Similar Triangles

SSS Conjecture

100

(Drawing on board) Are triangles ABC and DEF similar by the SSS conjecture?

No, the triangles are not similar by the SSS conjecture.

200

(Drawing on board) Are triangles COW and MLK similar by the SSS conjecture? *Hint: Pay attention to the triangle names' order.*

No, COW and MLK are not similar by the SSS conjecture.

300

(Drawing on board) Are triangles RON and RIM similar by the SSS conjecture?

Yes, RON and RIM are similar by the SSS conjecture.

400

(Drawing on board) Are triangles PUN and POB similar by the SSS conjecture?

No, PUN and POB are not similar by the SSS conjecture.

500

(Drawing on board) These are two different versions of triangles HYZ and HIJ. Use the SSS conjecture to determine which pair is similar.

Pair #1

SAS Conjecture

100

(Drawing on board) x=?

x=3

200

(Drawing on board) Is MOY similar to NOT? Explain why or why not.

Yes, because SAS conjecture proves this.

300

(Drawing on board) Is AUL similar to MST? Explain why or why not.

No, the ratios of sides AU:MS and LU:TS are not the same.

400

(Drawing on board) BAL is similar to EML. n=? *Hint: Redraw EML so that the corresponding sides match up*

n=54

500

(Drawing on board) Can you use the SAS conjecture to prove that MEN and WAK are similar?

No, the SAS conjecture does not prove this.

AA Conjecture

100

(Drawing on board) Can you use the AA theorem to prove that ABC and FDE are similar?

Yes, the triangles are similar by the AA conjecture.

200

(Drawing on board) Can you use the AA theorem to prove that ABC DEF are similar? *HINT: Pay attention to the triangle names' order*

No, the AA theorem does not prove this.

300

(Drawing on board) g=?

6

400

(Drawing on board) h=? k=?

h=40 k=40

500

(Drawing on board) m=?

m=28

Word Problems

100

You are 1.53 meters tall and have a shadow that is 11 meters long. A nearby telephone pole is 9.18 m tall and has a shadow the measures 66 meters long. If the distance from the top of your head to the tip of your shadow is approximately 11.1 m, how far is the distance from the top of the telephone pole to the tip of its shadow?

66.6 m

200

Two triangles are similar. The smaller triangle has a side of 10 and a median of 6. The larger one has a corresponding side that measures 65. What is the median of the larger one?

39

300

You are 1.55 meters tall and have a shadow that is 1 meters long. A nearby telephone pole is has a height of 7.75 m and a shadow the measures 5 meters long. If the distance from the top of your head to the tip of your shadow is approximately 1.8 m, then what is the distance from the top of the telephone pole to the tip of its shadow?

9 m

400

Two triangles are similar. The smaller triangle has a side of 5 and a height of 8. The larger one has a corresponding side that measures 20. What is the height of the larger one?

32

500

You want to determine the height of a flagpole. You have a friend place a small mirror on the ground so that you can see the reflection of the top of the flagpole. Your friend then measures from you to the mirror and finds that it is 3 feet. The distance from the mirror to the flagpole is 15 feet. The angle from the mirror to your eyes is about 15 degrees, and the angle from the top of the flagpole to the mirror is also about 15 degrees. If your eyes are 5 feet above the ground, how high is the flagpole?

25 ft

Similar or NOT?

100

There are two triangles, ABC and DEF. Side AB is 4 cm and side DE is 8 cm. Side BC is 10 cm and side EF is 20 cm. Are the triangles similar?

no (CBD)

200

There are two triangles, FAT and SKI. Side FA is 3 cm long, and side SK is 9 cm long. Angle A is 30 degrees and Angle K is also 30 degrees. Side AT is 6 cm and side KI is 24 cm. Are the triangles similar?

no

300

There are two triangles, ARE and IST. Angle A is 45 degrees and angle I is 20 degrees. Angle R is 30 degrees and so is angle S. Are the triangles similar?

No

400

There are two triangles, WAD and POL. Angle W is 20 degrees and angle P is also 20 degrees. Angle A is 30 degrees and so was angle O. Are the triangles similar?

yes

500

There are two triangles, PIT and RUG. Side PI is 3 cm, and side RU is 6 cm. Side IT is 9 cm and side UG is 18 cm. Angle T is 23 degrees and Angle G is also 23 degrees. Are the triangles similar?

yes