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 5: a pair of equal sides.
S for side.
BC and EF are both 7: a pair of equal sides.
S for side.
Angle B and angle E are both 40°: a pair of equal angles.
A for angle.
2 Find the rule
Angle B is between the two sides: AB and BC both touch corner B.
Go round: side, angle, side: S A S.
Two sides and the angle between them fix the triangle.
There is only one way to draw it.
So S A S shows the triangles are congruent.
3 Use the matching parts
DF matches AC: D with A, F with C.
In congruent triangles, matching parts are equal.
So x + 9 = 4.
4 Remove the + 9
We want x by itself.
The + 9 is in the way.
To remove + 9, we take away 9.
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.
+ 9 and − 9 make zero.
Cross them out.
4 − 9 = −5.
So x = −5!
5 Check
Let's check: put x = −5 in x + 9.
We get 4, the same as AC.
So x = −5 is right!
Let's look back.
First: match the parts.
Then: find the rule.
Then: use the matching parts.
Then: remove the + 9.
Last: check.