Download 4.9 (M1) Prove Triangles Congruent by SAS & HL

4.9 (M1) Prove Triangles
Congruent by SAS & HL
Vocabulary
In a right triangle, the sides adjacent to
the right angle are the legs.
 The side opposite the right angle is the
hypotenuse.
 Side-Angle-Side (SAS) Congruence
Postulate: If two sides and the included
angle of one triangle are congruent to two
sides and the included angle of another
triangle, the two triangles are congruent.


Hypotenuse-Leg (HL) Congruence
Theorem – If the hypotenuse and one
leg of a right triangle are congruent to the
hypotenuse and leg of another right
triangle, the triangles are congruent.
Tell whether the pair of triangles is congruent or not
and why.
ANSWER
Yes; HL
Thm.
Is there enough given information to prove the
triangles congruent? If there is, state the postulate or
theorem.
1.
ABE, CBD
ANSWER
SAS
Post.
Is there enough given information to prove the
triangles congruent? If there is, state the postulate or
theorem.
2.
FGH, HJK
ANSWER
HL
Thm.
State a third congruence that would allow you to
prove RST
XYZ by the SAS Congruence
postulate.
3. ST YZ, RS XY
ANSWER
S
Y.
EXAMPLE 1
Use the SAS Congruence Postulate
Write a proof.
GIVEN
BC
DA, BC AD
ABC
PROVE
CDA
STATEMENTS
S
REASONS
1.
BC
DA
1. Given
2.
BC
AD
2. Given
A 3.
S 4.
BCA
AC
ABC
DAC
CA
CDA
3. Alternate Interior
Angles Theorem
4. Reflexive Property of
Congruence
5. SAS
EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
Write a proof.
GIVEN
PROVE
WY
XZ, WZ ZY, XY ZY
WYZ
XZY
SOLUTION
Redraw the triangles so they are
side by side with corresponding
parts in the same position. Mark
the given information in the
diagram.
EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
STATEMENTS
1.
WY
4.
ZY
2. Given
3. Definition of
Z and Y are
lines
right angles
WYZ and XZY are 4. Definition of a right
triangle
right triangles.
L 5. ZY
6.
1. Given
XZ
2. WZ ZY, XY
3.
REASONS
WYZ
YZ
5. Reflexive Property of
Congruence
XZY
6. HL Congruence
Theorem