# WORKSHEET ON SIMILAR TRIANGLES

Problem 1 :

In the diagram shown below ΔACB ∼ ΔDCE.

a. Write the statement of proportionality.

b. Find ∠CDE. Problem 2 :

Color variations in the tourmaline crystal shown below lie along the sides of isosceles triangles. In the triangles each vertex angle measures 52°. Explain why the triangles are similar. Problem 3 :

Use properties of similar triangles to explain why any two points on a line can be used to calculate the slope. Find the slope of the line using both pairs of points shown. Problem 4 :

Low-level aerial photos can be taken using a remote-controlled camera suspended from a blimp. we want to take an aerial photo that covers a ground distance g of 50 meters. Use the proportion f/h  =  n/g to estimate the altitude h that the blimp should fly at to take the photo. In the proportion, use f = 8 cm and n = 3 cm. These two variables are determined by the type of camera used. Problem 5 :

Find the length of the altitude DG in the diagram shown below.  Problem 1 :

In the diagram shown below ΔACB ∼ ΔDCE.

a. Write the statement of proportionality.

b. Find ∠CDE. Solution (a) :

DC / AC  =  CE / CB  =  ED / BA

Solution (b) :

Because ΔACB ∼ ΔDCE,

∠A  ≅  ∠CDE

Then, we have

∠CDE  =  ∠A  =  79°

Solution (c) :

Write proportion.

ED / BA  =  DC / AC

Substitute.

3 / 12  =  DC / 20

Multiply each side by 20.

20 ⋅ (3 / 12)  =  (DC / 20) ⋅ 20

Simplify.

5  =  DC

Because AD  =  AC - DC,

So, DC is 5 units and AD is 15 units.

Problem 2 :

Color variations in the tourmaline crystal shown below lie along the sides of isosceles triangles. In the triangles each vertex angle measures 52°. Explain why the triangles are similar. Solution :

Because the triangles are isosceles, we can determine that each base angle is 64°. Using the AA Similarity Postulate, we can conclude that the triangles are similar.

Problem 3 :

Use properties of similar triangles to explain why any two points on a line can be used to calculate the slope. Find the slope of the line using both pairs of points shown. Solution :

By the AA Similarity Postulate ΔBEC ∼ ΔAFD, so the ratios of corresponding sides are the same.

In particular,

CE / DF  =  BE / AF

By a property of proportions, we have

CE / BE  =  DF / AF

The slope of a line is the ratio of the change in y to the corresponding change in x. The ratios CE/BE and DF/AF represent the slopes of BC and AD respectively.

Because the two slopes are equal, any two points on a line can be used to calculate its slope. We can verify this with specific values from the diagram.

Using slope formula,

Slope of BC  =  (3 - 0) / (4 - 2)  =  3 / 2

Slope of AD  =  [6 - (-3)] / (4 - 2)  =  9 / 6  =  3 / 2

Problem 4 :

Low-level aerial photos can be taken using a remote-controlled camera suspended from a blimp. we want to take an aerial photo that covers a ground distance g of 50 meters. Use the proportion f/h  =  n/g to estimate the altitude h that the blimp should fly at to take the photo. In the proportion, use f = 8 cm and n = 3 cm. These two variables are determined by the type of camera used. Solution :

Write proportion.

f / h  =  n / g

Substitute.

8 / h  =  3 / 50

By reciprocal property of proportion,

h / 8  =  50 / 3

Multiply each side by 8.

⋅ (h / 8)  =  8 ⋅ (50 / 3)

Simplify.

h  ≈  133

So, the blimp should fly at an altitude of about 133 meters to take a photo that covers a ground distance of 50 meters.

Problem 5 :

Find the length of the altitude DG in the diagram shown below. Solution :

Find the scale factor of ΔADC to ΔFDE.

AC / FE  =  (12 + 12) / (8 + 8)

AC / FE  =  24 / 16

AC / FE  =  3 / 2

Now, because the ratio of the lengths of the altitudes is equal to the scale factor, we can write the following equation.

DB / DG  =  3 / 2

Substitute 6 for DB and and solve for DG.

6 / DG  =  3 / 2

By reciprocal property of proportion,

DG / 6  =  2 / 3

Multiply each side by 6.

⋅ (DG / 6)  =  (2 / 3) ⋅ 6

Simplify.

DG  =  4

So, the length of the altitude DG is 4 units. Apart from the stuff given aboveif you need any other stuff in math, please use our google custom search here.

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