Download Similar Triangles and Circle`s Proofs Packet #4

Similar Triangles and Circle’s Proofs Packet #4
Methods of Proving Triangles Similar – Day 1
SWBAT: Use several methods to prove that triangles are similar.
Warm – Up
1
2
Example 2:
Example 3:
3
You try it!
Explain how you know the following triangles are similar!
1.
2.
3.
4
Challenge
SUMMARY
5
SUMMARY Continued
Vertical Angles are Congruent.
Opposite sides ∥ in a
∥
𝑨𝑰𝑨 ≅
Exit Ticket
6
Homework
1.
2.
3. Given: GH DE
Prove: ∆FGH  ∆FDE
7
4.
5.
6.
8
Methods of Proving Triangles Similar – Day 2
SWBAT: Students will be able to prove
 Proportions involving Line Segments
 Products involving Line Segments
Warm – Up
9
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?
10
B.
Given:
Prove:
AB CD
AE BE

ED CE
C.
11
D.
CHALLENGE
12
SUMMARY
13
Day 2 – HW
1.
2.
14
3.
𝐴𝐵
𝐷𝐶
=
𝐵𝐺
𝐶𝐹
4.
15
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.
16
Review of Proving Triangles Similar – Day 3
1.
17
2.
3.
Prove:
TS x ZW  SZ x QW
18
A
4. ABC is isosceles with AB  AC , altitudes CE and AD are drawn.
Prove that  AC  EB    CB  DC 
E
B
D
C
5.
19
Circle Proofs – Day 4
Warm – Up
1.
Find x and y.
20.
3.
4.
20
Theorem #1 – All Radii of a circle are congruent
Example 1:
You Try!
21
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: ⃗⃗⃗⃗⃗
̅̅̅̅
̅̅̅̅
22
Challenge
SUMMARY
23
Day 4 - Homework
1.
2.
24
3.
4. Find x.
5.
25
Circles Proofs – Day 5
Warm – Up
1.
2.
26
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
27
28
You Try it!
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SUMMARY
Exit Ticket
30
Homework – Day 5
1. Fdfdf
2.
31
3.
Regents Questions
4. Solve for x.
5.
32
Circle Proofs – Day 6
Warm – Up
1.
2.
Find x and then find the perimeter.
33
Theorem #6 – A Tangent is
Theorem #7 – An
radius (or diameter) at point of point of contact.
inscribed in a semi
 right
Example 1:
34
Theorem #8 – 2 Tangents drawn from the same external point  2  segs .
(Two-Tangent Theorem)
Example 2:
Prove: ∡AOB ≅∡COB
35
More Angle Relationships
Theorem #9 – Two inscribed
or tangent-chord angles that intercept the
same or congruent arcs 
≅
36
Theorem #10 - ∥
 ≅
Example 3:
37
5.
Challenge
38
SUMMARY
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Homework – Day 6
1.
2.
40
3.
4.
41
5.
6.
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