4.4 - prove triangles congruent by sas and hl
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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
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.
and GH HI
H
1. Use the diagram to name the included angle between the given pair of sides.
HIG
and HI IG
1. Use the diagram to name the included angle between the given pair of sides.
JGI
and JG IG
Side-Angle-Side (SAS) Congruence Postulate
A B C D4cm 4cm
E F
CDAB
CFAE
CA
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
Right Triangles:
leg
leghypotenuse
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
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SSS
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SSS
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
2. Decide whether the triangles are congruent. Explain your reasoning.
No, AD ≠ CD
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, HL
2. Decide whether the triangles are congruent. Explain your reasoning.
No, Not a right triangle
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SSS
2. Decide whether the triangles are congruent. Explain your reasoning.
Yes, SAS
3. State the third congruence that must be given to prove ABC DEF.
GIVEN: B E, , ______ ______. Use the SAS Congruence Postulate.
EFBC BA ED
3. State the third congruence that must be given to prove ABC DEF.
GIVEN: , ______ ______. Use the SSS Congruence Postulate.
EFBCDEAB , AC DF
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
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
5. Given:
Prove: ∆ABD ∆CDB
CDAB
CDAB
Statements Reasons
CDAB Given
D
A
B
C
1. 1.
D
A
B
C
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
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
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
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
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