SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
X
M is the midpoint of 𝑻𝑲
s𝐞𝐠 𝒃𝒊𝒔𝒆𝒄𝒕𝒐𝒓 → 𝒎𝒊𝒅𝒑𝒕
𝑺𝟏
𝑇𝑀  𝐾𝑀
𝒎𝒊𝒅𝒑𝒕 → 2 ≅ 𝒔𝒆𝒈𝒔
  right ∡s
𝑨𝟏
∡PMT and ∡PMK are rt ∡s
∡PMT  ∡PMK
𝑺𝟏
𝑃𝑀  𝑃𝑀
∆PMT  ∆PMK
𝑺𝟐 𝑨𝟐
∡TPM  ∡KPM, 𝑇𝑃  𝐾𝑃
All right angles are ≅
Reflexive Property
SAS (3,5,6)
CPCTC (7)
SWBAT: Use Theorems for Right Angles
X
𝑺𝟐 𝑨𝟐
7. ∆PMT  ∆PMK
7. SAS (3,5,6)
8. ∡TPM  ∡KPM,
8. CPCTC (7)
𝑇𝑃  𝐾𝑃
9. Reflexive Property
9. 𝑃𝑆  𝑃𝑆
10. ∆PTS  ∆PKS 10. SAS (8,8,9)
11. ∡PTS  ∡PKS 11. CPCTC (10)
𝑺𝟐
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
X
X
S, S
S
𝐴𝐵  𝐴𝐶, 𝐵𝐷  𝐶𝐷
𝐴𝐷  𝐴𝐷
Reflexive Property
∆ABD  ∆ACD
SSS (1,1,2)
∡ADB  ∡ADC
∡ADB is suppl. to ∡ADC
∡ADB and ∡ADC are rt ∡’s
𝐴𝐷 ⊥ 𝐶𝐵
CPCTC
Linear Pair Thm
∡s  & suppl.  rt ∡s
rt ∡s  ⊥
⊥  Altitude
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
𝑺𝟏
𝑺𝟏
𝑨𝟏
𝑋𝑌  𝑊𝑌
Draw 𝑂𝑋 and 𝑂𝑊
2 points determine a line
𝑂𝑋  𝑂𝑊
All radii of a ⊙ 𝑎𝑟𝑒 ≅
𝑺𝟐
∡OXZ  ∡OWZ 𝑨𝟐
∡OXY  ∡OWY
∆OXY  ∆OWY
𝐴𝟐
∡XOY  ∡WOY
Addition Post. (1, 5)
SAS (2,6,4)
CPCTC (7)
SWBAT: Use Theorems for Right Angles
9. ∆OXZ  ∆OWZ 9. ASA (5,4,8)
10. ∡OZX  ∡OZW 10. CPCTC (9)
𝑊𝑍  𝑋𝑍
11. Z is the midpt of 𝑾𝑿 11. 2  𝐬𝐞𝐠𝐬 → 𝒎𝒊𝒅𝒑𝒕
12. 𝑶𝒁 𝒃𝒊𝒔𝒆𝒄𝒕𝒔 𝑾𝑿
12. 𝒎𝒊𝒅𝒑𝒕 → 𝒔𝒆𝒈 𝒃𝒊𝒔𝒆𝒄𝒕𝒐𝒓
13. ∡ OZX is suppl. to ∡OZW 13. Linear Pair Thm
14. ∡ OZX and ∡OZW are rt ∡’s
14. ∡s  & suppl.  rt ∡s
15. 𝑂𝑌 ⊥ 𝑋𝑊
16. 𝑂𝑌 ⊥ bis. 𝑋𝑊
15. rt ∡s  ⊥
16. def. of ⊥ bis. (15, 12)
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
X
L
H
𝑇𝑊  𝑈𝑊 𝑺𝟐
R
∡TVW and ∡UXW are rt ∡’s
𝒎𝒊𝒅𝒑𝒕 → 2 ≅ 𝒔𝒆𝒈𝒔
⊥  rt ∡’s
RHL (3,2,1)
∡T  ∡U
CPCTC (4)
∆TVW  ∆UXW
𝑺𝟐
𝑇𝑆  𝑈𝑆
𝑺𝟐
𝑆𝑊  𝑆𝑊
∆TSW  ∆USW
Reflexive Property
SSS (2,6,7)
SWBAT: Use Theorems for Right Angles
X
8. ∆TSW  ∆USW
9. ∡TWS  ∡UWS
8. SSS (2,6,7)
9. CPCTC (8)
10. ∡ TWS is suppl. to ∡UWS 10. Linear Pair Thm
11. ∡ TWS and ∡UWS are rt ∡’s
11. ∡s  & suppl.  rt ∡s
12. 𝑆𝑊 ⊥ 𝑇𝑈
12. rt ∡s  ⊥
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles
X
D is the midpoint of 𝑩𝑪
s𝐞𝐠 𝒃𝒊𝒔𝒆𝒄𝒕𝒐𝒓 → 𝒎𝒊𝒅𝒑𝒕
𝐵𝐷  𝐶𝐷
𝒎𝒊𝒅𝒑𝒕 → 2 ≅ 𝒔𝒆𝒈𝒔
  right ∡s
𝑨𝟏
∡BDA and ∡CDA are rt ∡s
∡BDA  ∡CDA
𝑺𝟏
𝐴𝐷  𝐴𝐷 , 𝐴𝐹  𝐴𝐹 𝑺𝟐
𝑺𝟏
∆BAD  ∆CAD
𝑨𝟐 𝑺𝟐
∡BAD  ∡CAD, 𝐵𝐴  𝐶𝐴
All right angles are ≅
Reflexive Property
SAS (3,5,6)
CPCTC (7)
SWBAT: Use Theorems for Right Angles
X
9. ∆ACF  ∆ABF
10. ∡1  ∡2
9. SAS (6,8,8)
10. CPCTC (9)
SWBAT: Use Theorems for Right Angles
SWBAT: Use Theorems for Right Angles