4.4 - Prove Triangles Congruent by SAS and HL
description
Transcript of 4.4 - Prove Triangles Congruent by SAS and HL
![Page 1: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/1.jpg)
4.4 - Prove Triangles Congruent by SAS and HL
![Page 2: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/2.jpg)
Included Angle:Angle in-between two congruent sides
![Page 3: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/3.jpg)
1. Use the diagram to name the included angle between the given pair of sides.
and GH HI
H
![Page 4: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/4.jpg)
1. Use the diagram to name the included angle between the given pair of sides.
HIG
and HI IG
![Page 5: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/5.jpg)
1. Use the diagram to name the included angle between the given pair of sides.
JGI
and JG IG
![Page 6: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/6.jpg)
Side-Angle-Side (SAS) Congruence Postulate
A B C D4cm 4cm
E F
CDAB
CFAE
CA
![Page 7: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/7.jpg)
If two sides and the _____________ angle of one triangle are __________ to two sides and the included angle of a second triangle, then the two triangles are ____________
included
congruent
congruent
![Page 8: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/8.jpg)
Right Triangles:
leg
leghypotenuse
![Page 9: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/9.jpg)
Hypotenuse-Leg (HL) Congruence Theorem:
If the _______________ and a ________ of a ___________ triangle are ____________ to the _____________ and ________ of a second _________ triangle, then the twotriangles are _________________.
hypotenuse legright congruent
hypotenuse legright
congruent
![Page 10: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/10.jpg)
![Page 11: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/11.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SSS
![Page 12: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/12.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SSS
![Page 13: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/13.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
![Page 14: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/14.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
No, AD ≠ CD
![Page 15: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/15.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
![Page 16: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/16.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, HL
![Page 17: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/17.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
No, Not a right triangle
![Page 18: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/18.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SSS
![Page 19: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/19.jpg)
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
![Page 20: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/20.jpg)
3. State the third congruence that must be given to prove ABC DEF.
GIVEN: B E, , ______ ______. Use the SAS Congruence Postulate.
EFBC BA ED
![Page 21: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/21.jpg)
3. State the third congruence that must be given to prove ABC DEF.
GIVEN: , ______ ______. Use the SSS Congruence Postulate.
EFBCDEAB , AC DF
![Page 22: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/22.jpg)
3. State the third congruence that must be given to prove ABC DEF.
GIVEN: A is a right angle and A D. Use the HL Congruence Theorem.
,DFAC
EFBC
![Page 23: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/23.jpg)
4. Given: Prove: ∆RGI ∆TGH
1. 1. given
2. 2. Def. of midpt
3. 3. Def. of midpt
4. 4.
5. 5.
Vertical angles
GIHG
RGI TGH
∆RGI ∆TGH
is the midpoint of and G RT HI
is the midpoint of and G RT HI
RG GT
SAS
![Page 24: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/24.jpg)
5. Given:
Prove: ∆ABD ∆CDB
CDAB
CDAB
Statements Reasons
CDAB Given
D
A
B
C
1. 1.
![Page 25: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/25.jpg)
D
A
B
C
![Page 26: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/26.jpg)
CDAB
CDAB
CDAB Given
CDAB
CDB ABD Alternate Interior Angles
Given
∆ABD ∆CDB SAS
DBDB Reflexive
D
A
B
C
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
Statements Reasons
5. Given:
Prove: ∆ABD ∆CDB
![Page 27: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/27.jpg)
6. Given:
Prove: ∆ACD ∆ACB
A
BCD
bisects AC DAB
DA BA
Given
Def. of Angle Bisector
Given
∆ACD ∆ACB SAS
AC AC Reflexive
1. 1.
2. 2.
3. 3.
4. 4.
5. 5.
Statements Reasons bisects AC DAB
DA BA
DAC BAC
![Page 28: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/28.jpg)
7. Given:
Prove: ∆ACD ∆ACB
AD ABAC BD
A
BCD
GivenGiven
Def. of perp. lines
Reflexive
ACD ACB All right angles are
1. 1.2. 2.
3. 3.
4. 4.
5. 5.
Statements ReasonsAD ABAC BD
∆ACD ∆ACB HL6. 6.
ACD and ACB are right angles
AC AC
![Page 29: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/29.jpg)
Ans: BC EF
HW ProblemSectio
nPage # Assignment Spiral ?
s
4.4 243 3-7odd, 9-11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all)
9-11
# 27
![Page 30: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader036.fdocuments.us/reader036/viewer/2022081511/56813c0f550346895da58505/html5/thumbnails/30.jpg)
HW ProblemSectio
nPage # Assignment Spiral ?
s
4.4 243 3-7odd, 9-11, 13, 14, 20, 21, 25, 27, 35, 37, 38 (draw a picture for all)
9-11
# 26