Similarity Transformations Unit Test (60% lmfao)

Quadrilateral JKLM was dilated according to the ruleDO,One-half(x,y)(one-half x, one-half y) to create the image quadrilateral J'K'L'M', which is shown on the graph.On a coordinate plane, quadrilateral J prime K prime L prime M prime has points (0, negative 2), (3, 2), (6, negative 2), and (3, negative 6).What are the coordinates of vertex J of the pre-image?

(0, -4)

The graph shows parallelogram FGHJ and the location of vertex F' after a dilation with respect to the origin. What are the coordinates of J'?

(3, -5)

Which value of x would make Line segment T V is parallel to Line segment Q S?

10

Line segment Q R , Line segment R S are Line segment S Q midsegments of ΔWXY. Triangle R Q S is inside triangle X Y W. Point R is the midpoint of side X Y, point S is the midpoint of side Y W, and point Q is the midpoint of side X W. The length of Q R is 2.93 centimeters, the length of R S is 2.04 centimeters, and the length of Q S is 2.28 centimeters. What is the perimeter of ΔWXY? 11.57 cm 12.22 cm 12.46 cm 14.50 cm

14.50 cm

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of S T is 9 and the length of T Q is 16. The length of S R is x.What is the value of x?

15 units

Triangle S R Q is shown. Angle S R Q is a right angle. An altitude is drawn from point R to point T on side S Q to form a right angle. The length of T Q is 16 and the length of R Q is 20. What is the length of Line segment S R? 9 units 12 units 15 units 18 units

15 units

What is the length of AC?

18

What is the value of y?

2nd option

Rectangle ABCD is transformed to A'B'C'D' by a dilation. What is the scale factor used for the dilation?

3

Which value of y would make OP ll LN?

36

Parallelogram FGHJ was dilated and translated to form similar parallelogram F'G'H'J'. On a coordinate plane, 2 parallelogram are shown. Parallelogram F G H J has points (negative 4, 5), (negative 2, 5), (negative 1.5, 3), and (negative 3.5, 3). Parallelogram F prime G prime H prime J prime has points (negative 5, 2), (3, 2), (5, negative 6) and (negative 3, negative 6). What is the scale factor of the dilation? One-eighth One-fourth 4 8

4

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?

4:1.

Triangle W X Z is shown. An altitude is drawn from point W to point Y on side Z X, forming a right angle. Angles Z W Y and W X Y are congruent. If ΔYWZ ~ ΔYXW, what is true about AngleXWZ?

<XWZ is a right angle.

A right triangle is drawn on the coordinate plane. Which is a dilation of this triangle with respect to the origin by a factor of ?

A

Which statements can be concluded from the diagram and used to prove that the triangles are similar by the SAS similarity theorem?

A

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.

Isosceles triangle ABC is transformed to the image, triangle A'B'C'. Which describes the transformation that could have been applied to triangle ABC?

An isometric transformation could have been applied because all of the vertices moved 2 units left and 2 units up.

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

B

On a number line, the directed line segment from Q to S has endpoints Q at -14 and S at 2. Point R partitions the directed line segment from Q to S in a 3:5 ratio. Which expression correctly uses the formula to find the location of point R?

B

Consider the two triangles. To prove that the triangles are similar by the SAS similarity theorem, it needs to be shown that

C

In the diagram, DG = 12, GF = 4, EH = 9, and HF = 3. Triangle D E F is shown. Line G H is drawn parallel to side D E within the triangle to form triangle G F H. The length of D G is 12, the length of G F is 4, the length of E H is 9, and the length of H F is 3. To prove that △DFE ~ △GFH by the SAS similarity theorem, it can be stated that StartFraction D F Over G F EndFraction = StartFraction E F Over H F EndFraction and ∠DFE is 4 times greater than ∠GFH. ∠FHG is One-fourth the measure of ∠FED. ∠DFE is congruent to ∠GFH. ∠FHG is congruent to ∠EFD.

C. ∠DFE is congruent to ∠GFH.

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.

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 best explains why all equilateral triangles are similar?

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

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

a translation and a dilation