Step by step
The question
Question: which rule shows that triangles KLM and PQR are congruent?
Angle L = angle Q = 90°.
KM = PR = 20.
LM = QR = 12.
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: K with P, L with Q, M with R.
PQR is turned over.
That does not matter.
Angle L and angle Q are both 90°: a pair of equal angles.
A for angle.
KM and PR are both 20: a pair of equal sides.
S for side.
LM and QR are both 12: a pair of equal sides.
S for side.
2 Find the rule
Angle L is 90°: a right angle.
KM is across from it: the hypotenuse.
Right angle, hypotenuse, side: R H S.
Why?
Pythagoras: KL² is the hypotenuse squared take away the other side squared: 256.
So KL is 16.
PQ is the same, 16.
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.