Lesson: Grade 8 Math Proving triangle congruency

1. Proving Triangle
Congruency

2. How to determine the Congruency
between two Triangles?
What are the Parts of the Triangles that should
be corresponding ?

3. Look at the figure

4. The SSS Postulate
If three sides of one triangle
are congruent to the
corresponding sides of the
other triangle, then two
triangles are congruent under
SSS postulate

5. Examples

6. Look at the figure

7. The SAS Postulate
If two sides and an included
angle of one triangle are
congruent to the corresponding
two sides and an included angle
of the other triangle, then two
triangles are congruent under
SAS postulate

8. INCLUDED ANGLE
The angle formed by two given
sides
In Triangle ABC and DEF, <B and
<D are included angles.

9. Examples

10. Look at the figure

11. The ASA Postulate
If two angles and an included
side of one triangle are
congruent to the corresponding
two angles and an included side
of the other triangle, then two
triangles are congruent under
ASA postulate

12. INCLUDED SIDE
The side common between two
angles
In Triangle ABB’ and CBB’, AB
and BC are included sides

13. Examples

15. The L-L Theorem (The Leg-Leg Theorem)
If two legs of one right triangle
are congruent to the
corresponding legs of another
right triangle, then the two
triangles are congruent

16. Examples

17. The L-AA Theorem (Leg - Acute Angle Theorem)
If a leg and an acute angle of
one right triangle are congruent
to the corresponding leg and an
acute angle of another, then
the two triangles are congruent

18. The H-AA Theorem (The Hypotenuse- Acute Angle Theorem)
If the hypotenuse and an acute
angle of one right triangle are
congruent to the corresponding
hypotenuse and an acute angle
of another, then the two
triangles are congruent

19. The H-L Theorem (The Hypotenuse-leg Theorem)
If the hypotenuse and leg of
one right triangle are congruent
to the corresponding
hypotenuse and leg of another,
then the two triangles are
congruent