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Quizzes > High School Quizzes > Mathematics

Practice Quiz: Ratios & Similar Figures

Master ratios and similar figures with practice

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Paper art promoting Ratio Figures Frenzy, a practice quiz for high school math students.

What is the simplest form of the ratio 4:8?
1:2
1:4
2:4
4:8
Dividing both terms of 4:8 by 4 gives 1:2, which is the simplest form. Simplifying ratios involves using the greatest common divisor for both numbers.
Which ratio is equivalent to 3:4?
3:5
6:8
5:6
4:5
Multiplying both parts of 3:4 by 2 gives 6:8, making it equivalent. Equivalent ratios maintain the same proportional relationship.
If a figure is scaled by a factor of 3, what happens to its dimensions?
The area is multiplied by 3
Each dimension is divided by 3
Each dimension is multiplied by 2
Each dimension is multiplied by 3
Scaling by a factor of 3 means every linear measurement is increased by multiplying by 3. It is important to note that while dimensions are multiplied by 3, the area would be multiplied by 3².
What is the definition of similar figures in geometry?
Figures that have equal areas
Figures with the same shape but different sizes, having proportional corresponding sides and equal corresponding angles
Figures with the same size but different shapes
Figures that overlap exactly
Similar figures have identical shapes with corresponding angles equal and sides proportional, even if their sizes differ. This definition is fundamental in understanding geometric similarity.
What is the scale factor from a small triangle with a side of 2 cm to a larger similar triangle with a side of 6 cm?
4
2
3
6
Dividing the larger side (6 cm) by the smaller side (2 cm) results in a scale factor of 3. This indicates that every dimension in the larger triangle is three times that of the corresponding dimension in the smaller triangle.
Solve for x: If 2/3 = x/9, what is the value of x?
x = 8
x = 5
x = 7
x = 6
Using cross multiplication, 2 multiplied by 9 equals 3 multiplied by x, leading to 18 = 3x. Dividing both sides by 3 results in x = 6.
If two similar rectangles have corresponding lengths in the ratio 1:4, what is the ratio of their areas?
1:8
4:1
1:16
1:4
The area of similar figures scales by the square of the scale factor. Since (1:4) squared is 1:16, the area ratio becomes 1:16.
In similar triangles, triangle A has a side of 4 units and triangle B has its corresponding side of 10 units. What is the length of the side in triangle B corresponding to a 3-unit side in triangle A?
9
6
7.5
8
The scale factor from triangle A to B is 10/4 = 2.5. Multiplying the unknown side (3 units) by 2.5 gives 7.5 units.
If the ratio of blue to red marbles is 5:3 and there are 40 blue marbles, how many red marbles are there?
20
30
24
36
Since the blue marbles represent 5 parts and there are 40 of them, each part equals 8 marbles. Multiplying 3 by 8 gives 24 red marbles.
Which of the following ratios is already in its simplest form?
9:12
3:4
12:16
6:9
The ratio 3:4 cannot be simplified further since 3 and 4 have no common factors other than 1. The other options can be reduced further.
When two similar figures have a scale factor of k, how does the perimeter of the larger figure compare to that of the smaller figure?
It is multiplied by k²
It remains the same
It is divided by k
It is multiplied by k
The perimeter of any figure scales directly with its linear dimensions. Therefore, if the scale factor is k, the perimeter of the larger figure is k times the perimeter of the smaller figure.
Which of the following expresses a valid ratio for mixing ingredients if a recipe requires 2 parts flour to 1 part sugar?
2/3
1:2
2:1
1/2
The ratio 2:1 correctly indicates 2 parts of flour to 1 part of sugar. This standard expression ensures the ingredients are mixed in the proper proportion.
In two similar figures, if the smaller has an area of 8 square units and the scale factor is 2, what is the area of the larger figure?
32 square units
40 square units
16 square units
24 square units
The area scales by the square of the scale factor. Since 2² = 4, multiplying the original area (8) by 4 gives 32 square units.
Given triangle A with sides 3, 4, 5 and a similar triangle B with the longest side measuring 15, what is the length of the side in triangle B corresponding to the side of length 3 in triangle A?
9
6
15
12
The scale factor is determined by dividing the longest side of triangle B by the longest side of triangle A: 15/5 = 3. Multiplying the corresponding side (3) by 3 gives 9.
If two similar polygons have corresponding side lengths in the ratio 5:7, what is the ratio of their perimeters?
5:7
7:5
25:49
5:6
The perimeter of similar polygons scales in the same ratio as their side lengths. Therefore, if the sides are in a 5:7 ratio, the perimeters will also be in a 5:7 ratio.
Two similar triangles have corresponding side lengths in the ratio 3:5. If the smaller triangle has sides measuring 6, 8, and 10 units, what is the perimeter of the larger triangle?
40 units
35 units
50 units
45 units
The scale factor is 5/3. Multiplying each side of the smaller triangle by 5/3 gives sides of 10, 40/3, and 50/3, which sum to 40 units. This shows how linear scaling affects the perimeter.
A scale drawing of a park uses a ratio of 1:250. If a bench in the drawing measures 0.2 cm, what is the actual length of the bench in centimeters?
75 cm
100 cm
50 cm
25 cm
A scale of 1:250 means that each centimeter on the drawing represents 250 cm in reality. Thus, 0.2 cm corresponds to 0.2 × 250 = 50 cm in actual length.
If the ratio of the sides of two similar figures is 2:3, by what factor does the area of the figures change?
2/3
4/9
9/4
3/2
The area of similar figures scales with the square of the scale factor. Since (3/2)² equals 9/4, the area of the larger figure is 9/4 times that of the smaller one.
In similar triangles, if the corresponding medians are in the ratio 4:7, what is the scale factor of the triangles?
4:6
4:7
7:4
6:7
For similar triangles, all corresponding linear measurements, including medians, share the same scale factor. Thus, a median ratio of 4:7 directly indicates a scale factor of 4:7.
A model car is built at a scale of 1:20. If the model measures 15 cm in length, what is the actual length of the car?
300 cm
150 cm
350 cm
200 cm
A 1:20 scale indicates that each centimeter on the model represents 20 centimeters in real life. Multiplying the model length (15 cm) by 20 yields an actual length of 300 cm.
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Study Outcomes

