Similarity Transformations Unit Test 84%
Triangle MNP will be dilated according to the rule (x,y), where point P is the center of dilation. What will be the coordinates of vertex N' of the image?
(-2, 6)
Quadrilateral JKLM was dilated according to the rule DO,(x,y) -> (1/2x, 1/2y)0, -4) to create the image quadrilateral J'K'L'M', which is shown on the graph. What are the coordinates of vertex J of the pre-image?
(0, -4)
If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =
1
Triangle ABC was dilated using the rule DY, 5/4. If CA = 8, what is C'A'?
10 units
Triangle RST was dilated by a scale factor of . The image, triangle R'S'T', is an isosceles triangle, with each leg measuring 8 units. What is the length of a leg of the pre-image, triangle RST?
16 units
Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'. What is the scale factor of the dilation?
4
Triangle JKL was dilated using the rule DM, 1/3. The image, triangle J'K'L', is the result of the dilation. What is L'L?
5 units
Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?
A
Which would prove that △ABC ~ △XYZ? Check all that apply.
A, C
Read the proof. Given: AB ∥ DE Prove: △ACB ~ △DCE We are given AB ∥ DE. Because the lines are parallel and segment CB crosses both lines, we can consider segment CB a transversal of the parallel lines. Angles CED and CBA are corresponding angles of transversal CB and are therefore congruent, so ∠CED ≅ ∠CBA. We can state ∠C ≅ ∠C using the reflexive property. Therefore, △ACB ~ △DCE by the
AA similarity theorem.
Consider the two triangles. To prove that the triangles are similar by the SSS similarity theorem, it needs to be shown that
AB = 25 and HG = 15
Which best explains why all equilateral triangles are similar?
All equilateral triangles can be mapped onto each other using dilations.
Consider △RST and △RYX. If the triangles are similar, which must be true?
B
Which diagram can be used to prove △ABC ~ △DEC using similarity transformations?
B
Is triangle A'B'C' a dilation of triangle ABC? Explain.
No, it is not a dilation because the points of the image are not moved away from the center of dilation proportionally.
Triangle TVW is dilated according to the rule DO 3/4,(x,y) -> (3/4x 3/4y) to create the image triangle T'V'W', which is not shown. What are the coordinates of the endpoints of the segment T'V'?
T'(-3, 6) and V'(0, 3)
In the diagram below, m∠A = 55° and m∠E = 35°. Which best explains the relationship between triangle ACB and triangle DCE?
The triangles are similar because all pairs of corresponding angles are congruent.
Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?
Yes, because both figures are rectangles and all rectangles are similar.
Which transformations could have occurred to map △ABC to △A"B"C"?
a dilation and a rotation
Which composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?
a dilation with a scale factor of and then a translation
Why is the information in the diagram enough to determine that △LMN ~ △PON using a rotation about point N and a dilation?
because one pair of congruent corresponding angles is sufficient to determine similar triangles
Two similar triangles are shown. Triangle MNO was dilated, then ____________, to create triangle YHQ.
rotated
Which piece of additional information can be used to prove △CEA ~ △CDB?
∠BDC and ∠AED are right angles
In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3. To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that DF/GF = EF/HF and
∠DFE is congruent to ∠GFH.
Triangle DEF was dilated according to the rule DO1/3,(x,y) -> (1/3x, 1/3y) to create similar triangle D'E'F'. Which statements are true? Check all that apply.
∠F corresponds to ∠F'. The distance from point D' to the origin is the distance of point D to the origin. △DEF △D'E'F'
