Constructing Triangles Worksheet | Printable PDF Worksheets - Free Printable

You're looking at a worksheet on constructing triangles using geometric tools like a protractor and ruler, and in Section D, without a protractor. Since I can’t physically draw or construct the triangles for you (as I’m text-based), I’ll provide detailed step-by-step instructions for constructing each triangle as if you were doing it on paper — including which construction method to use (SAS, ASA, SSS, etc.) and how to execute it with your tools.

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## 🔧 General Tools Needed:
- Ruler (with cm/mm markings)
- Protractor
- Pencil
- Compass (for Section D — without protractor)

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# ✔ SECTION A: Construct using Protractor & Ruler

These are SAS (Side-Angle-Side) constructions.

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1) Triangle ABC: AB = 4 cm, BC = 5 cm, ∠B = 35°

Method: SAS

Steps:
1. Draw side BC = 5 cm.
2. At point B, use protractor to draw a 35° angle from BC.
3. Along this angle ray, measure 4 cm from B to mark point A.
4. Join A to C.
✔ Triangle ABC constructed.

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2) Triangle EFG: EF = 8 cm, FG = 7 cm, ∠F = 110°

Method: SAS

Steps:
1. Draw side FG = 7 cm.
2. At point F, draw a 110° angle opening towards G.
3. From F, along the angle ray, measure 8 cm to mark point E.
4. Join E to G.
✔ Triangle EFG constructed.

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3) Triangle HIJ: IJ = 6 cm, HJ = 3.5 cm, ∠J = 90° (right angle)

Method: SAS (Right Angle)

Steps:
1. Draw side IJ = 6 cm.
2. At point J, use protractor to draw a 90° angle upwards (perpendicular to IJ).
3. From J, measure 3.5 cm up the perpendicular to mark point H.
4. Join H to I.
✔ Triangle HIJ constructed (right-angled at J).

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# ✔ SECTION B: Construct using Protractor & Ruler

These are ASA (Angle-Side-Angle) constructions.

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1) Triangle KLM: ∠M = 33°, ∠L = 121°, ML = 2 cm

Method: ASA

Steps:
1. Draw side ML = 2 cm.
2. At point M, draw a 33° angle opening upwards.
3. At point L, draw a 121° angle opening upwards (on same side as M’s angle).
4. Extend both rays until they meet at point K.
✔ Triangle KLM constructed.

> 💡 *Note: The third angle (∠K) should be 180° - 33° - 121° = 26° — good to check.*

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2) Triangle NOP: ∠N = 42°, ∠P = 42°, NP = 8 cm

Method: ASA

Steps:
1. Draw side NP = 8 cm.
2. At point N, draw a 42° angle upwards.
3. At point P, draw a 42° angle upwards (on same side).
4. Extend rays to meet at O.
✔ Triangle NOP constructed (isosceles since base angles equal).

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3) Triangle QRS: ∠Q = 19°, ∠S = 78°, QS = 5.5 cm

Method: ASA

Steps:
1. Draw side QS = 5.5 cm.
2. At Q, draw a 19° angle upwards.
3. At S, draw a 78° angle upwards (same side).
4. Extend rays to meet at R.
✔ Triangle QRS constructed.

> 💡 *Check: ∠R = 180° - 19° - 78° = 83°*

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# ✔ SECTION C: Construct and leave construction lines

These are SSS (Side-Side-Side) constructions. Use compass for arcs.

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1) Triangle TUV: TU = 6 cm, UV = 5 cm, TV = 8 cm

Method: SSS

Steps:
1. Draw side TV = 8 cm.
2. With compass, set width to 6 cm → draw arc from T.
3. Set compass to 5 cm → draw arc from V.
4. Where arcs intersect is point U.
5. Join U to T and V.
✔ Triangle TUV constructed. Leave arcs visible.

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2) Triangle WXY: WX = 3 cm, XY = 6.5 cm, WY = 9 cm

Method: SSS

Steps:
1. Draw side WY = 9 cm.
2. From W, draw arc radius 3 cm.
3. From Y, draw arc radius 6.5 cm.
4. Intersection = point X.
5. Join X to W and Y.
✔ Triangle WXY constructed. Leave arcs visible.

> ⚠️ Check triangle inequality: 3 + 6.5 = 9.5 > 9 → OK.

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3) Triangle AZB: AZ = 5.4 cm, ZB = 4.9 cm, AB = ? (but marked equal sides — wait!)

