FREE Printable Triangle Congruence Worksheets [PDFs] Brighterly - Free Printable

Let's solve each of the triangle congruence problems on this worksheet. We'll determine whether each pair of triangles is congruent and, if so, identify the congruence theorem that supports the conclusion.

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Problem 1

Triangles: ΔABC and ΔDCB
- Right angles at C (indicated by square symbol).
- AC = CB (marked with one tick)
- BC = DC (also marked with one tick)
- AB and DB are not directly marked.

Wait — let’s examine carefully:

Actually, in this diagram:
- ∠ACB and ∠DCB are both right angles.
- Side AC ≅ side DC (both have one tick mark)
- Side BC is common to both triangles.
- But we don't see markings for AB or DB.

Wait — actually, looking again:
In triangle ABC and triangle DCB:
- ∠C is a right angle in both.
- AC ≅ DC (one tick)
- BC ≅ CB (same side, reflexive)

So we have:
- Two legs of right triangles: AC ≅ DC, BC ≅ CB
- Right angles at C

Therefore, by LL Theorem (Leg-Leg), which is a special case of SAS for right triangles, these two right triangles are congruent.

✔ Answer: Yes, congruent by LL (Leg-Leg) Theorem (or SAS).

But wait — LL is not always listed as a standard name; it's often called SAS since the included angle is the right angle.

So better: SAS Congruence (two legs and included right angle).

✔ Answer: Yes, by SAS.

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Problem 2

Triangles: ΔABD and ΔCBD
- Shared side BD
- AB ≅ CB (both have one tick)
- AD ≅ CD (both have one tick)
- Also, angle at B appears to be bisected? But no marking.

Wait:
- AB ≅ CB (one tick)
- AD ≅ CD (one tick)
- BD is common

So: AB ≅ CB, AD ≅ CD, BD ≅ BD → all three sides equal?

Wait — but look at the diagram: Points A and C are on opposite sides, and D is connected.

We have:
- AB ≅ CB
- AD ≅ CD
- BD is shared

So yes: All three sides of ΔABD and ΔCBD are congruent.

✔ SSS Congruence

Answer: Yes, by SSS.

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Problem 3

Triangles: ΔOBE and ΔFCE
- OE ≅ FE (both have two ticks)
- OB ≅ FC (both have one tick)
- BE ≅ CE (both have one tick)

Wait — but also note: angles at E may be vertical angles?

Wait — look closely: Point E is where lines cross.

We see:
- OE ≅ FE (two ticks)
- OB ≅ FC (one tick)
- BE ≅ CE (one tick)

But also: ∠OEB and ∠FEC are vertical angles → congruent.

So we have:
- OE ≅ FE
- BE ≅ CE
- ∠OEB ≅ ∠FEC (vertical angles)

This is SAS: two sides and included angle.

✔ Answer: Yes, by SAS

Note: It might look like SSS, but only two sides are clearly marked. However, the third side isn’t shown marked, but since we have two sides and included angle, SAS applies.

Wait — actually, OE and FE are marked with two ticks, BE and CE with one tick, and OB and FC with one tick.

But OB and FC are not sides of the same triangle.

Let’s label:

ΔOBE and ΔFCE:
- OB ≅ FC (one tick)
- BE ≅ CE (one tick)
- OE ≅ FE (two ticks)
- ∠BEO and ∠CEF are vertical angles → congruent

So:
- BE ≅ CE
- OE ≅ FE
- ∠BEO ≅ ∠CEF

So two sides and included angle → SAS

✔ Yes, by SAS

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Problem 4

Triangles: ΔABC and ΔDEF
- Both have right angles at C and F
- AC ≅ DF (both have one tick)
- BC ≅ EF (both have two ticks)

So: Two legs of right triangles are congruent.

→ LL Theorem (a form of SAS)

✔ Yes, by LL (or SAS)

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Problem 5

Triangles: ΔABC and ΔKJH
- AB ≅ KJ (both have one tick)
- BC ≅ JH (both have one tick)
- AC ≅ KH (both have two ticks)

All three sides are marked as congruent.

✔ Yes, by SSS

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Problem 6

Triangles: ΔABC and ΔDEC
- AB ≅ DE (both have one tick)
- BC ≅ EC (both have two ticks)
- AC ≅ DC (both have one tick)

Wait — but are they sharing a side?

No. Let’s check:
- AB ≅ DE (one tick)
- BC ≅ EC (two ticks)
- AC ≅ DC (one tick)

So all three sides are congruent → SSS

But wait — is there a common vertex?

Points: A-B-C and D-E-C

So point C is shared.

But in ΔABC and ΔDEC:
- AB ≅ DE
- BC ≅ EC
- AC ≅ DC

Yes, all three sides are marked as congruent.

✔ Yes, by SSS

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Problem 7

Triangles: ΔDRT and ΔTUD
- DR ≅ TU (both have one tick)
- RT ≅ UD (both have one tick)
- DT is common side

Also, DT is shared.

So:
- DR ≅ TU
- RT ≅ UD
- DT ≅ TD (reflexive)

So all three sides are congruent → SSS

✔ Yes, by SSS

Wait — but look at the markings:
- DR has one tick
- TU has one tick → yes
- RT has one tick
- UD has one tick → yes
- DT is common

So yes, SSS

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Problem 8

Triangles: ΔUXV and ΔVYU
- UX ≅ VY (both have one tick)
- XV ≅ YU (both have one tick)
- UV is common

So:
- UX ≅ VY
- XV ≅ YU
- UV ≅ VU

All three sides → SSS

✔ Yes, by SSS

Wait — but is that correct?

Let’s label:
- Triangle UXV and triangle VYU

Points: U-X-V and V-Y-U

So:
- UX ≅ VY (one tick)
- XV ≅ YU (one tick)
- UV is common

Yes, all three sides match.

So SSS

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✔ Final Answers:

| Problem | Congruent? | Theorem |
|--------|------------|--------|
| 1 | Yes | SAS (or LL) |
| 2 | Yes | SSS |
| 3 | Yes | SAS |
| 4 | Yes | SAS (or LL) |
| 5 | Yes | SSS |
| 6 | Yes | SSS |
| 7 | Yes | SSS |
| 8 | Yes | SSS |

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📌 Explanation Summary:

- SSS (Side-Side-Side): All three sides of one triangle congruent to corresponding sides of another.
- SAS (Side-Angle-Side): Two sides and the included angle congruent.
- LL (Leg-Leg): For right triangles, if the two legs are congruent, then the triangles are congruent (special case of SAS).

In all cases here, either SSS or SAS applies.

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✔ Final Answer Sheet:

1. Yes, SAS
2. Yes, SSS
3. Yes, SAS
4. Yes, SAS (or LL)
5. Yes, SSS
6. Yes, SSS
7. Yes, SSS
8. Yes, SSS

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