  1. Apply ratio principles to determine proportional relationships in geometric figures.
  2. Analyze similar figures to identify corresponding sides and angles.
  3. Calculate missing dimensions using given ratios and scale factors.
  4. Evaluate the effects of scaling on the properties of similar figures.
  5. Interpret problem statements to set up and solve ratio equations.

Quiz: 6-1 Ratios & Similar Figures Cheat Sheet

  1. Similar Figures Basics - Similar figures share the same shape but come in different sizes, which means all corresponding angles are equal and corresponding sides are proportional. Getting this concept down helps you tackle any similarity problem with confidence! OpenStax: Solve Proportions & Similar Figures
  2. Setting Up Proportions - Learn to match corresponding sides of similar figures and write a proportion to find unknown lengths. It's like a puzzle where each side fits perfectly into your equation! Purplemath: Proportion Practice
  3. Area Ratio Rule - The ratio of areas of two similar figures equals the square of their side”length ratio. Squaring that ratio is simple once you know your side match”ups! Tutorela: Similarity Ratios Examples & Exercises
  4. Practice Corresponding Parts - Sharpen your eye by identifying matching sides and angles in diagrams before setting up proportions. The clearer you see those pairs, the smoother your solution process becomes! IXL: Ratios in Similar Figures Practice
  5. Real‑World Similarity - Apply similar”figure reasoning to real scenarios, like measuring a tree's height using shadows and proportions. It's math in action, turning theory into a fun field experiment! EffortlessMath: Similarity & Shadow Problems
  6. Perimeter Ratio Insight - For similar figures, the ratio of perimeters is exactly the same as the ratio of corresponding side lengths. This neat shortcut saves you extra calculations! MathBits: Perimeter Ratio Practice
  7. Angle‑Angle (AA) Criterion - Two triangles are similar if two pairs of corresponding angles are congruent. Mastering AA means you can spot similarity in a snap! MathBits: AA Similarity Practice
  8. Volume Ratio Rule - The ratio of volumes of similar solids is the cube of their side”length ratio. Cubing that number might sound big, but you'll soon love how it scales up! MathBits: Volume Ratio Practice
  9. Reinforcement Through Practice - Tackle a variety of similarity problems to build speed and accuracy. Practice makes perfect, and every problem solved is a confidence booster! MathBits: More Similarity Exercises
  10. Use Online Resources - Leverage interactive quizzes and tutorials to test your skills in ratios and similar figures. Mixing learning modes (reading, doing, and checking) keeps study sessions lively and effective! IXL: Additional Ratios & Similar Figures
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