4.4 - prove triangles congruent by sas and hl. included angle: angle in-between two congruent sides
TRANSCRIPT
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
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
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
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