1. 4.4 (M1) Prove Triangles Congruent by SAS & HL

2. 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.

3. Is there enough given information to prove the triangles congruent
Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem. 1.
ABE, CBD
ANSWER
SAS Post.

4. 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.

5. EXAMPLE 1
Use the SAS Congruence Postulate
Write a proof.
GIVEN
BC DA, BC AD
PROVE
ABC CDA
STATEMENTS
REASONS
Given
BC DA S
Given
BC AD
BCA DAC
Alternate Interior Angles Theorem A
AC CA
Reflexive Property of Congruence S
ABC CDA
5. SAS

6. Complete in your notebooks
3-11, 20, 21, 35

7. 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.

8. Tell whether the pair of triangles is congruent or not and why.
ANSWER
Yes; HL Thm.

9. Is there enough given information to prove the triangles congruent
Is there enough given information to prove the triangles congruent? If there is, state the postulate or theorem. 2.
FGH, HJK
ANSWER
HL Thm.

10. EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
Write a proof.
GIVEN
WY XZ, WZ ZY, XY ZY
PROVE
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.

11. EXAMPLE 3
Use the Hypotenuse-Leg Congruence Theorem
STATEMENTS
REASONS
WY XZ
Given
WZ ZY, XY ZY
Given
Definition of lines
Z and Y are right angles
Definition of a right triangle
WYZ and XZY are right triangles. L
ZY YZ
Reflexive Property of Congruence
WYZ XZY
HL Congruence Theorem

12. Extra Practice Complete in your notebooks.
Page ,22, 31, 32, 34