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To prove congruent triangles using the special cases, we should have in the two triangles:
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (8), the two triangles ABC and AED are congruent by:
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (3) and referring to the remarks, ABD and CBD are congruent by :
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (4), the two triangles AOC and BOD are congruent by:
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (2), MNO is a right triangle at O. the side MN is the:
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (1), XYZ is :
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (8), the triangle ACD is:
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
In figure (6), the two triangles ABD and ACD can be proven congruent by:
S A S
hypotenuse
isosceles with main vertex A
right angles, equal hypotenuses and pair of equal sides or angles
A S A
R H S or S S S or S A S
S S S
an isosceles triangle with main vertex Y
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