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Quizzes > High School Quizzes > Mathematics

7-2 Practice Test: Similar Polygons

Boost your skills with polygon challenges

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Paper art promoting a 7-2 Similarity Sprint quiz for middle school geometry students.

Which condition is necessary for two polygons to be similar?
Corresponding angles are supplementary
All sides are equal in length
They have the same perimeter
Corresponding angles are congruent and corresponding sides are proportional
Similar polygons must have all corresponding angles equal and their corresponding sides in proportion. This is the fundamental definition of similarity in geometry.
Which pair of elements can be used to establish that two triangles are similar?
One pair of congruent angles and one pair of congruent sides
Two pairs of congruent angles
Two pairs of congruent sides
Three pairs of congruent sides
If two angles of one triangle are congruent to two angles of another triangle (AA postulate), the triangles are similar. This criterion is sufficient to establish similarity.
In similar polygons, the constant ratio of corresponding sides is known as the:
Similarity constant
Scale factor
Proportional ratio
Equal multiplier
The ratio of any two corresponding sides in similar figures is called the scale factor. It shows how much one figure is enlarged or reduced compared to the other.
If two similar polygons have a scale factor of 1, they are:
Similar but different in size
Not comparable
Reflections of each other
Congruent
A scale factor of 1 indicates that the figures are of equal size, meaning they are congruent. All corresponding sides and angles are identical.
True or False: In similar polygons, all corresponding angles are equal.
Not necessarily
It depends on the polygon type
True
False
By definition, similar polygons have equal corresponding angles. This is one of the key properties that define geometric similarity.
Two similar rectangles have corresponding lengths in the ratio 3:5. If the shorter rectangle has a length of 9, what is the corresponding length in the larger rectangle?
15
18
12
10
The scale factor is found by dividing 9 by 3, which gives 3. Multiplying the corresponding part 5 by the scale factor (3) results in 15.
In two similar triangles, if the ratio of their perimeters is 2:3, what is the scale factor from the smaller to the larger triangle?
1.5
0.67
3
2
Since the ratio of the perimeters is 2:3, the scale factor from the smaller to the larger triangle is 3 divided by 2, or 1.5.
Given two similar polygons, if one side in the smaller polygon measures 4 units and the corresponding side in the larger polygon measures 10 units, what is the scale factor from the smaller to the larger polygon?
10
2.5
4
0.4
The scale factor is calculated by dividing the larger side by the smaller side: 10/4 equals 2.5. This factor scales every dimension of the smaller polygon.
Which method is most appropriate to verify if two quadrilaterals are similar?
Checking that all corresponding angles are congruent and corresponding sides are proportional
Comparing only the corresponding angles
Comparing only the side lengths
Ensuring the diagonals are equal in length
Both conditions - equal corresponding angles and proportional sides - must be met for two quadrilaterals to be similar. Relying on a single condition does not guarantee similarity.
Two similar pentagons have areas in the ratio 9:16. What is the scale factor between their corresponding sides?
9/16
4/3
16/9
3/4
Since the area ratio of two similar figures is the square of the scale factor, taking the square root of 16/9 gives 4/3 as the scale factor.
The corresponding side lengths of two similar triangles are 7, 9, and 12 in the smaller triangle, and 14, x, and 24 in the larger triangle. What is the value of x?
18
21
16
20
The scale factor from the smaller to the larger triangle is 14/7, which equals 2. Applying this factor to the unknown side (9) gives 9 x 2 = 18.
If two similar hexagons have corresponding side lengths in the ratio 5:8, what is the ratio of their perimeters?
8:5
25:64
5:8
5:2
The perimeter of a polygon is the sum of its side lengths, and in similar polygons the perimeters have the same ratio as the corresponding sides, hence 5:8.
How does the ratio of the areas of two similar figures relate to their scale factor?
It is the square root of the scale factor
It is equal to the scale factor
It is the square of the scale factor
It is the cube of the scale factor
The area of similar figures scales by the square of the scale factor because area is a two-dimensional measure. This means if the scale factor is k, the area ratio is k².
Which approach is most effective for finding a missing side length in a diagram involving similar figures?
Subtracting the corresponding angles
Adding all the given side lengths
Measuring the diagonals
Setting up and solving a proportion using corresponding sides
Using proportional relationships between corresponding sides allows you to solve for unknown side lengths in similar figures. This method is based on the defining properties of similarity.
Two similar polygons have corresponding sides in the ratio 3:7. If one polygon has an area of 27 square units, what is the area of the other polygon?
49
81
147
112
The area ratio is the square of the scale factor: (7/3)² = 49/9. Multiplying the area of 27 by 49/9 results in 147 square units.
In two similar triangles, if the sides of the first triangle are 8, 15, and 17, and the corresponding side to 15 in the second triangle is 25, what are the lengths of the other corresponding sides?
40/2 and 85/3
40/3 and 85/3
40/3 and 85/2
40/3 and 85/4
The scale factor is determined by 25/15 = 5/3. Multiplying the other sides (8 and 17) by 5/3 gives 40/3 and 85/3 respectively.
A large similar polygon has a perimeter of 96 cm and a smaller similar polygon has a perimeter of 64 cm. If a side of the smaller polygon measures 16 cm, what is the corresponding side length in the larger polygon?
22 cm
18 cm
24 cm
26 cm
The scale factor between the polygons is the ratio of their perimeters, 96/64 = 1.5. Multiplying the smaller side (16 cm) by 1.5 gives 24 cm.
For two similar trapezoids, if the area of the smaller one is 50 square units and the scale factor for the sides is 3/2, what is the area of the larger trapezoid?
75 sq units
85 sq units
112.5 sq units
120 sq units
Area scales by the square of the scale factor. Since (3/2)² = 9/4, multiplying 50 by 9/4 results in an area of 112.5 square units for the larger trapezoid.
If you set up the proportion 5/x = 8/12 while solving a similarity problem, what is the value of x?
8
6
7.5
7
Cross multiplying the proportion gives 5 × 12 = 8x, i.e., 60 = 8x. Solving for x yields x = 7.5, which confirms the proportional relationship.
Two similar irregular hexagons have corresponding side lengths in the ratio 2:3. If the perimeter of the smaller hexagon is 48 units, what is the perimeter of the larger hexagon?
64 units
72 units
80 units
96 units
Since the perimeters of similar polygons scale by the same ratio as their corresponding sides, multiply 48 by the scale factor 3/2 to obtain 72 units.
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Study Outcomes

