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Geometrical Properties and Proportions in Similar Triangles Quiz

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#1

In similar triangles, if one angle is 45 degrees, what are the measures of the other two angles?

60° and 75°
Explanation

The sum of angles in a triangle is 180°, and in similar triangles, corresponding angles are congruent.

#2

What is the ratio of the corresponding sides in similar triangles?

They are proportional
Explanation

Corresponding sides in similar triangles maintain a constant ratio.

#3

In similar triangles, what is the relationship between the measures of corresponding angles?

They are congruent
Explanation

Corresponding angles in similar triangles are equal.

#4

If the ratio of the areas of two similar triangles is 9:16, what is the ratio of their corresponding sides?

4:3
Explanation

The ratio of corresponding sides is the square root of the ratio of areas.

#5

If the area of a triangle is doubled by doubling the lengths of all its sides, what is the ratio of the corresponding altitudes?

2:1
Explanation

Doubling the sides doubles the area but does not change the altitude ratio.

#6

If the ratio of corresponding sides of two similar triangles is 2:3, what is the ratio of their areas?

4:9
Explanation

The ratio of areas is the square of the ratio of corresponding sides.

#7

In similar triangles, what is the relationship between the lengths of corresponding altitudes?

They are proportional
Explanation

Altitudes of similar triangles are in the same ratio as corresponding sides.

#8

What is the Pythagorean Theorem?

a² + b² = c²
Explanation

In a right triangle, the sum of the squares of the lengths of the legs equals the square of the length of the hypotenuse.

#9

If the lengths of the corresponding sides of two similar triangles are in the ratio 2:5, what is the ratio of their perimeters?

5:2
Explanation

Perimeters of similar triangles are in the same ratio as corresponding sides.

#10

If the ratio of the areas of two similar triangles is 25:64, what is the ratio of their corresponding heights?

5:8
Explanation

The ratio of heights is the square root of the ratio of areas.

#11

If the perimeter of one triangle is 30 cm and the perimeter of another similar triangle is 45 cm, what is the ratio of their perimeters?

2:3
Explanation

Perimeters of similar triangles are in the same ratio as corresponding sides.

#12

In similar triangles, if the ratio of the lengths of two corresponding sides is 3:4, what is the ratio of their altitudes drawn to those sides?

3:4
Explanation

The ratio of altitudes is the same as the ratio of corresponding sides.

#13

In similar triangles, if the ratio of the lengths of corresponding sides is 5:8, what is the ratio of their perimeters?

8:5
Explanation

Perimeters of similar triangles are in the same ratio as corresponding sides.

#14

If the ratio of corresponding sides of two similar triangles is 3:4, what is the ratio of their areas?

16:9
Explanation

The ratio of areas is the square of the ratio of corresponding sides.

#15

If the ratio of the perimeters of two similar triangles is 3:5, what is the ratio of their corresponding sides?

5:3
Explanation

Perimeters of similar triangles are in the same ratio as corresponding sides.

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