7 Mid-Chapter Quiz

Do you know HOW?

1. A bookcase is 4 ft tall. A model of the bookcase is 6 in. tall. What is the ratio of the height of the model bookcase to the height of the real bookcase?
2. If a b = 9 10 , eh over b , equals , 9 tenths , comma  complete this statement: a 9 = □ □ . eh over 9 , equals , fraction white square , over white square end fraction , .

3. Are the two polygons shown below similar? If so, give the similarity ratio of the first polygon to the second. If not, explain.

   

Solve each proportion.

4. y 6 = 18 54 y over 6 , equals , 18 over 54
5. 5 7 = x − 2 4 5 sevenths , equals . fraction x minus 2 , over 4 end fraction
6. On the scale drawing of a floor plan 2  in  . = 5  ft  . 2 , in , . , equals 5 , ft , .  A room is 7 in. long on the scale drawing. Find the actual length of the room.

△ A B C ∼ △ D B F . white up pointing triangle eh b c tilde operator white up pointing triangle d b f .  Complete each statement.

7. m ∠ A = m ∠ _ ? _ m angle eh equals m angle , modified under bar with
8. A B D B = B C □ fraction eh b , over d b end fraction . equals , fraction b c , over white square end fraction
9. A postcard is 6 in. by 4 in. A printing shop will enlarge it so that the longer side is any length up to 3 ft. Find the dimensions of the biggest enlargement.

10. Algebra Find the value of x.

    

Are the triangles similar? If so, write a similarity statement and name the postulate or theorem you used. If not, explain.

Algebra Explain why the triangles are similar. Then find the value of x.

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17. In a garden, a birdbath 2 ft 6 in. tall casts an 18-in. shadow at the same time an oak tree casts a 90-ft shadow. How tall is the oak tree?

Do you UNDERSTAND?

18. Writing You find an old scale drawing of your home, but the scale has faded and you cannot read it. How can you find the scale of the drawing?
19. Reasoning The sides of one triangle are twice as long as the corresponding sides of a second triangle. What is the relationship between the angles?
20. Error Analysis Your classmate says that since all congruent polygons are similar, all similar polygons must be congruent. Is he right? Explain.

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