Step by step
The question
Question: which rule shows that triangles DEF and GHI are congruent?
Angle E = angle H = 90°.
DF = GI = 30.
DE = GH = 18.
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: D with G, E with H, F with I.
GHI is turned over.
That does not matter.
Angle E and angle H are both 90°: a pair of equal angles.
A for angle.
DF and GI are both 30: a pair of equal sides.
S for side.
DE and GH are both 18: a pair of equal sides.
S for side.
2 Find the rule
Angle E is 90°: a right angle.
DF is across from it: the hypotenuse.
Right angle, hypotenuse, side: R H S.
Why?
Pythagoras: EF² is the hypotenuse squared take away the other side squared: 576.
So EF is 24.
HI is the same, 24.
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.