Step by step
The question
Question: which rule shows that triangles ABC and XYZ are congruent?
Angle C = angle Z = 90°.
AB = XY = 15.
BC = YZ = 9.
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 X, B with Y, C with Z.
XYZ is turned over.
That does not matter.
Angle C and angle Z are both 90°: a pair of equal angles.
A for angle.
AB and XY are both 15: a pair of equal sides.
S for side.
BC and YZ are both 9: a pair of equal sides.
S for side.
2 Find the rule
Angle C is 90°: a right angle.
AB is across from it: the hypotenuse.
Right angle, hypotenuse, side: R H S.
Why?
Pythagoras: AC² is the hypotenuse squared take away the other side squared: 144.
So AC is 12.
XZ is the same, 12.
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.