Step by step
The question
Question: find x.
Triangles ABC and DEF 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: A with D, B with E, C with F.
DEF is turned over.
That does not matter.
AB and DE are both 6: a pair of equal sides.
S for side.
BC and EF are both 8: a pair of equal sides.
S for side.
AC and DF are both 10: 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 E matches angle B: E with B.
In congruent triangles, matching parts are equal.
So 3x = 90.
4 Remove the 3
3x means 3 times x.
We want just x.
To remove times 3, we divide by 3.
We do it on both sides.
Why both sides?
The = sign means both sides are the same amount.
If we change only one side, they are not the same any more.
3 divided by 3 is 1.
So just x is left.
90 divided by 3 is 30.
So x = 30!
5 Check
Let's check: put x = 30 in 3x.
We get 90°, the same as angle B.
So x = 30 is right!
Let's look back.
First: match the parts.
Then: find the rule.
Then: use the matching parts.
Then: remove the 3.
Last: check.