4.4 - prove triangles congruent by sas and hl
DESCRIPTION
4.4 - Prove Triangles Congruent by SAS and HL. Included Angle:. Angle in-between two congruent sides. 1. Use the diagram to name the included angle between the given pair of sides. H. 1. Use the diagram to name the included angle between the given pair of sides. HIG. - PowerPoint PPT PresentationTRANSCRIPT
![Page 1: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/html5/thumbnails/2.jpg)
Included Angle:Angle in-between two congruent sides
![Page 3: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/html5/thumbnails/8.jpg)
Right Triangles:
leg
leghypotenuse
![Page 9: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/html5/thumbnails/10.jpg)
![Page 11: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/html5/thumbnails/25.jpg)
D
A
B
C
![Page 26: 4.4 - Prove Triangles Congruent by SAS and HL](https://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/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://reader035.vdocuments.mx/reader035/viewer/2022081516/56813b04550346895da3a5a2/html5/thumbnails/29.jpg)
HW Problem
# 26
4.4 243 1-7odd, 9-11, 13, 14, 20, 21, 25-27, 34, 35, 37, 38
Ans: AB DE