Grade 12 Geometry: Similarity
This worksheet covers key concepts of similarity in geometry, including similar polygons, triangles, and their properties.
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Grade 12 Geometry: Similarity
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Read each question carefully and provide your best answer. Show all your work for full credit.
1. Which of the following conditions is NOT required for two polygons to be similar?
Corresponding angles are congruent.
Corresponding sides are proportional.
They have the same shape.
They have the same size.
2. If two triangles are similar, which of the following statements is always true?
Their perimeters are equal.
Their areas are equal.
The ratio of their corresponding sides is constant.
They are congruent.
3. If two figures are similar, their corresponding angles are and their corresponding sides are .
4. The ratio of the perimeters of two similar polygons is equal to the of their corresponding sides.
5. Given two triangles, \(\triangle ABC\) and \(\triangle XYZ\), where \(\angle A = \angle X\), \(\angle B = \angle Y\), and \(\angle C = \angle Z\). If \(AB = 6\), \(BC = 8\), \(AC = 10\), and \(XY = 9\), find the lengths of \(YZ\) and \(XZ\).
6. A rectangular garden has dimensions 10 feet by 15 feet. If a smaller, similar garden is to be built with a perimeter of 20 feet, what are the dimensions of the smaller garden?
7. All squares are similar.
True
False
8. All rectangles are similar.
True
False
9. The two triangles below are similar. Find the value of x.
10. A map has a scale of 1:5000. If a park on the map has dimensions of 4 cm by 6 cm, what are the actual dimensions of the park in meters?