The question
Question: which rule shows that triangles ABC and DEF are congruent?
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.
AB = DE = 5 S
BC and EF are both 7: a pair of equal sides.
S for side.
BC = EF = 7 S
AC and DF are both 6: a pair of equal sides.
S for side.
AC = DF = 6 S
2 Find the rule
All three pairs are sides.
Side, side, side: S S S.
AB, BC, AC
Three sides fix the triangle.
Like three sticks: they join up in only one way.
So S S S shows the triangles are congruent.
SSS → congruent
Let's look back.
First: match the parts.
Last: find the rule.
▶ Watch it solved
The question
Question: which rule shows that triangles ABC and DEF are congruent?
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.
Angle A and angle D are both 45°: a pair of equal angles.
A for angle.
angle A = angle D = 45° A
Angle B and angle E are both 70°: a pair of equal angles.
A for angle.
angle B = angle E = 70° A
BC and EF are both 8: a pair of equal sides.
S for side.
BC = EF = 8 S
2 Find the rule
BC is not between the two angles: it does not touch corner A.
Go round: angle, angle, side: A A S.
angle A → angle B → BC
Two angles fix the third one too, because all three add up to 180°.
The angles fix the shape.
The side fixes the size.
So A A S shows the triangles are congruent.
AAS → congruent
Let's look back.
First: match the parts.
Last: find the rule.
▶ Watch it solved
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.
Angle A and angle D are both 45°: a pair of equal angles.
A for angle.
angle A = angle D = 45° A
Angle B and angle E are both 70°: a pair of equal angles.
A for angle.
angle B = angle E = 70° A
BC and EF are both 8: a pair of equal sides.
S for side.
BC = EF = 8 S
2 Find the rule
BC is not between the two angles: it does not touch corner A.
Go round: angle, angle, side: A A S.
angle A → angle B → BC
Two angles fix the third one too, because all three add up to 180°.
The angles fix the shape.
The side fixes the size.
So A A S shows the triangles are congruent.
AAS → congruent
3 Use the matching parts
DF matches AC: D with A, F with C.
In congruent triangles, matching parts are equal.
So 2x + 4 = 10.
2x + 4 = 10
We want x by itself.
Two things are stuck to x: times 2 and + 4.
The + 4 is on the outside, so it comes off first.
Then the times 2.
4 Remove the + 4
To remove + 4, we take away 4.
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.
2x + 4 − 4 = 10 − 4
+ 4 and − 4 make zero.
Cross them out.
10 − 4 = 6.
10 − 4 = 6
Now we have 2x = 6.
2x = 6
5 Remove the 2
2x means 2 times x.
We want just x.
To remove times 2, we divide by 2.
We do it on both sides, so they stay equal.
2x2 = 62
2 divided by 2 is 1.
So just x is left.
6 divided by 2 is 3.
62 = 3
So x = 3!
x = 3
6 Check
Let's check: put x = 3 in 2x + 4.
2x + 4 = 2 × 3 + 4 = 10
We get 10, the same as AC.
So x = 3 is right!
Let's look back.
First: match the parts.
Then: find the rule.
Then: use the matching parts.
Then: remove the + 4.
Then: remove the 2.
Last: check.
▶ Watch it solved
