geometry a - unit 5: dilations and similarity lessons 20-25

lesson 24

proportions in triangles

lesson 21

similarity

lesson 25

similarity and proportions

a dilation by a factor of 7/8 maps triangle abc to triangle xyz. segment bc has a length of 4 cm. what is the length of segment yz?

7/8 * 4 = 3.5 cm

a graphic is printed on a circular banner that has a diameter of 4 feet. the same graphic undergoes a dilation with a scale factor of 1/6 to be printed on circular stickers. the diameter of the dilated graphic is _[blank]_ inches.

8

under a dilation with a scale factor of 4/5, a 10-inch segment becomes a _[blank]_-inch segment.

8

use the diagram and information to complete the proof. given: abc and def prove: abc ~ def match each numbered statement with the correct reason.

1. given 2. the ratio of corresponding sides 3. transitive property of equality 4. sss similarity theorem

use the following image and information to complete the proof. given: triangle abc - a = 61, b = 36, triangle fde - f = 61, e = 83 prove: triangle abc is similar to triangle fde

1. given 2. triangle angle sum theorem 3. substitution 4. subtraction property of equality 5. definition of congruent angles 6. aa similarity postulate

examine the following figure. if de is parallel to ac, what is the measure of length a?

21

use the diagram and information to complete the proof. the following table shows steps 1 through 5 of the proof. for steps 6 through 11, match each numbered statement with the correct reason.

6. segment addition postulate 7. substitution property of equality 8. expansion of fractions 9. division 10. subtraction property of equality 11. reciprocals of both sides

use the following diagram and information to determine steps 7 to 11 in the proof. given: ed is a midsegment of △abc prove: de = 1/2bc match each numbered statement with its correct reason to complete steps 7 to 11 in the proof.

7. ratios of corresponding sides 8. reflexive property 9. sas similarity theorem 10. similar triangles have proportional sides 11. division

use the diagram to answer the question. which statement correctly explains how to prove abc ~ def?

calculate the ratios ab/de, bc/ef, and ac/df. if the ratios are the same, the triangles are similar

use the graph of △abc and △def to answer the question. triangle abc is reflected over the y-axis. which additional transformation proves that △abc ∼ △def?

dilate about the origin with a scale factor of 3 to get △def.

lesson 20

dilations

examine the following triangle, where segment ef is a midsegment of triangle abc. which statement best explains why ef∥ab?

it can be proven that △cef ∼ △cab, which means that their corresponding angles are congruent. when two lines are cut by a transversal to form congruent corresponding angles, the lines must be parallel.

a right triangle is dilated by a factor of 3.5 which statements about the resulting triangle must be true? select all that apply.

it is a right triangle. it is larger than the original triangle.

use the diagram and information to complete the proof. given: triangle abc is a right triangle with legs ab = 2.5 and bc = 6, triangle def is a right triangle with legs de = 12.5 and ef = 30 prove abc ~ def match each numbered statement with the correct reason

1. given 2. definition of right triangle 3. all right angles are congruent 4. the ratio of corresponding sides 5. transitive property of equality 6. sas similarity theorem

becky is standing near a sign post. she is 5 feet, 3 inches tall, and at a certain point in the day she casts a 6-foot shadow. at the same time, the sign post casts an 18-foot shadow. the following figure models this situation. how tall is the sign post?

15 feet, 9 inches

a woman who is 5 feet tall is standing in the park and notices that her shadow, cb, measures 7 feet. at the same time, she notices that the tree next to her, de, casts a shadow that measures 14 feet, fe. how tall is the tree?

10

use the triangles to answer the question. if triangle abc is similar to triangle def, what is the scale factor for the dilation that maps abc to def?

2

use the diagram and information to answer the question. given: abc ~ def what is the measure of angle d?

28

use the triangles to answer the question. by the sas similarity theorem, abc ~ def. what is the measure of side ed?

2sqrt13

use the diagram and information to complete the proof. the following table shows steps 1 through 5 of the proof. for steps 6 through 11, match each numbered statement with the correct reason.

6. segment addition postulate 7. substitution property of equality 8. reflexive property of congruence 9. sas similarity theorem 10. corresponding angles of similar triangles are congruent 11. converse of the corresponding angles theorem

use the diagram and information to complete the proof. the following table shows steps 1 through 5 of the proof. for steps 7 through 11, match each numbered statement with the correct reason.

7. substitution property of equality 8. reflexive property of congruence 9. sas similarity theorem 10. corresponding angles of similar triangles are congruent 11. converse of the corresponding angles theorem

use the diagram and information to complete the proof. the following table shows steps 1 through 6 of the proof. for steps 7 through 11, match each numbered statement with the correct reason.

