Similiar Triangles

Geometry

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Similar Triangles

Similar Triangles -- same shape, different size

• Angles Must Be Congruent (the same size)

• Sides Must Be Proportion (the ratios of corresponding sides will be equivalent fractions

Solve Ratios

• A proportion is a mathematical statement equating two ratios. Two ratios are said to be equal if, when written in fractional form, the fractions are equivalent fractions. You can compare and solve ratios using cross multiplications. If the cross products are equal, the ratios are equal.

Multiple Choice

Solve for g in the proportion

$$\frac{10}{h}=\frac{2}{10}$$  

• h=10

• h=2

• h=50

• h=100

Multiple Choice

Find the value of x

• 7

• 7.5

• 8

Multiple Choice

Solve for n

$$\frac{n}{4}=\frac{8}{7}$$  

• 5

• 32

• 4

• 32/7

Scale Factor

• A scale factor is the factor by which all the components of an object are multiplied in order to create a proportional enlargement or reduction.

Multiple Choice

Find the scale factor going from the small triangle to the larger triangle

• 3

• 1/3

• 2

• 5

Multiple Choice

Find the scale factor from triangle PQR to triangle DEF

• 1.5

• 2/3

• .6

• 2

Proving Triangle Similar

Finding the THREE ways to prove triangles similar

SSS~

Side Side Side Similarity

SAS~

Side Angle Side Similarity

AA ~

Angle Angle Similarity

Could be any kind SAS SSS or AA

Multiple Choice

State the postulate that proves these triangles are similar.

• SSS
• AA
• SAS
• Not similar

Multiple Choice

State the postulate that proves these triangles are similar.

• SSS
• AA
• SAS
• Not similar

Multiple Choice

Are the triangles similar?

• Yes

• No

Multiple Choice

The triangles are similar by...

• SAS
• AA
• ASA
• SSS

Multiple Choice

Determine if the triangles are similar, and if so, by which theorem.

• AA

• SSS

• SAS

• Not Similar

Multiple Choice

Determine if the triangles are similar, and if so, by which theorem.

• AA

• SSS

• SAS

• Not Similar

Multiple Choice

Which triangles are similar to triangle A?

• B

• C

• Both

• None

Multiple Choice

Determine if the triangles are similar, and if so, by which theorem.

• AA

• SSS

• SAS

• Not Similar

Multiple Choice

Determine if the triangles are similar, and if so, by which theorem.

• AA

• SSS

• SAS

• Not Similar

Multiple Choice

Which triangles are similar to triangle A?

• B

• C

• Both

• None

Multiple Select

Determine if the triangles are similar, and if so, by which theorem.

• AA

• SSS

• SAS

• Not Similar

Multiple Choice

Determine if the triangles are similar, and if so, by which theorem.

• AA

• SSS

• SAS

• Not Similar

Similar right triangles

Multiple Choice

What is the ratio of  $$\overline{\frac{AB}{\overline{BC}}}$$ ? 

• $$\frac{4}{3}$$  

• $$\frac{3}{4}$$  

• $$\frac{3}{5}$$  

• $$\frac{5}{3}$$  

Multiple Choice

What is the ratio of  $$\overline{\frac{AB}{\overline{BC}}}$$ ? 

• $$\frac{4}{3}$$  

• $$\frac{3}{4}$$  

• $$\frac{3}{5}$$  

• $$\frac{5}{3}$$  

Multiple Choice

What is the ratio of $$\overline{\frac{EF}{\overline{DE}}}$$  ?

• $$\frac{3}{4}$$  

• $$\frac{4}{3}$$  

• $$\frac{3}{5}$$  

• $$\frac{5}{4}$$  

Multiple Choice

What is the value of x? round to the nearest tenth

• 31.2

• 39.5

• 40

• 18

Multiple Choice

Find the missing side

• 24

• 36

• 12

• 15

Multiple Choice

Find the missing side

• 1/3

• 3

• 1/2

• 2

Multiple Choice

Lance the alien is 5 feet tall. His shadow is 8 feet long. At the same time of day, a tree’s shadow is 32 feet long. What is the height of the tree?

• 20 feet

• 24 feet

• 29 feet

• 51 feet

Similar Triangles

After we practiced with similar polygons, we used our knowledge of proportions to use the Triangle Proportionality Theorem.

Example

Similar Triangles

Then, we used our knowledge of scale factors to utilize the Converse of the Triangle Proportionality Theorem.

Example 2

Multiple Choice

Find the value of x

• 7

• 7.5

• 8

Multiple Choice

Find the value of x

• 6

• 16

• 26

Multiple Choice

Determine whether

$$PS\ \parallel\ QR$$  

• Parallel

• Not Parallel

Multiple Choice

Determine whether

$$PS\ \parallel\ QR$$  

• Parallel

• Not Parallel

Multiple Choice

Determine whether

$$PS\ \parallel\ QR$$  

• Parallel

• Not Parallel

Multiple Choice

Determine whether

$$MN\ \parallel\ GH$$  

• Parallel

• Not Parallel