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Similar Triangles and Circle’s Proofs Packet #4
Similar Triangles and Circle’s Proofs Packet #4
1
Know how to draw conclusions from “Key” Vocabulary Words 1. Midpoint → 2 segments
2. Bisector → 2 segments
3. Median → Midpoint → 2 segments
4. Angle bisector → 2 angles
5. Perpendicular ( ) → right angles → all right angles are
6. Altitude → Perpendicular ( ) → right angles → all right angles are
7. Vertical Angles → angles are 8. → Alternating Interior Angles (A.I.A’s)
9. → Alternating Exterior Angles (A.E.A’s)
10. → Corresponding Angles (CA’s)
11. → Alternating Interior Angles (A.I.A’s)
12. → Same Side Interior Angles (SSIA’s) Supplementary
13. Linear pair supplementary
14.
15.
16.
17.
18.
19.
Circle Theorems
20. intercept the same arcs
21. intercept the congruent arcs
22. inscribed in a semi right
23. Tangent Radius (or Diameter) at point of contact
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Methods of Proving Triangles Similar – Day 1
SWBAT: Use several methods to prove that triangles are similar.
Warm – Up
2
Example 1:
Statements Reasons
1. 1. Given
2.
2.
3. 3.
4. 4.
5. 5.
3
Example 2:
Example 3:
4
More Angle Relationships
Theorem – intercept the same arcs
Theorem – intercept congruent arcs
5
Example 4:
Example 5:
6
Challenge
SUMMARY
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SUMMARY Continued
Exit Ticket
Vertical Angles are Congruent.
Opposite sides in a
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Homework
1.
2. Given: DEGH
Prove: ∆FGH ∆FDE
3.
9
4.
5.
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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
11
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?
Statements Reasons
1. 1. Given
2.
2.
3. 3.
4. 4.
5. 5. AA
6. 6.
7. KM x LB = LM x KD 7.
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B. Given:
Prove:
C.
CE
BE
ED
AE
CDAB
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D.
Theorem –
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Theorem – Tangent Radius (or Diameter) at point of contact
E.
Prove:
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CHALLENGE
SUMMARY
Exit Ticket
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Day 2 – HW
1.
2.
17
3.
4.
18
5.
6.
Prove: AD x AC = AB x AB
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Review of Proving Triangles Similar – Day 3
1.
2.
20
3.
4.
Prove:
QWxSZZWxTS
21
5.
6.
Prove:
22
7.
Prove: CD x BF = CA x BA
8.
