Transformations Practice

Two similar triangles are shown. Triangle MNO was dilated, then ____________, to create triangle YHQ.

rotated

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)

If an image of a triangle is congruent to the pre-image, then the scale factor of the dilation must be n =

1

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 composition of similarity transformations maps polygon ABCD to polygon A'B'C'D'?

a dilation with a scale factor of 1/4 and then a translation

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)

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

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

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.

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

Which diagram can be used to prove △ABC ~ △DEC using similarity transformations?

A

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.

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'