Transformations
Similar Figures
Similar Triangles
Similarity Postulates
Miscellaneous
100
Is a transformation that shifts figures up, down, left or right. An example of the mapping is (x,y)->(x-3,y+4)
What is translation?
100
Know this about the angles of any two polygons, we can say that the polygons are similar.
What is corresponding angles are congruent.
100
True or False: All right triangles are similar.
What is false.
100
The minimum number of corresponding angles that must be congruent to say two triangles are similar.
What is 2?
100
Segment 𝐸𝐺 is the perpendicular bisector of 𝐻𝐹.
Which of these MUST be TRUE?
A. 𝐻𝐼≅𝐹𝐼
B. 𝑚∠𝐻𝐸𝐹=𝑚∠𝐺𝐻𝐸
C. 𝐸𝐹𝐺𝐻 is a square.
D. Triangle 𝐸𝐹𝐺 is an equilateral triangle.
A. 𝐻𝐼≅𝐹𝐼
200
It is the transformation that enlarges or reduces the size of the figure by using a scale factor, from a reference point.
What is dilation?
200
It is the value found by find the ratio of corresponding sides of two similar polygons.
What is the scale factor?
200
△ABC△𝐴𝐵𝐶 and △DEF△𝐷𝐸𝐹 are equilateral triangles of different lengths.
Why are the sides proportional in △ABC△𝐴𝐵𝐶 and △DEF△𝐷𝐸𝐹?
Corresponding angles are congruent. Therefore similar.
200
The SSS Similarity postulates requires this for two triangles to be similar.
What is ratios of 3 pairs of corresponding sides be equal.
200
Consider the two triangles.
Which theorem could we use to prove that the two triangles are congruent?
SAS Congruence
300
This rigid transformation has a mapping of (x,y) => (-x,y). (Be specific)
What is reflection about the y-axis?
300
True or false: You need to check all pairs of corresponding sides for the same scale factor to check for similarity. (If you know nothing about the angles)
What is true?
300
Which transformations would result in proving these triangles similar? What is the correct statement of similarity?
A. Rotating and dilating; △ACB∼△ECD
B. Rotating and dilating; △ACB∼△DCE
C. Translating and dilating; △ACB∼△ECD
D. Translating and dilating; △ACB∼△DCE
A
300
True or False: The angle in SAS Similiarity Postulate can be any corresponding angle of the two triangles.
What is false? It must be the included angle between the two pairs of corresponding sides used to find the ratio.
300
Point B(−2,0) is transformed to point B′(−4,2).
Which function represents the transformation from B to B′?
(2x, y+2)
400
This transformation has the mapping (x,y) => (x-3,y-5). (Be specific)
What is translation of 5 units down and 3 units left?
400
List the corresponding angles from the given similarity statement: quadrilateral ABCD ~ quadrilateral WXYZ.
What are A and W, B and X, C and Y, D and Z?
400
What is the length of 𝐴𝑄?
21in
400
Consider the four sets of triangles in which the first triangle has been transformed using rigid transformations to create the second triangle.
Which set of triangles is guaranteed to be similar?
Set B
400
The solution to the proportion: (4/x)=(5/7)
What is x=28/5 ?
500
This transformation has the mapping:
(x,y) => (-y,x).
(Be specific)
What is rotation of 90 degrees counterclockwise around (0,0).
500
The scale factor between two similar polygons ABCD and WXYZis 2.5. AB corresponds to WX. AB = 10. This the value of XY
What is 25?
500
∠ADB and ∠AEC are right angles in the diagram.
Which TWO reasons support that △ADB∼△AEC?
A. △ABD is reflected over BD
B. △AEC is reflected over BD.
C. △ABD is translated to the right.
D. △AEC is dilated by a factor less than 1.
E. △ADB is dilated by a factor greater than 1.
E
500
Which of these is TRUE?
A. The triangles are similar by SSS.
B. The triangles are similar by AA.
C. The triangles are similar by SAS.
D. The triangles are not similar.
B. The triangles are similar by AA.
500
The geometric mean is such that
(a/x)=(x/b), where a and b are real numbers. This is the expression equal to x
What is sqrt(ab)?