Question

1. which of the rulers are similar in shape?

Explanation:

Step1: Find the unknown angles

For the top - right ruler (right - angled triangle), using the angle sum property of a triangle (\(180^{\circ}\)), if one angle is \(90^{\circ}\) and let the other two angles be \(x\). Then \(90 + x+x=180\), \(2x = 90\), \(x = 45^{\circ}\).
For the bottom - right ruler (right - angled triangle), one angle is \(90^{\circ}\) and another is \(45^{\circ}\) (given).
For the left - side ruler (right - angled triangle), one angle is \(90^{\circ}\) and another is \(60^{\circ}\) (given). Using the angle sum property \(180^{\circ}\), the third angle is \(180-(90 + 60)=30^{\circ}\).

Step2: Apply the AA (Angle - Angle) similarity criterion

Two triangles are similar if their corresponding angles are equal.
The top - right and bottom - right rulers are right - angled (\(90^{\circ}\)) and have another equal angle of \(45^{\circ}\).

Answer:

The top - right and bottom - right rulers are similar.