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PLANE GEOMETRY
HONORS
Proving Triangles congruent
Congurent= The Same
Evan Nieslawski
TABLE OF CONTENTS
Proving Triangles by:
 Side, side, side (SSS)
 Side, angle, side (SAS)
 Angle, side, angle (ASA)
 Hypotenuse leg (HL)
 Angle, Angle, Side (AAS)
SIDE, SIDE, SIDE (SSS)
Proving Triangles Congruent by SSS:
 Three sides of one triangle must be congruent to three corresponding
sides of another triangle.
 Mark sides congruent with tick marks as shown
SIDE, ANGLE, SIDE (SAS)
Proving Triangles Congruent by SAS:
 Two sides and the included angle of one triangle must be congruent to
two sides and the included angle of another triangle
 Mark sides and angles congruent with tick marks as shown
ANGLE, SIDE, ANGLE (ASA)
Proving Triangles Congruent by ASA:
 Two corresponding angles of the two triangles and the included side of
the triangles must congruent
 Mark sides and angles congruent with tick marks as shown
HYPOTENUSE LEG (HL)
Proving Triangles Congruent by HL:
 Triangles MUST be right triangles!!!
 Two right triangles that have a congruent hypotenuse and a
corresponding, congruent leg are congruent triangles
 Mark sides and angles congruent with tick marks as shown
ANGLE, ANGLE, SIDE (AAS)
Proving Triangles Congruent by AAS
 Two corresponding angles and the non-included side one triangle are
congruent to two corresponding angles and the non-included angle of
another triangle
 Mark sides and angles congruent with tick marks as shown
THE END
I hope you learned a lot