STAAR Math 8 RC3

In the diagram a person who is 6 ft tall is standing on the ground 3 ft away from point P. A line segment drawn from the top corner of the building to point P creates two similar triangles. Which proportion can be used to find h, the height of the building in feet?

• 3/h=18/6
• 6/3=h/18
• 3/15=h/6
• 6/3=18/h

Figure I and Figure II are similar pentagons. Which proportion must be true?

• y/x=4.2/3.15
• 6/x=5.25/7
• y/6=7/5.25
• x/4=3/6

Triangle QRS and triangle QTV are similar. Which equation must be true?

• TV/RS=TQ/RQ
• TQ/VQ=TV/TR
  
• VQ/SQ=RQ/RS
• TV/VQ=RS/RQ

Polygon QRST below was dilated by a scale factor of 9/5 to create polygon Q’R′S′T′. What is the length in centimeters of R’S′?

• 3.6
• 11.7
• 8.3
• 4.7

Circle I was dilated with the origin as the center of dilation to create Circle II. Which rule best represents the dilation applied to Circle I to create Circle II?

• (x, y) → (⅜ x, ⅜ y)
• (x, y) → (8/3 x, 8/3 y)
  
• (x, y) → (x + 5, y + 5)
  
• (x, y) → (x – 5, y – 5)

Figure S, the small arrow, was dilated with the origin as the center of dilation to create Figure T, the large arrow. Which rule best represents the dilation that was applied to Figure S to create Figure T?

• (x, y) → (2x, 2y)
• (x, y) → (4x, 4y)
• (x, y) → (½ x, ½ y)
• (x, y) → (¼ x, ¼ y)

Quadrilateral ABCD was dilated with the origin as the center of dilation to create quadrilateral A’B’C’D’. Which rule best represent s the dilation that was applied to quadrilateral ABCD to create quadrilateral A’B’C’D’?

• (x, y) →(⅜ x, ⅜ y)
• (x, y) → (8/3 x, 8/3 y)
• (x, y) → (x + 5, y + 5)
• (x, y) → (x – 5, y – 5)

Four triangles are shown.
Based on these triangles, which statement is true?

• w = 75°, because 45 + 60 = 105 and 180 – 105 = 75
• w = 105°, because 180 – (45 + 60) = 75 and 180 – 75 = 105
• w = 285°, because 45 + 60 = 105 and 105 + 180 = 285
• w = 165°, because 180 – 60 = 120 and 120 + 45 = 165

In each diagram, line p is parallel to line f, and line t intersects lines p and f. Based on these diagrams, which  statement is true?

• The value of x should be 75, because the angles shown in the diagrams are congruent.
• The value of x should be 105, because the measures of the angles shown in the diagrams add up to 180°.
• The value of x should be 140, because the measures of the angles shown in the diagrams should add up to 360° and 360 − (110 + 110) = 140.
• The value of x should be 70, because the measures of the angles shown in the diagrams are both 70°.

Pentagon ABCDE is rotated 180° clockwise about the origin to form pentagon A’B’C’D’E’. Which statement is true? 

• Pentagon ABCDE is congruent to pentagon A’B’C’D’E′.
• The sum of the angle measures of pentagon ABCDE is 180° more than the sum of the angle measures of pentagon A’B’C’D’E’.
• Each side length of pentagon A’B’C’D’E’ is 2 times the corresponding side length of pentagon ABCDE.
• Each side length of pentagon A’B’C’D’E’ is the corresponding side length of pentagon ABCDE.