___.

enlargement

4) Given: `bar(BC)∥bar(DE)∥bar(FG);\ bar(BD)~=bar(DF)` Prove: `bar(CE)~=bar(EG)`

f. Prop. of = c. Division b. Corollary 1 e. `~=` segments d. Symmetric Prop. of =

2) Given: `(AB)/(BC)=(AE)/(ED)` Prove: `bar(BE)∥bar(CD)`

f. Reflexive e. `DeltaABE~=DeltaACD` d. Corresponding Angles g. Parallel Lines

8) After finding the perimeter from the dimensions of the first polygon, find the perimeter of the similar polygon after finding the similarity ratio.

f. `42` inches b. `1/3` a. `56` inches

12) A(n) ___ is a congruent transformation about a point called the center of rotation, such that each point and its image are the same distance from the center of rotation, and such that all angles formed by each point and its image are congruent.

rotation

The _____ is the ratio of the size of a model of an object to the size of the actual object.

scale ratio

The ___ ratio is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.

similarity

7) Compare the ratios of the corresponding sides to prove or disprove that the polygons are similar.

b 20/30 e 22/33 d 24/36 f yes

Find the ratios of the corresponding sides.

b. 6/9 c. 2/3 a. 10/15

3) The ___ is the point of intersection of the lines that connect each point of the preimage with the corresponding point on the image of dilation.

center of dilation

9) A(n) ___ is a noncongruent transformation in which the size, but not the shape of a geometric figure is changed.

dilation

8) Compare the ratios of the corresponding sides to prove or disprove that the polygons are similar.

e. 2/3 f. 2/3 g. 1.2/2.4 c. 3/4.4 yes

11) Choose the correct word. The name of the quantities x and y in the expression w/x=y/z .

extremes

3) The first and last terms in a proportion are called the ___.

extremes

The first and last terms in a proportion are called the _____.

extremes

4) Given: BADF=ACFE; BA¯≅GF¯; GH¯∥DE¯; ∠A≅∠F Prove: ΔBAC~ΔDFE

i. SAS g. AA~Postulate f. `(BA)/(DF)=(FH)/(FE)` h. `(FH)/(FE)=(AC)/(FE)` c. Def. of `~=Delta"s"` e. `∠ABC~∠FGH`

7) Theorem 9.8.C says a composition of two isometries is a(n) ___.

isometry

4) The ___ are the second and third terms in a proportion.

means

The second and third terms in a proportion are called the _____.

means

15) Are the two images reflections?

no

4) A(n) ___ is a transformation in which the size or the shape of a geometric figure is changed.

noncongruent transformation

10) Choose the correct word. The number of peas to carrots is the same as the number of corn to green beans.

proportion

2) A ___ is an equation that states that two ratios are equal.

proportion

5) The Means-Extremes Property states that in a(n) ___, the product of the means is equal to the product of the extremes.

proportion

9) Choose the correct word. The name of the quantities, 3 and 2 in the expression 3:6 = 1:2.

proportion

A _____ is an equation that states that two ratios are equal.

proportion

Given: `bar(JK)∥bar(LM)∥bar(NO)` Prove: `(JL)/(LN)=(KM)/(MO)`

proportionality transitive

1) A(n) ___ is a relationship between two similar quantities.

ratio

Choose the graphic that shows the translation of the preimage using the given vector.

red triangle on upper right side

8) A(n) ___ is a dilation with a scale factor greater than zero but less than 1.

reduction

11) A(n) ___ is a congruent transformation across a line, called the line of reflection, so that the line of reflection is the perpendicular bisector of each segment joining each point and its image.

reflection

2) Match the description with the term. Any drawing that represents an object as smaller or larger than the size of the original object.

scale drawing

5) A ___ is the ratio of any linear measurement of the image to the corresponding measurement of the preimage in a dilation.

scale factor

7) A ___ is the physical representation of an object to the size of the actual object.

scale model

A physical representation of an object to the size of the actual object is called a _____.

scale model

5) A(n) ___ is a noncongruent transformation in which the points on a given line in a geometric figure remain fixed while other points of the figure are shifted parallel to the line by a distance proportional to their perpendicular distance from the line.

shear transformation

5) The ___ is the ratio of the length of one side of a polygon with the length of a corresponding side of a similar polygon.

similarity ratio

13) Sarah has a picture that fits a 3 inch wide by 5 inch long picture frame. She wants to make the picture proportionately bigger so the picture fits a frame with a length of 15 inches. What would the width of the frame need to be?

