SME
Grade 10 Math · Problem type
Congruent parts with an unknown
Use this for “△ABC ≅ △DEF, AB = 3x + 2 and DE = 2x + 8. Find x and AB.”
Diagram
△ABC ≅ △DEF by SSS: three pairs of equal sides.
This is an example. Type your own values to start a new problem.
p
x
+
q
=
r
x
+
s
x
x
worked out (not typed)
AB
AB = DE
worked out (not typed)
Formulas
p
×
x
+
q
=
r
×
x
+
s
3 × 6 + 2 = 2 × 6 + 8
AB
=
p
×
x
+
q
20 = 3 × 6 + 2
Assumptions
•
Corresponding parts of congruent triangles are congruent, so AB = DE: set the expressions equal.
•
The order of the letters pairs the parts: A with D, B with E, C with F.
Step-by-step
WE KNOW
p = 3, q = 2, r = 2, s = 8
FIND
x (x), AB = DE (AB)
Step 1 · Find x (x)
Use p × x + q = r × x + s
Take
the
smaller
x
term
from
both
sides,
then
the
number
beside
the
x
left,
then
divide.
x
=
s
−
q
p
−
r
x
=
8 − 2
3 − 2
Take
2
x
from
both
sides:
x
+
2
=
8
Take
2
from
both
sides:
x
=
6
x
=
6
Step 2 · Find AB = DE (AB)
Use AB = p × x + q
Put
x
back
into
AB.
AB = 3 × 6 + 2
AB = 18 + 2
AB = 20
Check
Put the numbers back in. Both sides should match.
3 × 6 + 2 = 2 × 6 + 8 ✓
20 = 3 × 6 + 2 ✓
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Congruent triangles: SSS, SAS, ASA, AAS and HL
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△ABC ≅ △KLM: must it be true?
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