Warm up

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# Warm up - PowerPoint PPT Presentation

Warm up. Let’s grade your homework. Congruence vs. Similarity. Let’s practice our new knowledge of similarity shortcuts. Determine whether the triangles are similar. If so, explain why then write a similarity statement and name the postulate or theorem you used. If not, explain.

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Presentation Transcript

### Warm up

Let’s practice our new knowledge of similarity shortcuts.

• Determine whether the triangles are similar.
• If so, explain why then write a similarity statement and name the postulate or theorem you used.
• If not, explain.

Yes, they are similar because

LM || OP (given) which creates congruent corresponding angles:

<L and <O are congruent as are

<M and <P.

Therefore: LMN ~OPN

AA~

Yes, they are similar because

AB || CD (given) which creates congruent alternate interior angles:

<A and <D are congruent as are

<B and <C.

Therefore: ABE ~DCE

AA~

Let’s practice some more.

Not similar.

There is no way of knowing if the corresponding angles are congruent, or if the corresponding sides are proportional. Not enough information is given for us to make a certain determination.

Yes, MNL~QPO

The sides are all in the same proportion, having the scale factor of 2.

SSS~

Next… Similarity in right triangles

• One piece of colored paper
• Straight edge
• Scissors

Using your compass and straightedge, create a rectangle.

Draw a diagonal

You have created two right triangles =)

In one triangle, draw the altitude from the right angle to the hypotenuse

Number the angles as shown

Cut out the three triangles.

How can you match the angles of the triangles to show that all three triangles are similar?

Explain how you know the matching angles are congruent.

7

6

5

1

8

9

4

2

3

Essential Understanding:

When you draw the altitude to the hypotenuse of a right triangle, you form three pairs of similar right triangles.

What similarity statement can you write relating the three triangles in the diagram?

X

W

XYZ ~ YWZ ~ XWY

Z

Y

a = x

xb

Geometric Mean

A proportion in which the means are equal.

Example

What is the geometric mean of 6 and 15?

6 = x

x15

x2 = 90

x = √90

9 ▪ 10

3 ▪ 3 ▪ 2 ▪ 5

x = 3 √10

What is the geometric mean of 3 and 16?

What is the geometric mean of 4 and 10?

3 = x

x16

x2 = 48

x = √48

6 ▪ 8

2 ▪ 3 ▪ 2 ▪ 2 ▪ 2

x = 4 √3

4 = x

x10

x2 = 40

x = √40

4 ▪ 10

2 ▪ 2 ▪ 2 ▪ 5

x = 2 √10

Solve for x and y…. (Pull the triangles apart)

X

y = 3

9y

3

12 = x

x 9

W

y = 3 √3

x = 6√3

9

y

Y

X

Z

x

Y

12

Z

x

W

X

y

3

9

y

W

Z

x

Y

Y