13

7) Use the conversion factors to convert the measurement using proportions. 1 yard = 3 feet; 1 foot = 12 inches How many inches are there in 5 yards?

180 inches

5) A 6.5 foot street sign casts a 10-foot shadow while a telephone pole casts a 40-foot shadow. How tall is the telephone pole?

26 feet

Given the perimeter of the first polygon, find the perimeter of the similar polygon after finding the similarity ratio.

48 cm

If Carlos ran 100 meters in 15 seconds, how long would it take him to run 44 meters?

6.6 seconds

5) Choose the theorem or corollary that matches the statement. If three or more parallel lines intersect two transversals, then they divide the transversals proportionally.

Corollary 1 of the `Delta` Proportionality Theorem

Match the description with the term. If one transversal intersects three or more parallel lines so that it is divided into congruent segments, then any transversal that intersects the same parallel lines will be divided into congruent segments.

Corollary 2 of the `Delta` Proportionality Theorem

Match the description with the term. If two sides of one triangle are proportional to two sides of another triangle and their included angles are congruent, then the triangles are similar.

SAS Similarity Theorem

1) Match the description with the term. If the measures of the three sides of one triangle are proportional to the measures of the corresponding three sides of another triangle, then the triangles are similar.

SSS Similarity Theorem

Match the description with the term. If the measures of the three sides of one triangle are proportional to the measures of the corresponding three sides of another triangle, then the triangles are similar.

SSS Similarity Theorem

. Choose the correct term. If one polygon is similar to a second polygon, then the second polygon is similar to the first polygon.

Symmetric

1) The ___ Property of Similarity is a geometric property of similarity that states if one polygon is similar to a second polygon, then the second polygon is similar to the first polygon.

Symmetric

Choose the correct term. A polygon is similar to itself

Symmetric

4) The ___ Property of Similarity is a geometric property of similarity that states if one polygon is similar to a second polygon, and the second polygon is similar to a third polygon, then the first polygon is also similar to the third polygon.

Transitive

Choose the correct term. If one polygon is similar to a second polygon, and the second polygon is similar to a third polygon, then the first polygon is also similar to the third polygon.

Transitive

9) Choose the property represented by the picture.

Transitive Property

6) A(n) ___ is a transformation that does not change the size or shape of a geometric figure so that the preimage and image are congruent.

congruent transformation

Given: `(DE)/(EF)=(DH)/(HG)` Prove: `bar(EH)∥bar(FG)`

d. Symmetric e. `DeltaDEH=DeltaDFG`

2) A ___ is a noncongruent transformation in which the lines connecting each point with its image all intersect at a point called the center of dilation.

dilation

9) After finding the area from the dimensions of the first polygon, find the area of the similar polygon after finding the similarity ratio.

e. `2/3` g. 192 ft2

2) A(n) ___ is the resulting image after a transformation.

image

3) Match the description with the term. Any method that uses formulas, figures, and/or proportions to measure an object.

indirect measurement

1) A change in the position, size, or shape of a geometric figure is called a(n) ___.

transformation

3) Given: `bar(AB)∥bar(CD)∥bar(EF)` Prove: `(AC)/(CE)=(BD)/(DF)`

transitive proportionality symmetric

1) Theorem 9.8.A states that the composition of two reflections across two parallel lines is equivalent to a ___.

translation

10) A(n) ___ is a congruent transformation along a vector such that each segment joining a point and its image has the same length as the vector and is parallel to the vector.

translation

7) A congruent transformation is also known as a(n) ___.

translation

13) Are the two images reflections?

yes

14) Are the two images reflections?

yes

16) Are the two images reflections?

yes

Are these polygons similar?

yes