Similarity in Right Triangles

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Similarity in Right Triangles - PowerPoint PPT Presentation

Chapter 7.4. Similarity in Right Triangles. Right Triangles. Leg. Leg. Altitude. Hypotenuse. The altitude is the Geometric Mean of the Segments of the Hypotenuse. Leg. Leg. Altitude. Short segment. Long segment. Short seg. =. Alt. Use the formula:. Alt. Long seg. Leg. Leg.

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Similarity in Right Triangles

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Chapter 7.4

Similarity in Right Triangles

Right Triangles

Leg

Leg

Altitude

Hypotenuse

Leg

Leg

Altitude

Short segment

Long segment

Short seg

=

Alt

• Use the formula:

Alt

Long seg

Leg

Leg

Altitude

Short segment

Long segment

Short seg

• 2. Write the formula

=

Alt

• 1. Label the triangle
• Ex 1: Write the formula for the geometric mean

Alt

Long seg

Leg

Leg

b

a

Altitude

c

e

d

Short segment

Long segment

Short seg

c

d

=

Alt

• 3. Plug into the formula

c

e

• Ex 1: Write the formula for the geometric mean

Alt

Long seg

Leg

Leg

b

a

Altitude

c

e

d

Short segment

Long segment

Short seg

z

u

=

Alt

z

v

• Ex 2: Write the formula for the geometric mean

Alt

Long seg

Leg

y

Leg

x

Altitude

z

v

u

Short segment

Long segment

p

Short seg

n

=

=

Alt

• Ex 3: Write the formula for the geometric mean

n

q

Alt

Long seg

Leg

Leg

k

m

Altitude

n

q

p

Short segment

Long segment

4

Short seg

2

=

=

Alt

4

• Ex 4: Write the formula for the geometric mean

8

Alt

Long seg

Leg

Leg

k

m

Altitude

4

2

8

Short segment

Long segment

Short segment

d

• 1. Label the triangle

Leg

c

• Ex 5: Write the formula for the geometric mean

a

Hypotenuse

Altitude

Long segment

e

Leg

b

Short segment

d

• 2. Write the formula

Leg

c

• Ex 5: Write the formula for the geometric mean

a

Altitude

Long segment

e

Leg

b

Short seg

=

Alt

Alt

Long seg

Short segment

d

• 3. Plug into the formula

Leg

c

• Ex 5: Write the formula for the geometric mean

a

Altitude

Long segment

e

Leg

b

Short seg

c

d

=

Alt

c

e

Alt

Long seg

The leg is the Geometric Mean between the whole Hypotenuse and the Segment of the Hypotenuse adjacent to the leg

Leg

Leg

Altitude

Hypotenuse

Whole Hyp

=

Leg

• Use the formula:

Leg

Leg

Leg

Altitude

Short segment

Long segment

Whole Hyp

• 2. Write the formula

=

Leg

• 1. Label the triangle
• Ex 6: Write the formula for the geometric mean using leg a.

Leg

Leg

Leg

b

a

c

e

d

What is the whole hyp?

What is the length of the whole hypotenuse?

4

9

12

y

5

2

3

x

2 + 4 = 6

3 + 12 = 15

5 + 9 = 14

x + y = x + y

Whole Hyp

a

d+e

=

Leg

• 3. Plug into the formula

a

• Ex 6: Write the formula for the geometric mean using leg a.

d

Leg

Leg

Leg

b

a

Altitude

c

e

d

Whole Hyp

x

u+v

=

Leg

• 3. Plug into the formula

x

u

• Ex 7: Write the formula for the geometric mean using leg x.

Leg

Leg

Leg

y

x

Altitude

z

v

u

p+q

Whole Hyp

m

=

Leg

• 3. Plug into the formula

m

p

• Ex 8: Write the formula for the geometric mean using leg m.

Leg

Leg

Leg

k

m

Altitude

n

q

p

Whole Hyp

2+6

4

8

=

Leg

• 3. Plug into the formula

4

2

• Ex 9: Write the formula for the geometric mean using leg x.

Leg

Leg

Leg

4

Altitude

2

6

d

• 1. Label the triangle

Leg

c

• Ex 10: Write the formula for the geometric mean for side a.

a

Hypotenuse

e

Leg

b

d

• 2. Write the formula

Leg

c

• Ex 10: Write the formula for the geometric mean for side a.

a

e

Leg

b

Whole Hyp

=

Side

Side

d

• 3. Plug into the formula

Leg

c

• Ex 10: Write the formula for the geometric mean for side a.

a

e

Leg

b

Whole Hyp

a

d+e

=

Side

a

d

Side

Whole Hyp

b

d+e

=

Leg

• 3. Plug into the formula
• Ex 11: Write the formula for the geometric mean using leg b.

b

e

Leg

Leg

Leg

b

a

c

e

d

5+4

Whole Hyp

9

6

=

Leg

• 3. Plug into the formula

4

• Ex 11: Write the formula for the geometric mean using leg b.

6

Leg

Leg

Leg

6

a

c

4

5

When to use which formula

When you’re given the Altitude

Short seg

=

Alt

Alt

Long seg

Or

When you need to find the Altitude

When to use which formula

When you’re given a Leg

Whole Hyp

Leg

=

Leg

Or

When you need to find a Leg

Short segment

d

Leg

• 3. Plug into the formula

c

• Ex 10: Write the formula for the geometric mean

a

Altitude

Long segment

e

Leg

b

Short seg

=

Alt

Alt

Long seg