Transcript 4.4 PowerPoint

4.4 - Prove Triangles Congruent by SAS and HL
Included Angle:
Angle in-between two congruent sides
Side-Angle-Side (SAS) Congruence Postulate
E
A
4cm
AB  CD
A  C
AE  CF
F
B
C
4cm
D
included
If two sides and the _____________
angle of
congruent to two sides and
one triangle are __________
the included angle of a second triangle, then the
congruent
two triangles are ____________
Right Triangles:
hypotenuse
leg
leg
Hypotenuse-Leg (HL) Congruence Theorem:
hypotenuse
If the _______________
and a ________
of a
leg
right
congruent
___________
triangle are ____________
to
the _____________
of a second
hypotenuse and ________
leg
_________
right
triangle, then the two
triangles are _________________.
congruent
Decide whether the triangles are congruent.
Explain your reasoning.
Yes, SSS
Decide whether the triangles are congruent.
Explain your reasoning.
Yes, SSS
Decide whether the triangles are congruent.
Explain your reasoning.
Yes, SAS
Decide whether the triangles are congruent.
Explain your reasoning.
No, AD ≠ CD
Decide whether the triangles are congruent.
Explain your reasoning.
Yes, SAS
Decide whether the triangles are congruent.
Explain your reasoning.
Yes, HL
Decide whether the triangles are congruent.
Explain your reasoning.
No, Not a right
triangle
Decide whether the triangles are congruent.
Explain your reasoning.
Yes, SSS
2. State the third congruence that must be given to
prove ABC  DEF.
BA  ______.
ED
GIVEN: B  E, BC  EF , ______
Use the SAS Congruence Postulate.
2. State the third congruence that must be given to
prove ABC  DEF.
DF
AC  ______.
GIVEN: AB  DE , BC  EF , ______
Use the SSS Congruence Postulate.
2. State the third congruence that must be given to
prove ABC  DEF.
GIVEN: AC  DF , A is a right angle and A  D.
Use the HL Congruence Theorem.
BC  EF
A
Given:
AB CD
AB  CD
Prove:
∆ABD  ∆CDB
Statements
AB CD
B
D
C
Reasons
Given
A
B
D
C
Given:
Prove:
A
AB CD
AB  CD
∆ABD  ∆CDB
B
D
C
Statements
Reasons
AB CD
Given
CDB  ABD
Alternate Interior Angles
AB  CD
Given
DB  DB
Reflexive
∆ABD  ∆CDB
SAS
Given: RI TH
G is the midpoint of HI
RGI is a right angle
Prove: ∆RGI  ∆TGH
1.
2.
3.
4.
5.
6.
RI  TH
1.
G is the midpoint of HI 2.
3.
HG  GI
RGI is a right angle 4.
TGH is a right angle 5.
RGI & TGH are right 6.
given
given
Def. of midpt
given
Vertical angles
Def. of right triangles
triangles
7. ∆RGI  ∆TGH
7. HL