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Quizzes > High School Quizzes > Mathematics

Similar Polygons Practice Quiz

Quickly master similar polygon concepts with practice

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting a trivia quiz on polygon similarity for high school geometry students.

What does it mean for two polygons to be similar?
They are exactly the same in size and shape.
They have the same number of sides regardless of angle measures.
They have identical angles and proportional corresponding side lengths.
Only their perimeters are proportional.
Two polygons are similar if their corresponding angles are equal and their corresponding side lengths are proportional. This definition establishes that the shapes are the same, even if their sizes differ.
If two polygons are similar, what can be said about their corresponding angles?
They are congruent (equal in measure).
They are supplementary.
They differ by a fixed amount.
They add up to 90° each.
Similar polygons maintain equal corresponding angles as one of the key conditions for similarity. This property ensures that the overall shape is preserved.
For two similar polygons, the constant ratio between their corresponding side lengths is known as what?
Area ratio
Scale factor
Angle ratio
Perimeter ratio
The scale factor represents the multiplier by which the side lengths of one polygon are increased or decreased to yield the side lengths of the other. It is the key constant in establishing similarity between two figures.
Which pair of polygons cannot be similar?
A triangle and a square
Two regular pentagons
A square and a rectangle
Two triangles
For two polygons to be similar, they must have the same number of sides along with congruent corresponding angles and proportional side lengths. A triangle and a square do not have the same number of sides, so they cannot be similar.
If one side of a polygon measures 4 units and the corresponding side of a similar polygon measures 8 units, what is the scale factor from the first to the second polygon?
2
8
4
0.5
The scale factor is determined by dividing the corresponding side length of the larger polygon by that of the smaller polygon. Since 8 divided by 4 equals 2, the scale factor is 2.
Given two similar quadrilaterals, if corresponding sides are in the ratio 3:5 and a side in the smaller quadrilateral is 9 cm, what is the corresponding side in the larger quadrilateral?
18 cm
10 cm
12 cm
15 cm
Using the proportion, multiply 9 cm by the ratio 5/3 to find the corresponding side length. This calculation results in 15 cm, confirming the proportional relationship.
If the scale factor between two similar polygons is k, how is the area of the larger polygon related to the area of the smaller polygon?
Area is multiplied by 2k
Area is multiplied by k
Area is multiplied by k²
Area is divided by k
The area of similar figures scales as the square of the scale factor because area is a two-dimensional measure. This quadratic relationship is essential when comparing the sizes of similar polygons.
A regular hexagon and another regular hexagon are similar. If the perimeter of the smaller hexagon is 30 cm and the scale factor to the larger is 1.5, what is the perimeter of the larger hexagon?
45 cm
35 cm
40 cm
50 cm
Since perimeters scale directly with the scale factor, multiplying 30 cm by 1.5 results in a perimeter of 45 cm for the larger hexagon. This straightforward multiplication confirms the effect of scaling.
Two similar polygons have a ratio of corresponding side lengths of 4:7. If the smaller polygon has an area of 32 square units, what is the area of the larger polygon?
98 square units
84 square units
56 square units
112 square units
The area ratio between similar polygons is the square of the side ratio. Here, (7/4)² equals 49/16, and multiplying 32 by 49/16 gives 98 square units.
Which method is most effective in determining if two polygons are similar?
Comparing the sum of the interior angles only
Comparing one corresponding side
Comparing only the perimeters
Comparing corresponding angles and checking the proportionality of corresponding sides
To determine similarity, both the equality of corresponding angles and the proportionality of corresponding sides must be verified. This comprehensive method ensures that the entire shape is properly scaled.
Two similar triangles have corresponding side lengths in the ratio 3:4. If one side of the smaller triangle measures 9 units, what is the length of the corresponding side in the larger triangle?
8 units
13 units
10 units
12 units
Multiplying the 9-unit side by the ratio 4/3 yields 12 units, which is the length of the corresponding side in the larger triangle. This maintains the proportionality required for similarity.
If the scale factor from one similar polygon to another is 0.75, what percentage of the original's area will the new polygon have?
56.25%
50%
75%
25%
The area of a similar polygon scales by the square of the scale factor. Here, 0.75² equals 0.5625, or 56.25%, indicating the new polygon's area relative to the original.
Can a triangle and a rectangle ever be considered similar if they have identical interior angle measures?
Yes, if the angles match
No, because similar polygons must have the same number of sides
Yes, if their areas are the same
No, because their perimeters differ
Even if a triangle and a rectangle have matching angle measures, similarity also requires the figures to have the same number of sides. Since a triangle has three sides and a rectangle has four, they cannot be similar.
When comparing two similar pentagons, if one has side lengths of 6, 7, 8, 9, and 10 units, and the scale factor is 1.5, what is the length of the corresponding longest side in the second pentagon?
12 units
14 units
10 units
15 units
Multiplying the longest side of 10 units by the scale factor 1.5 results in 15 units. This demonstrates the direct proportionality of corresponding side lengths in similar figures.
Which transformation produces a polygon similar to the original?
Dilation (scaling)
Translation (sliding)
Reflection (flipping)
All of the above
Dilation changes the size proportionally, while translation and reflection preserve the original shape and angles. All these transformations yield a polygon that is similar to the original.
Given two similar polygons, if the ratio of their areas is 9:16, what is the scale factor from the smaller to the larger polygon?
3/4
4/3
9/16
16/9
The area ratio given is the square of the side length ratio. Taking the square root of 9/16 gives 3/4 as the ratio of the smaller to the larger polygon. To convert from the smaller to the larger, you take the reciprocal, resulting in a scale factor of 4/3.
In two similar polygons, if one angle in the first polygon measures 120° and corresponds to an angle in the second polygon, what is the measure of the corresponding angle in the second polygon?
120°
150°
100°
60°
Corresponding angles in similar polygons are congruent; hence, the angle in the second polygon remains 120°. This consistency in angle measures is essential to the concept of similarity.
For two similar polygons with corresponding side lengths in the ratio 5:8, if a side in the larger polygon measures 24 units, what is the corresponding side length in the smaller polygon?
15 units
30 units
10 units
20 units
The side length in the smaller polygon is determined by multiplying the larger side by the ratio 5/8. Calculating 24 Ã - (5/8) results in 15 units, which is the correct corresponding side length.
After a dilation transformation with a scale factor of 3 is applied to a polygon, which of the following statements holds true?
All corresponding sides are 3 times longer, and all angles are 3 times larger.
All corresponding sides are 3 times longer, and all angles remain unchanged.
All corresponding sides are 3 times shorter, and angles remain unchanged.
Only the perimeter increases while the shape remains identical.
Dilation scales all linear dimensions by the scale factor, so each side becomes 3 times longer. However, the angles of the polygon remain unchanged, preserving the overall shape.
Two similar decagons have corresponding sides that differ by 6 units. Can this information determine the scale factor between them?
No, because you must use the ratio of side lengths, not the difference.
No, because decagons cannot have constant side differences.
Yes, because the side difference indicates the scale factor directly.
Yes, because the difference equals the scale factor.
The concept of similarity is based on the ratio of corresponding side lengths rather than their absolute differences. A constant difference does not provide the proportional information necessary to determine the scale factor.
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Study Outcomes

