SIMILARITY TRANFORMS UNIT TEST -

If ΔYWZ ~ ΔYXW, what is true about XWZ?

XWZ is a right angle.

Which transformations could have occurred to map △ABC to △A"B"C"?

a dilation and a rotation

What are the x- and y- coordinates of point P on the directed line segment from A to B such that P 2/3 is the length of the line segment from A to B?

(-1, 2)

Quadrilateral JKLM was dilated according to the rule What are the coordinates of vertex J of the pre-image?

(0, -4)

A treasure map says that a treasure is buried so that it partitions the distance between a rock and a tree in a 5:9 ratio. Marina traced the map onto a coordinate plane to find the exact location of the treasure. What are the coordinates of the treasure? If necessary, round the coordinates to the nearest tenth.

(7.6, 8.8)

Which value of x would make line segment TV parallel to line segment QS?

10

If CA = 8, what is C'A'?

10 units

What is the value of x?

12 units

What is the length of line segment SR?

15 units

What is the length of a leg of the pre-image, triangle RST?

16 units

What is the length of line segment AC?

18 feet

Which value of y would make OP parallel to LN?

36

If point P is 4/7 of the distance from M to N, what ratio does the point P partition the directed line segment from M to N into?

4:3

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.

Is rectangle EFGH the result of a dilation of rectangle ABCD with a center of dilation at the origin? Why or why not?

No, because corresponding sides have different slopes.

Triangle TVW is dilated according to the rule DO(3/4x and 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, 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.

If an image of a triangle is congruent to the pre-image, what is the scale factor of the dilation?

1

What is the value of y?

6√3

Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'. What is the scale factor of the dilation?

8

Which best explains why all equilateral triangles are similar?

All equilateral triangles can be mapped onto each other using dilations.

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.

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

Consider △RST and △RYX. If the triangles are similar, which must be true?

ry/rs = rx/rt = xy/ts