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geometry a - unit 2: transformations and congruent triangles lessons 6-11
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lesson 6
define transformations
match each type of transformation with the correct description of that transformation.
rotation : the distance between the center of rotation and a point in the preimage is the same as the distance between the center of rotation and the corresponding point on the image.
translation: every point in the preimage is mapped the same distance and direction to the image.
reflection: every point in the preimage is mapped the same distance from the line of reflection to the image.
in the following graph, triangle abc has been transformed in three different ways, resulting in triangle def, triangle ghi, and triangle jkl.
https://cdstools.flipswitch.com/asset/media/1158133
match each triangle with the single transformation that maps △abc to that triangle.
△def : rotation
△ghi : translation
△jkl : reflection
use the following graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1158135
which answer choices correctly describe the rotation that maps figure abcd to figure a'b'c'd'?
select two that apply.
a 270 clockwise rotation about the origin
a 90 counterclockwise rotation about the origin
use the following graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1158136
which statements are true about the transformation that maps triangle abc to triangle a'b'c'?
select all that apply.
triangle a'b'c' is the result of a reflection
the transformation is a rigid transformation
the transformation preserves side lengths and angle measures.
draw a line. now draw a line perpendicular to the first line that passes through point g (which is not at the intersection). measure the distance of g from the first line. draw another point on the second line that is the same distance as g, but is on the opposite side of the first line.
if g is the preimage, and the second point is the image, what transformation does this show?
reflection
use the graph of figure abcd and its image, figure a'b'c'd' to answer the question.
https://cdstools.flipswitch.com/asset/media/1157370
which function correctly describes the transformation?
(x, y) -> (-x, y)
the following transformation maps abc to a'b'c'.
(x, y) -> (x - 4, y + 1)
which answer correctly describes the transformation applied to abc?
abc is moved 4 units left and 1 unit up to create a'b'c'.
select two of the following mapping statements that are the result of the same translation.
(2, -3) -> (5, -8)
(-1, 2) -> (2, -3)
in the following graph, trapezoid abcd is transformed by a reflection in the y-axis followed by a rotation 180 clockwise about the origin to obtain trapezoid a'b'c'd'.
which answer correctly shows the image, trapezoid a'b'c'd'?
https://cdstools.flipswitch.com/asset/media/1158169
use the graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1158143
which series of transformations correctly maps parallelogram abcd to parallelogram a'b'c'd'?
a rotation 90∘ clockwise about the origin, followed by a translation 3 units down
use the graph to answer the question.
triangle abc is reflected over line l to result in the image, triangle a'b'c'.
which statements are true about the transformation that maps triangle abc to triangle a'b'c?
select all that apply.
the transformation is a rigid transformation.
the side lengths remain the same from the preimage to the image.
the angle measures remain the same from the preimage to the image.
draw a line segment with endpoints m and r. now draw a parallel line segment that is the same length as mr with the endpoints m' and r' in the same order.
which answer correctly describes the transformation from mr or m'r'?
a translation
use the graph to answer the question.
which series of transformations correctly maps rectangle abcd to rectangle a'b'c'd'?
a reflection in the y-axis, followed by a translation 1 unit down
the coordinates of the vertices of trapezoid abcd are a(-1, 4), b(0, 2), c(1, 2), d(2, 4)
abcd is first rotated 90 counterclockwise, and then translated 3 units right. which graph shows the final image a'b'c'd'?
https://cdstools.flipswitch.com/asset/media/1157542
the following graph shows abcd and a'b'c'd'.
the following mapping statements describe the transformation of the vertices of the quadrilateral. which function rule correctly describes the transformation from quadrilateral abcd to quadrilateral a'b'c'd'.
(x, y) -> (x + 2, y - 2)
use the graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1157536
which answer correctly describes the transformation from the preimage to the image?
a translation 10 units left and 8 units down
the following mapping statements describe the transformation of the vertices of abc to the vertices of its image, a'b'c'.
what is the correct description of the transformation that maps triangle abc to triangle a'b'c'?
a reflection in the y-axis
lesson 7
transformations and symmetry
use the following regular polygon to answer the question.
https://cdstools.flipswitch.com/asset/media/1157551
which answer gives all of the lines of symmetry that carry the regular polygon onto itself?
reflection across lines a, b, c, d, e, f and g
use the graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1157552
which of the following transformations map polygon abcd to itself?
select all that apply.
0.6 of 1
a 180∘ clockwise rotation about the origin
a reflection in the y-axis
a 90∘ clockwise rotation about the origin
use the following regular polygon to answer the question.
https://cdstools.flipswitch.com/asset/media/1157553
what is the angle of rotational symmetry for the figure?
divide 360 by the number of sides the polygon has.
