They then had two right triangles which are similar. Which are the corresponding sides?

They also knew the lengths of three sides of these triangles. Which three?

2. If OR=50 ft., RS=25 ft., and RT=371⁄2 ft., find OP. 3. When RS is of OR, then ST is what part of OP? 4. If CD in figure 5 is 2 rd., CE is 5 rd., and AD is 10 rd., find AB.

5. Having found the length of AB, how can you find the length BF from figure 5?

6. How would you find

B

the length of BF in the

field after knowing AB?

E

Fi8.5

7. If in figure 5 the ratio of CD to AD were, what

would be the ratio of CE to AB? Of ED to DB?

9. Why are the two triangles similar? What are the corresponding sides?

10. What is the ratio of DO to OB? What must be the ratio of CD to AB? How long is AB?

11. Knowing OB and AB, in what two ways may you find the distance OA from the figure?

USING SIMILAR TRIANGLES

59

12. A boy 5 ft. 6 in. tall casts a shadow 8 ft. 3 in. long. How high is a tree that casts a shadow 40 ft. long at the same time?

13. At 10 o'clock a certain 6-foot post casts a 4-foot shadow. How high is the building which casts a 50-foot shadow at the same time and place?

To measure the height of this little tree two pupils placed a 6-foot stake between the tree and the drinking fountain so that the top of the stake was in the line of sight with the outer edge

Fi8.8

of the top of the fountain and the top of the tree. They knew that the fountain was 3 feet high.

1. Study the figure and then tell how a knowledge of similar triangles would help the pupils solve the problem in the field.

2. In the figure the fountain is in. high. Using your knowledge of scale drawing and of similar triangles find (1) The height of the tree.

(2) The distance from the center of the fountain to the center of the tree trunk at the base.

(3) The diameter of the fountain base.

(4) The distance of the stake from the tree.

3. When the sun's rays have the direction of the hypotenuse of AABC, what is the length of the shadow of the little tree? What is the length of the shadow of the fountain? Of the 6-foot stake EH?

4. When the shadow of the little tree is 16 ft., how long is the shadow of the fountain?

5. When the shadow of the fountain is 2 ft., what is the shadow of the tree?

6. If you know the length of the shadow of a tree and your own height and shadow, how can you find the height of the tree?

Measuring Triangles and Trapezoids Drawn to Scale

Mr. Banks bought the land between Clay St. and Adams St. making the triangle MNO. He later laid off the blocks and made cross streets as shown in the map on the next page. This map is drawn to the scale in. =50 ft.

1. What is the perimeter of AMRP? next page.

Of AMON? See

Fi8. 10 (16in = 50ft)

2. How many acres in the AMON?

3. Why are As MRP and MON similar?

4. What is the width of Adams St.? Of each of the cross streets?

5. What kind of figure is block g? What are its dimensions?

6. Block ƒ was sold at 25¢ a square foot. How much did it bring?

7. How many square yards of paving in Adams St. from M to O?

8. Knowing MO and ON in feet, how can you find NM without measuring? Do it. Then compare your answer with the measured distance.

9. Mr. Jones, who owned block c, claimed to have a third more land than Mr. Smith, who owned block b. How nearly was he right?

10. Miss Ross, the owner of block d, said she had twice as much land as the owner of b. How nearly was she right?

HINT.-Compare the average width of d with that of b.