  1. Analyze properties of similar polygons and identify corresponding sides and angles.
  2. Apply similarity ratios to solve geometrical problems accurately.
  3. Interpret immediate feedback to refine problem-solving strategies.
  4. Evaluate results from quick-paced challenges to prepare for tests and exams.
  5. Demonstrate improved understanding of key concepts in similarity through practical application.

7-2 Similar Polygons Practice Cheat Sheet

  1. Definition of Similar Polygons - Similar polygons have the same shape because their corresponding angles are congruent and their sides are proportional, even if their sizes differ. Think of a tiny triangle and a giant one that look identical but one is just a stretched copy! Grasping this idea is your first step to mastering polygon similarity. CliffsNotes guide on similar polygons
  2. Scale Factor - The scale factor is the magic ratio that scales one polygon up or down to match another. If one polygon's side is twice as long as another, the scale factor is 2, unlocking unknown dimensions in shape puzzles. Use this ratio to find missing sides and solve similarity problems with confidence. Deep dive into scale factors
  3. Angle Congruence - In any set of similar polygons, each pair of corresponding angles is a perfect match, like matching hats in a party favor set. This ensures the overall shape stays the same, whether you're looking at a small sketch or a huge billboard. Spot those matching angles, and you've nailed half the similarity test! Explore angle congruence
  4. Proportional Sides - Proportional sides mean each side of one polygon relates to its counterpart in another by the same ratio - think of them as best friends wearing the same size hats in different colors. If one side is half as long, every side keeps that 1:2 relationship, preserving the shape's integrity. This consistency is key for solving geometry puzzles quickly! CliffsNotes on proportional sides
  5. Perimeter Ratio - The ratio of the perimeters of two similar polygons equals the scale factor, making it super easy to compare outlines. If the scale factor is 3, the bigger shape's perimeter is exactly three times the smaller one's, like tripling a recipe. This neat property saves you time when calculating fences, frames, or any boundary measurement! Learn about perimeter ratios
  6. Area Ratio - When you square the scale factor, you get the area ratio - big news for covering surfaces! So if the scale factor is 2, the larger polygon has 2² = 4 times the area, like moving from a mini pizza to a large one with four times as much cheesy goodness. This principle is essential for architects, artists, and anyone curious about space coverage. Discover area ratio secrets
  7. Identifying Similar Polygons - To prove two polygons are similar, check both matching angles and proportional sides - like detective work in geometry! Both clues must line up before you can declare them similar, ensuring no sneaky shapes slip past unverified. Mastering this double-check routine is critical for acing similarity problems. Identify similar shapes
  8. Solving for Unknown Sides - Grab your scale factor and set up a proportion to hunt down missing side lengths in similar polygons - it's like cracking a secret code! For example, if a side is 5 units in one and 10 units in another, you instantly know the scale factor is 2. Plug that into your proportion formula, and voilà, you'll calculate any unknown side with ease. Practice solving sides
  9. Real-Life Applications - Similar polygons pop up in scale models, mapmaking, and architectural designs, letting you shrink or enlarge objects accurately while keeping their proportions perfect. Imagine drafting a model of a dream house or designing a travel map with flawless scale - similarity makes it all possible. Understanding this concept turns math class into a toolkit for real-world creativity! See real-life examples
  10. Practice Problems - The more you flex your similarity muscles by solving problems, the sharper your understanding gets, priming you for exams and real-world challenges. Focus on setting up proportions and applying properties like angles and side ratios to unlock each problem's secrets. Keep practicing, and soon you'll tackle even the trickiest similar polygon puzzles like a pro! Start practicing now
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