360 ÷ 7 = 51.4
rectangle pqrs is shown below. points j, k, m and n are the midpoints of their respective sides.
areflection over which of the following line segments will carry rectangle pqrs onto itself?
select all that apply
mn
jk
use the diagram to answer the question.
https://cdstools.flipswitch.com/asset/media/1157555
which transformation maps polygon abcd to itself?
a reflection in the y-axis
use the following regular polygon to answer the question.
https://cdstools.flipswitch.com/asset/media/1157557
point g through l bisect the sides of the figure.
point ______ is the center of symmetry, and the angle of rotational symmetry is _____.
blank a: o
blank b: 60
use the following regular polygon to answer the question.
point h through n bisect the sides of the figure
which of the following transformations map the figure onto itself?
select all that apply.
0.63 of 1
a reflection over the line eh
a rotation of 180 about its center
a rotation of about 51.4 about its center
a reflection over line cm
lesson 8
transformations and congruence
use the graph to answer the question.
which series of transformations shows that polygon abcde is congruent to polygon a'b'c'd'e' by superimposing one onto the other?
a translation 4 units up, followed by a reflection in the y-axis
use the graph and given information to answer the question.
triangle abc is translated 1 unit right and 3 units down to produce its image, triangle def.
which statements are true?
select all that apply.
△abc≅△def
∠b≅∠e
ac ≅ df
use the triangles to answer the question.
https://cdstools.flipswitch.com/asset/media/1157573
which triangle is not congruent to the other three triangles?
triangle d
if triangle abc is reflected onto triangle def, then the triangles are congruent.
based on this information, what other statement is true?
ab ≅ de
tony needs to prove that the following two triangles are congruent using rigid transformations.
https://cdstools.flipswitch.com/asset/media/1157575
which set of transformations could tony use to show that figure 2 is an image of figure 1?
a reflection, then a rotation around point l
use the graph to answer the question.
which series of transformations shows that parallelogram abcd is congruent to parallelogram a'b'c'd' by superimposing one onto the other?
a rotation 90 clockwise about the origin, followed by a translation 3 units down
use the triangles to answer the question.
which of these two triangles are congruent?
△def
△abc
use the triangles to answer the question.
which series of transformations can be used to show that the lower triangle is an image of the upper triangle?
a rotation of 180 around point j, then a translation to the left
triangle abc is translated 1 unit right and 3 units down, and then reflected in the x-axis to produce an image, triangle def.
is △abc ≅ △def?
yes, the triangles are congruent to each other.
lesson 9
prove triangles congruent using side lengths
use the graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1157807
which transformation shows △abc ≅ △def, by mapping △abc to △def?
a reflection
use the graph to answer the question.
a series of rigid transformations are applied to △abc such that side ab coincides with side de, side bc coincides with side ef, and side ca coincides with side fd.
what is true about angle a?
angle a coincides with angle d, because the respective sides that form each of the angles coincide.
use the triangle to answer the question.
which answers need to be true to be able to use the sss congruence postulate to prove △abc ≅ △def?
select all that apply
ac ≅ df
ab ≅ de
bc ≅ ef
use the information to complete the proof.
given: ac ≅ad, ab bisects cd
prove: △abc ≅△abd
match each statement in the proof with the correct reason.
1. ac ≅ ad, ab bisects cd : given
2. bc ≅ bd : definition of bisect
3. ab ≅ ab : reflexive property of congruence
4. abc ≅ abd : sss congruence postulate
use the following triangles to complete the sentence.
https://cdstools.flipswitch.com/asset/media/1157815
if △abc ≅ △klm, then m∠b =
48
a window is made of two triangular panels of glass, as shown.
it is given that wx ≅ wy and wz bisects xy. four students explain how they can prove the two triangular panels, △xwz and △ywz are congruent.
which student is correct?
trisha says that it is given that wx ≅ wy. since wz bisects xy, xz ≅ yz, and wz is congruent to itself. then, by the sss congruence postulate, xwz ≅ ywz
a truss, shown below, needs to be made of two congruent triangles. the length of ac is 4 meters (m) and the length of bd is 3 m.
which measurements must be known to determine that the triangles are congruent?
select all that apply
ad = 4 cm
bc = 3 cm
a rug pattern is made of triangles, as shown.
if ab = 3, ac = 5 cm, cd = 3 cm, and ce = 5 cm, what additional information is needed to prove △abc ≅ △def?
bc = 4 cm and de = 4 cm
use the graph to answer the question.
which series of transformations correctly maps triangle abc to triangle a'b'c'?
a reflection in the y-axis, followed by a translation 3 units down
use the graph to answer the question.
https://cdstools.flipswitch.com/asset/media/1157893
which statement about △abc and △dfe is true?
abc ≅ dfe by sss congruence postulate
use the information to complete the proof.
given: ac≅ad , ab bisects cd
prove: △abc ≅ △abd
match each statement in the proof with the correct reason.
1. ac≅ad , ab bisects cd : given
2. bc ≅ bd : definition of bisect
3. ab ≅ ab : reflexive property of congruence
4. △abc ≅ △abd : sss congruence postulate
a reflection and a translation have been applied to triangle abc such that side ab coincides with side de, side bc coincides with side ef, and side ac coincides with side df.
what is true about angle c?
angle c coincides with angle f, because the respective sides that form each of the angles coincide.
lesson 10
side-angle-side triangle congruence
examine the measurements in the triangles.
https://cdstools.flipswitch.com/asset/media/1157857
which statements about the triangles are true?
select all that apply.
