Step by step
The question
Question: which rule shows that triangles ABC and DEF are congruent?
Angle B = angle E = 90°.
AC = DF = 10.
AB = DE = 6.
1 Match the parts
Congruent means the same shape and the same size.
One fits exactly on top of the other.
The order of the letters shows which corners match: A with D, B with E, C with F.
DEF is turned over.
That does not matter.
Angle B and angle E are both 90°: a pair of equal angles.
A for angle.
AC and DF are both 10: a pair of equal sides.
S for side.
AB and DE are both 6: a pair of equal sides.
S for side.
2 Find the rule
Angle B is 90°: a right angle.
AC is across from it: the hypotenuse.
Right angle, hypotenuse, side: R H S.
Why?
Pythagoras: BC² is the hypotenuse squared take away the other side squared: 64.
So BC is 8.
EF is the same, 8.
All three sides match, like S S S.
Careful!
S S A is not a rule.
But with a right angle and the hypotenuse, it is: R H S.
Pythagoras fixes the third side, so all three sides match.
There is only one way to draw it.
So R H S shows the triangles are congruent.
It is also called H L: hypotenuse, leg.
Let's look back.
First: match the parts.
Last: find the rule.