3.7.1 - Test: Similarity Unit Test Part 1
Q1. The Sears Tower in Chicago is 1,450 feet tall. A model of the tower is 24 inches tall. What is the ratio of the height of the model to the height of the actual Sears Tower?
A. 1:725
B. 725:1
C. 12:725
D. 725:12
Q2. Are the polygons similar? If they are, write a similarity statement and give the scale factor. The figures are not drawn to scale.
A. TUWV ~ DEFG; 4.5:2.8
B. TUWV ~ EFGD; 6:2.1
C. TUWV ~ DEFG; 6:4.5
D. The polygons are not similar
Q3. What similarity statement can you write relating the three triangles in the diagram?
A. ΔRST ~ ΔSRU ~ ΔSUT
B. ΔRST ~ ΔRUS ~ ΔSUT
C. ΔSUT ~ ΔSRU ~ ΔRTS
D. ΔRTS ~ ΔRSU ~ ΔTUSQ4.
Q4. What are the values of a and b?
A. a=400/21, b=580/21
B. a=400/21, b=20/21
C. a=580/21, b=29/21
D. a=20/21, b=580/21
Q5. What is the value of x to the nearest tenth? The figure is not drawn to scale.
A. x = 35.6
B. x = 10.5
C. x = 4.9
D. x = 1.5Q6.
Q7. Are the two triangles similar? How do you know?
A. no
B. yes; by AA ~
C. yes; by SAS ~
D. yes; by SSS ~
Q8. What is the geometric mean of 3 and 7?
A. square root of 21
B. 2 square root of six
C. 2 square root of 7
D. 21
Q9. What is the length of the altitude drawn to the hypotenuse? The figure is not drawn to scale.
A. 24
B. square root of 24
C. 143
D. square root of 143
Q10. What is the solution to the proportion? 6/11=m/121
A. 66
B. 11
C. 1/66
D. 1
Q11. What is the value of x, given that PQ || BC?
A. 10
B. 5
C. 7
D. 8
Essay Q12. Sarah is making a scale drawing of a painting that is 48 in. wide by 120 in. high. Her paper is 12 in. wide and 24 in. tall. She decides to use the scale 1 in. = 4 in. Is this a reasonable scale?
Essay Q13.Complete the proof.
Given: AB · BE = CB · BD
Prove: ΔABC ~ ΔDBE
1. AB * BE = CB * BD | 1. Given
2. CB/BE=AB/BD | 2. Property of?
3. Angle ABC is congruent to Angle DBE | 3. ?
4. Triangle ABC ~ Triangle DBE | 4. ?
I would really appreciate the help, thank you to who ever helps in advance.