Checkpoint: shapes, factors and shadows

A square has side 3. A rectangle is 3 by 5. All angles are 90°. Are they similar?

• Yes. Both have four sides and four right angles.
• Yes. All their angles are equal to 90°.
• No. Their sides are not in one ratio.

Triangles have sides 4, 5, 6 and 10, 12.5, 15. Are they similar?

• No. The lists are in a different order.
• No. One triangle is bigger.
• Yes. Every ratio is 2.5.

One triangle has angles 35° and 75°. Another has angles 75° and 70°. Are they similar?

• No. Only one pair of angles is equal, 75°.
• Yes. The third angles are 70° and 35°.
• Cannot say without the sides.

Two sides of one triangle are 5 and 10. Two of another are 8 and 16. What else does SAS need?

• The angles between those sides are equal.
• Nothing more. Both ratios are 1.6, so SAS holds.
• The third side of each triangle.

A pole 2 m tall casts a 3 m shadow. A tower's shadow is 45 m, at the same time. How tall is the tower?

• 30 m
• 67.5 m
• 90 m