Similar Triangles and Circle’s Proofs Packet #4

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Methods of Proving Triangles Similar – Day 1

SWBAT: Use several methods to prove that triangles are similar.

Warm – Up

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3

Example 2:

Example 3:

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You try it!

Explain how you know the following triangles are similar!

1.

2.

3.

5

Challenge

SUMMARY

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SUMMARY Continued

Exit Ticket

Vertical Angles are Congruent.

Opposite sides ∥ in a

∥ 𝑨𝑰𝑨 ≅

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Homework

1.

2.

3. Given: DEGH

Prove: ∆FGH ∆FDE

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4.

5.

6.

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Methods of Proving Triangles Similar – Day 2

SWBAT: Students will be able to prove

Proportions involving Line Segments

Products involving Line Segments

Warm – Up

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Given: ABCD is a parallelogram Prove: KM x LB = LM x KD

To develop a plan reason backwards from the “prove” by answering three questions

1. What proportion produces the product KM x LB = LM x KD?

2. Which pair of triangles must be proven to be similar?

3. How can I prove ∆KMD is similar to ∆LMB?

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B. Given:

Prove:

C.

CE

BE

ED

AE

CDAB

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D.

CHALLENGE

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SUMMARY

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Day 2 – HW

1.

2.

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3.

4.

𝐴𝐵

𝐵𝐺= 𝐷𝐶

𝐶𝐹

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5.

6. Two triangles are similar. The sides of the first triangle are 7, 9, and 11. The smallest side

of the second triangle is 21. Find the perimeter of the second triangle.

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Review of Proving Triangles Similar – Day 3

1.

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2.

3.

Prove:

QWxSZZWxTS

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4. ABC is isosceles with AB AC , altitudes CE and AD are drawn.

Prove that AC EB CB DC

5.

CB

A

E

D

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Circle Proofs – Day 4

Warm – Up

1.

Find x and y.

20.

3.

4.

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Theorem #1 – All Radii of a circle are congruent

Example 1:

You Try!

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Theorem #2 – If Radius Chord, then it bisects the chord

or

If Radius bisects chord, then the radius is Chord

You Try It!

Given: ̅̅ ̅̅ ̅̅ ̅̅

Prove: ⃗⃗⃗⃗ ⃗

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Challenge

SUMMARY

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Day 4 - Homework

1.

2.

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3.

4. Find x.

5.

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Circles Proofs – Day 5

Warm – Up

1.

2.

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Theorem #3 –

central angles arcs or arcs central angles

Theorem # 4 –

central angles chords or chords central angles

Theorem #5 –

chords arcs or arcs chords

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You Try it!

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SUMMARY

Exit Ticket

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Homework – Day 5

1. Fdfdf

2.

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3.

Regents Questions

4. Solve for x.

5.

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Circle Proofs – Day 6

Warm – Up

1.

2. Find x and then find the perimeter.

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Theorem #6 – A Tangent is radius (or diameter) at point of point of contact.

Theorem #7 – An inscribed in a semi right

Example 1:

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Theorem #8 – 2 Tangents drawn from the same external point 2 segs . (Two-Tangent Theorem)

Example 2:

Prove: ∡AOB ≅∡COB

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More Angle Relationships

Theorem #9 – Two inscribed or tangent-chord angles that intercept the

same or congruent arcs ≅

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Theorem #10 - ∥ ≅

Example 3:

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5.

Challenge

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SUMMARY

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Homework – Day 6

1.

2.

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3.

4.

42

5.

6.