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BELL WORK 11/29 5 minutes. Pay Day Planner & ID Pick up 8.3 WS Do BELL WORK on 8.3 WS. BELL WORK 11/29 5 minutes. Enlargement. Main Concept: Mana’o Nui. Similar Triangles. Skills & Content: Kumuhana Ha’awina. Intent: Mana’o Ho’okō. Unit Summary. Ratios Proportions Cross Products

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bell work 11 29 5 minutes
BELL WORK 11/295 minutes
  • Pay Day
  • Planner & ID
  • Pick up 8.3 WS
  • Do BELL WORK on 8.3 WS
unit summary

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

8 3 similar triangles

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
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

what is the side side side similarity sss conjecture c 23
What is the Side-Side-Side Similarity (SSS~) Conjecture? (C-23)

Need: All sides proportional

Then: Triangles are similar

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

what is the side angle side similarity sas conjecture c 24
What is the Side-Angle-Side Similarity (SAS~) Conjecture? (C-24)

Need: 2 sides in proportion

Angle in between 

Then: Triangles are similar

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

similarity summary
Similarity Summary

Unit 8: Similar Triangles & Indirect Measurements

example 1
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:

Flagpole shadow: 50 ft long

Woman: 5 ft 4 in tall

Woman shadow: 40 in long

E:

Unit 8: Similar Triangles & Indirect Measurements

slide10

Example 2

1. Given

Reasons

Statements

2. Definition of Congruent Angles

3. Reflexive Property

4. AA Similarity Conjecture

Unit 8: Similar Triangles & Indirect Measurements

slide11

Example 3

Unit 8: Similar Triangles & Indirect Measurements

slide12

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

slide13

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
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

what is the three parallel line proportionality conjecture c 26
What is the Three Parallel Line Proportionality Conjecture? (C-26)

Parallel lines divide transversals proportionally.

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

slide16

What is the Angle Bisector Proportionality Conjecture? (C-27)

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

IF

THEN

Unit 8: Similar Triangles & Indirect Measurements

example 6
Example 6

Unit 8: Similar Triangles & Indirect Measurements

example 7

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

example 8

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
Example 9

15 – x

Unit 8: Similar Triangles & Indirect Measurements

exit slip summary
Exit SlipSummary

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