Similar Figures worksheet - Free Printable

Let's solve each problem one by one with clear explanations.

---

Problem 1:

> Lance the alien is 5 feet tall. His shadow is 8 feet long. At the same time of day, a tree’s shadow is 32 feet long. What is the height of the tree?

Concept: This is a similar triangles problem. At the same time of day, the sun’s rays are parallel, so the triangle formed by the alien and his shadow is similar to the triangle formed by the tree and its shadow.

So, the ratios of corresponding sides are equal:

> (Height of alien) / (Shadow of alien) = (Height of tree) / (Shadow of tree)

Let the height of the tree be h.

So,

> 5 / 8 = h / 32

Now solve for h:

Multiply both sides by 32:

> h = (5 / 8) × 32
> h = 5 × 4
> h = 20 feet

✔ Answer: a) 20 feet

---

Problem 2:

> Pentagon JKLMN is similar to pentagon VWXYZ. What is the measurement of angle X?

Concept: In similar polygons, corresponding angles are equal.

We need to match the vertices in order:

Pentagon JKLMN ~ Pentagon VWXYZ

That means:

- J ↔ V
- K ↔ W
- L ↔ X ← we want angle X, which corresponds to angle L
- M ↔ Y
- N ↔ Z

From the diagram, angle L is labeled as 60°.

Therefore, angle X (which corresponds to angle L) is also 60°.

✔ Answer: b) 60°

*(Note: The 150° shown at angle J corresponds to angle V, but we don’t need that for this question.)*

---

Problem 3:

> Triangle PQR is similar to triangle DEF. Which describes the relationship between the corresponding sides of the two triangles?

Given:

- PQ = 4 cm, PR = 6 cm (in triangle PQR)
- DE = 6 cm, DF = 9 cm (in triangle DEF)

Since the triangles are similar, we must match corresponding sides.

The similarity is stated as: Triangle PQR ~ Triangle DEF

This implies:

- P ↔ D
- Q ↔ E
- R ↔ F

So, corresponding sides are:

- PQ ↔ DE
- QR ↔ EF
- PR ↔ DF

Now let’s check the ratios:

- PQ / DE = 4 / 6 = 2/3
- PR / DF = 6 / 9 = 2/3

So the scale factor is 2/3.

Now look at the options:

a) PQ / DE = 4/6 → ✔️ Correct! (This matches our calculation)

b) PQ / DE = 6/4 → Incorrect (that’s the reciprocal)

c) PQ / EF = 4/9 → Not corresponding sides (EF corresponds to QR, not PQ)

d) PR / DE = 6/6 → Not corresponding (PR corresponds to DF, not DE)

✔ Answer: a) PQ/DE = 4/6

---

✔ Final Answers:

1. a) 20 feet
2. b) 60°
3. a) PQ/DE = 4/6