Wait — look at diagram:
- AZ and AB have tick marks → so AZ = AB = 5.4 cm
- ZB = 4.9 cm

So this is Isosceles triangle with two sides equal.

Method: SSS (or Isosceles)

Steps:
1. Draw base ZB = 4.9 cm.
2. From Z, draw arc radius 5.4 cm.
3. From B, draw arc radius 5.4 cm.
4. Intersection = point A.
5. Join A to Z and B.
✔ Triangle AZB constructed. Leave arcs visible.

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# ✔ SECTION D: Construct WITHOUT a protractor

These are SSS constructions only — use compass and ruler.

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1) Triangle ESD: ES = SD = ? (tick marks) and ED = 6 cm

Diagram shows:
- ES and SD have tick marks → so ES = SD → isosceles
- ED = 6 cm (base)

But no side lengths given except base? Wait — likely ES = SD = same length, but not specified numerically. But in worksheet, usually implied that ticked sides are equal, and base is given.

Actually, looking again — no numerical values except base ED = 6 cm. That’s insufficient unless we assume the equal sides are arbitrary? But that doesn’t make sense.

Wait — perhaps the tick marks mean “equal”, and we’re to construct an isosceles triangle with base 6 cm and any equal sides (say, 5 cm or whatever). But since no length given, maybe it's a trick?

Actually — in many worksheets, when no length is given for ticked sides, you choose a reasonable length (e.g., 5 cm) as long as triangle inequality holds.

✔ So let’s assume:

> Construct isosceles triangle ESD with base ED = 6 cm, and legs ES = SD = 5 cm (chosen arbitrarily, but valid).

Steps:
1. Draw ED = 6 cm.
2. From E, draw arc radius 5 cm.
3. From D, draw arc radius 5 cm.
4. Intersection = S.
5. Join S to E and D.
✔ Triangle ESD constructed. No protractor needed.

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2) Triangle GTX: GT = TX = 3.2 cm, GX = ? (base has single tick — but no length?)

Wait — diagram shows:
- GT and TX have tick marks → so GT = TX = 3.2 cm
- Base GX has single tick → probably just indicating it’s the base, not equal.

But no length given for GX? That’s impossible to construct without more info.

Actually — looking closely, GX is the base, and its length isn't labeled. This might be an error, OR — perhaps the tick on GX means it’s also equal? But then it would be equilateral, but 3.2 ≠ ?

Wait — in diagram, GT and TX have double ticks? Or same tick? Actually, in most worksheets, if only two sides are ticked, and base isn't, then it’s isosceles with those two equal.

But without base length, we can’t construct it uniquely.

➡️ Likely intention: You are to construct an isosceles triangle with two sides = 3.2 cm, and base = any length that satisfies triangle inequality (e.g., 4 cm).

So let’s assume base GX = 4 cm.

Steps:
1. Draw GX = 4 cm.
2. From G, draw arc radius 3.2 cm.
3. From X, draw arc radius 3.2 cm.
4. Intersection = T.
5. Join T to G and X.
✔ Triangle GTX constructed.

> ✔ Triangle inequality: 3.2 + 3.2 > 4 → 6.4 > 4 → OK.

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3) Triangle FKB: FK = FB = 7.1 cm, KB = ? (base has single tick)

Again, similar issue — base KB not labeled.

Assume we choose KB = 6 cm (arbitrary but valid).

Steps:
1. Draw KB = 6 cm.
2. From K, draw arc radius 7.1 cm.
3. From B, draw arc radius 7.1 cm.
4. Intersection = F.
5. Join F to K and B.
✔ Triangle FKB constructed.

> ✔ Triangle inequality: 7.1 + 7.1 > 6 → 14.2 > 6 → OK.

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## 📝 Summary of Construction Methods:

| Section | Type | Method Used |
|---------|------------|------------------|
| A | SAS | Protractor + Ruler |
| B | ASA | Protractor + Ruler |
| C | SSS | Compass + Ruler (leave arcs) |
| D | SSS / Isosceles | Compass + Ruler (no protractor) |

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## ✔ Final Tips:

- Always label your vertices clearly.
- For SSS, use compass to draw arcs — intersection is the third vertex.
- For SAS/ASA, use protractor to draw angles accurately.
- In Section D, if side lengths aren’t fully given, choose reasonable lengths that satisfy triangle inequality.
- Leave construction lines (arcs) for Section C as instructed.

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If you’d like me to generate printable construction diagrams or animations, I can describe them further — but since I can’t draw, these steps will guide you perfectly to complete the worksheet!

Happy constructing! 📐📏