7. substitution property of equality 8. expansion of fractions 9. division 10. subtraction property of equality 11. reciprocals of both sides

use the graph to answer the question. which single transformation maps figure abcd to figure a'b'c'd'?

a dilation

use the graph to answer the question. which series of transformations correctly maps trapezoid abcd to trapezoid a'b'c'd'?

a dilation with a scale factor of 2 about the origin, followed by a reflection in the y-axis

use the triangles to answer the question. grady wants to prove that abc is similar to def. he notices that abc is congruent to def. which other piece of information can he use to prove the triangles are similar using the side-angle-side similarity theorem?

ab/de = bc/ef

in the figure provided angle b is congruent to ___, then it is possible to show that triangle ade is similar to triangle abc to justify the aa similarity postulate.

angle ade

use the diagram and information to answer the question. which answer correctly fills in the blank in statement 2 to complete the proof?

angle c is congruent to angle e

examine the following figure, where de is parallel to ac. the measure of eb is __blank a___ units by the ___blank b__. thus, bc must measure ___blank c___ units.

blank a: 60 blank b: triangle proportionality theorem blank c: 100

a triangle undergoes a dilation with a scale factor of 9/5. the resulting triangle is _[blank]_ the original triangle.

larger than

segments af and be are medians of triangle abc. nicki is trying to prove that △feg ∼△abg. she determines that ef∥ab, but she needs to provide a reason. which reason proves that ef ∥ab?

midsegment Theorem

a dilation is a transformation that maps every point on a line segment to a point on a parallel line segment. the image has a length that is determined by the preimage and a scale factor, which is a fixed _[blank]_ of the original segment's length.

multiple

examine the measurements of △abc and △a'b'c' to answer the question. did △abc undergo a dilation to produce the image △a'b'c'?

no

the dilation of a line segment creates a _[blank]_ line segment, provided the center of dilation is not on the line segment and the scale factor does not equal 1.

parallel

lesson 22

prove similarity in triangles using angles

lesson 23

prove similarity in triangles using sides

a triangle undergoes a dilation with a scale factor of 7/10. the resulting triangle is _[blank]_ the original triangle.

smaller than

if point b is the center of dilation for a dilation of line ab, the image of the dilation is _[blank]_.

the same as line ab

use the graph to answer the question. quadrilateral abcd is dilated, with the center of dilation at the origin (0,0), to result in the image, quadrilateral a'b'c'd'. which answers are true statements about the transformation that maps quadrilateral abcd to quadrilateral a'b'c'd'? select all that apply.

the transformation doesn't preserve side lengths. the transformation is a nonrigid transformation. the transformation preserves angle measures.

use the graph to answer the question. which answers are true statements about the transformation that maps triangle prs to triangle p'r's'? select all that apply.

the transformation is a nonrigid transformation. the transformation doesn't preserve side lengths. the transformation preserves angle measures.

examine the following triangles, abc and def, where ab = 6, bc = 8, ac = 10, ef = 20, de = 13, df = 25, e = 98° and d = 52° which statement best explains whether abc is similar to def?

the triangles are not similar because 6/13 =/ 8/20

use the triangles to answer the question. which statement best explains whether triangle abc is similar to triangle def?

the triangles are similar because df/ac = ef/bc, and angle c is congruent to angle f.

use the image to answer the question. which statement best describes the relationship between the triangles?

the triangles are similar because they have 3 pairs of congruent angles

examine the following triangles, abc and def, where ab = 5, b = 75°, de = 8, e = 75°, and ef = 9.5. which statement best explains whether abc is similar to def?

there is not enough information to determine whether the triangles are similar

use the image to answer the question. triangle abc: a = 64, b = 38 triangle def: f = 64 which statement best describes the relationship between the triangles?

there is not enough information to determine whether the triangles are similar.

use the graph to answer the question. https://cdstools.flipswitch.com/asset/media/1158935 a dilation maps figure abcd to figure a'b'c'd'. which statement best interprets the relationship between the two figures?

they are similar because dilations are similarity transformations.

which statements describe two similar triangles? select all that apply

two isosceles right triangles two triangles with two pairs of congruent angles

study the following triangle, where segments be and cd are medians of triangle abc, and segment de is drawn. which steps are required to prove that the medians of triangle abc are concurrent? select all that apply.

use proportions to show ge =1/3be, and gd = 1/3cd draw a median and another midsegment, and repeat the steps to show fg =1/3fa. use the midsegment theorem to prove de = 1/2bc draw a line segment from e to d, which is a midsegment. prove △edg ∼ △bcg

the following image shows △abc before and after its transformation. examine the measurements of △abc and △a'b'c' to answer the question. does the transformation represent a dilation?

yes

use the graph to answer the question. https://cdstools.flipswitch.com/asset/media/1158930 which similarity statement is true?

△srp ∼ △s'r'p'