△abc ≅ △def by the sas congruence postulate
a rotation will map △abc onto △def
use the triangles to answer the question.
a translation can be applied to △abc in a way that ac coincides with km and bc coincides with lm. this causes ∠c to correspond to ∠m.
how can you be sure that ab ≅ kl?
the endpoints a and b coincide with the endpoints k and l.
use the triangles and the scenario to answer the question.
tabitha says she can prove that the triangles are congruent by using the sas congruence postulate. is she correct? why?
_[blank a]_, the triangles have _[blank b]_ labeled with equal measures, so _[blank c]_.
a: no
b: three pairs of corresponding sides, but no pairs of corresponding angles
c: it cannot be proven that the triangles are congruent using the sas congruence postulate
use the information and diagram to create a proof.
given: bc ≅ cd, ac bisects ∠bcd.
prove: △abc ≅△adc
match each statement in the proof with the correct reason.
1. bc ≅ cd, ac bisects ∠bcd : given
2. ∠1 ≅∠2 : definition of bisect
3. ac ≅ ac : reflexive property of congruence
4. △abc ≅ △adc : sas congruence postulate
joe's house is located at point a. there is a grocery store located at point b and a convenience store located at point c. joe thinks the two stores are the same distance from his house. but he can't measure directly from a to b or a to c to find out for sure because his neighbors have fences around their yards.
joe knows that ab and bc are perpendicular roads. if he can prove △abd ≅△acd, he can be sure that the two stores are the same distance from his house.
which roads or sections of roads should joe measure to use the sas congruence postulate to prove △abd ≅△acd?
bd and cd
a scientist created the following diagram to measure the width of a sinkhole.
the segments in the diagram represent the following measurements.
ac = 75 m, ae = 80 m, ad = 75 m, de = 125 m, ab = 80 m
to find the width of the sinkhole, find the distance between points c and b.
what is the distance across the sinkhole?
125 m
use the triangles to answer the question.
what is the measure of side fd?
3.4 units
use the triangles to answer the question.
1. what is true about △abc and △def?
2. how do you know?
a rotation can map △abc onto △def
a rotation is a rigid transformation
△abc ≅ △def
use the information and diagram to complete the proof.
given: ac≅ae ab≅ad
∠cab is a rotation of ∠ead.
prove: △abc≅△ade
match each statement in the proof to the correct reason.
1. ac≅ae ab≅ad,∠cab is a rotation of ∠ead : given
2. m∠cab = m∠ead : vertical angles are congruent
3. ∠cab ≅∠ead : definition of congruent angles
4. △abc≅△ade : sas congruence postulate
anna is standing on the roof of a 35-foot building and is located at point a. there is a 60-foot rope hanging from a point on the roof. when the rope is stretched out, it reaches to point c. she wants to know how far she is from point b.
if anna can show that triangles abd and acd are congruent, she can find the distance from a to b.
which additional segment lengths could be used to prove that △adb≅△adc by using the sas congruence postulate?
select all that apply.
cd = 8 ft
bd = 8 ft
use the triangles to answer the question.
is it possible to prove that the triangles are congruent by using the sas congruence postulate?
yes, there is enough information to use the sas congruence postulate to prove the triangles are congruent.
use the triangles to answer the question.
a translation can be applied to △abc in a way that ab coincides with de and bc coincides with ef. this causes ∠b to correspond to ∠e.
how can you be sure that ac ≅ df?
endpoints a and c coincide with endpoints d and f
lesson 11
angle-side-angle triangle congruence
use the diagram to answer the question.
https://cdstools.flipswitch.com/asset/media/1157819
which transformation will show that △abd≅△abc?
a reflection over ab
use the triangles to answer the question.
grace states that she can use the asa congruence theorem to prove the given triangles are congruent.
is she correct? why or why not?
grace is incorrect because there are no pairs of corresponding angles with the same measures.
use the information, diagram, and proof to answer the question.
given:∠d≅∠b, ad≅ab
prove: △ade≅△abc
match each statement in the proof with the correct reason.
1. ∠d≅∠b, ad≅ab : given
2. ∠a ≅ ∠a : reflexive property of congruence
3. △ade≅△abc : asa congruence theorem
use the triangles to answer the question.'
https://cdstools.flipswitch.com/asset/media/1157826
If △abc ≅△def, what is the length of df?
4.5
two swatches of cloth are laid on top of each other as shown.
if m∠d = 35∘, m∠b = 35∘, ad = 3 inches, and ab = 3 inches, are the two swatches congruent? how do you know?
yes, the swatches are congruent.
by the reflexive property of congruence, ∠a ≅∠a, so the swatches are congruent by the asa congruence theorem.
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