Step by step
The question
Question: find angle Z.
Triangles PQR and XYZ have the marked parts equal.
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: P with X, Q with Y, R with Z.
XYZ is turned over.
That does not matter.
PQ and XY are both 8: a pair of equal sides.
S for side.
QR and YZ are both 6: a pair of equal sides.
S for side.
PR and XZ are both 7: a pair of equal sides.
S for side.
2 Find the rule
All three pairs are sides.
Side, side, side: S S S.
Three sides fix the triangle.
Like three sticks: they join up in only one way.
So S S S shows the triangles are congruent.
3 Use the matching parts
Angle Z matches angle R: Z with R.
In congruent triangles, matching parts are equal.
So angle Z = angle R.
So angle Z = 75°.
Let's look back.
First: match the parts.
Then: find the rule.
Last: use the matching parts.