Foundation and Higher · congruence

Four ways to prove
two triangles
are congruent.

…and the one that
never works

first, the word itself —

Congruent

same shape and same size

flipped or turned still counts

congruence test 1 of 4

SSSside, side, side

1. All three pairs of sides match.

2. Three fixed sides make only
one possible triangle.

✓ Write: congruent, SSS

congruence test 2 of 4

SASside, angle, side

1. Two pairs of sides match…

2. …and so does the angle
between them.

✓ Write: congruent, SAS

congruence test 3 of 4

ASAangle, side, angle

1. Two pairs of angles match…

2. …and so does a side in the
same position.

✓ Write: congruent, ASA

congruence test 4 of 4

RHSright angle, hypotenuse, side

1. Both triangles have a right angle.

2. The hypotenuse and one other
side match.

✓ Write: congruent, RHS

four tests that prove it —

SSS

three sides

SAS

two sides, the angle between

ASA

two angles, a matching side

RHS

right angle, hypotenuse, side

AAA proves nothing — same angles
only means similar.

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