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# BELL WORK 11/29 5 minutes - PowerPoint PPT Presentation

BELL WORK 11/29 5 minutes. Pay Day Planner &amp; ID Pick up 8.3 WS Do BELL WORK on 8.3 WS. BELL WORK 11/29 5 minutes. Enlargement. Main Concept: Manaâ€™o Nui. Similar Triangles. Skills &amp; Content: Kumuhana Haâ€™awina. Intent: Manaâ€™o Hoâ€™okÅ. Unit Summary. Ratios Proportions Cross Products

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Presentation Transcript
BELL WORK 11/295 minutes
• Pay Day
• Planner & ID
• Pick up 8.3 WS
• Do BELL WORK on 8.3 WS

Main Concept:

Mana’o Nui

Similar Triangles

Skills & Content:

Kumuhana Ha’awina

Intent:

Mana’o Ho’okō

### Unit Summary

• Ratios
• Proportions
• Cross Products
• Geometric Mean
• Similarity
• Scale Factor
• Dilation: Enlargement & Reduction
• Similar Triangles
• AA, SSS, SAS Similarity
• Proportionality Conjectures
• Ratios
• Proportions
• Cross Products
• Geometric Mean
• Similarity
• Scale Factor
• Dilation: Enlargement & Reduction
• Similar Triangles
• AA, SSS, SAS Similarity
• Proportionality Conjectures

Benchmark MA.G.5.2: Use corresponding parts to prove that triangles are similar. Use similar triangles to solve real-world problems.

Unit 8: Similar Triangles & Indirect Measurements

Intent:

• Prove that triangles are similar
• Skills:
• AA, SSS, SAS Similarity
• Proportionality Conjectures

### 8.3 Similar Triangles

Unit 8: Similar Triangles & Indirect Measurements

What is the Angle-Angle Similarity (AA~) Conjecture? (C-22)

Need: 2 congruent angles

Then: Triangles are similar

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

Need: All sides proportional

Then: Triangles are similar

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

Need: 2 sides in proportion

Angle in between 

Then: Triangles are similar

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

Similarity Summary

Unit 8: Similar Triangles & Indirect Measurements

Example 1

A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is five feet four inches tall casts a shadow that is 40 inches long. How tall is the flagpole to the nearest foot?

80

S:

The flagpole is ___ feet tall.

E:

Woman: 5 ft 4 in tall

E:

Unit 8: Similar Triangles & Indirect Measurements

Example 2

1. Given

Reasons

Statements

2. Definition of Congruent Angles

3. Reflexive Property

4. AA Similarity Conjecture

Unit 8: Similar Triangles & Indirect Measurements

Example 3

Unit 8: Similar Triangles & Indirect Measurements

Example 4

1. Given

Reasons

Statements

• Ratio of Corresponding Side Lengths

3. Transitive Property

4. SSS Similarity Conjecture

5. Definition of Similar Polygons

Unit 8: Similar Triangles & Indirect Measurements

Example 5

1. Given

Reasons

Statements

2. Ratio of CorrespondingSide Lengths

3. Transitive Property

4. Vertical Angles Conjecture

5. SAS Similarity Conjecture

6. Corresponding Lengths inSimilar Polygons

Unit 8: Similar Triangles & Indirect Measurements

What is the Triangle Proportionality Conjecture? (C-25)

Lines parallel to the base of a triangle divide the sides proportionally.

IFF

Unit 8: Similar Triangles & Indirect Measurements

Parallel lines divide transversals proportionally.

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

The angle bisector divides the opposite side proportional to the other two sides.

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

Example 6

Unit 8: Similar Triangles & Indirect Measurements

S:

Thus, the shelf is not parallel to the floor.

Example 7

E:

AB = 33 cm

BC = 27 cm

CD = 44 cm

DE = 25 cm

E:

Unit 8: Similar Triangles & Indirect Measurements

S:

The distance between Main Street and South Main Street is _____ yards.

Example 8

360

E:

GF = 120 yd

DE = 150 yd

CD = 300 yd

Angles 1, 2, and 3 are congruent.

E:

Corresponding angles are congruent,

hence the streets are parallel.

Unit 8: Similar Triangles & Indirect Measurements

Example 9

15 – x

Unit 8: Similar Triangles & Indirect Measurements

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