  1. Understand the criteria that define polygon similarity.
  2. Analyze corresponding sides and angles to verify similarity.
  3. Apply proportional reasoning to calculate unknown side lengths.
  4. Evaluate and justify the similarity of polygons using geometric properties.

Similar Polygons Quick Check Cheat Sheet

  1. Definition of Similar Polygons - Two polygons are similar if their corresponding angles match up exactly and their side lengths scale proportionally. In other words, they're the same shape but can be giants or minis of each other - mathematical twins differing only in size! CliffsNotes Study Guide
  2. Angle-Angle (AA) Similarity Criterion - If two angles in one triangle are congruent to two angles in another, you unlock similarity without measuring a single side. It's the ultimate two-for-one deal: just match angle pairs and you're done! MathPrep: AA Criterion
  3. Side-Side-Side (SSS) Similarity Criterion - When each corresponding side in two triangles scales by the same factor, the triangles are similar. Compare the smallest sides, then the next, then the biggest - like lining up stage actors by height! MathPrep: SSS Criterion
  4. Side-Angle-Side (SAS) Similarity Criterion - If an angle in one triangle matches an angle in another, and the sides hugging those angles are proportional, bingo - similar triangles! It's the perfect combo of angles and sides working together. MathPrep: SAS Criterion
  5. Scale Factor - The scale factor is the magic ratio linking similar polygons, telling you exactly how many times bigger or smaller one shape is compared to another. Flip it around to find missing side lengths and resize shapes like a pro! Owlcation: Scale Factor
  6. Perimeter Ratio - The perimeters of similar polygons scale by the same factor as their sides. If your scale factor is 2:1, the perimeter doubles too - no surprises there! Owlcation: Perimeter Ratios
  7. Area Ratio - Here's where the magic squares up: the ratio of areas between similar polygons is the square of the scale factor. So 1:3 in sides explodes into 1:9 in area - a huge jump! Owlcation: Area Ratios
  8. Identifying Similar Polygons - To confirm similarity, make sure all angles are congruent and all sides line up proportionally. Both must hold true, or you've got a case of "false friends" in geometry! SchoolTube Lesson
  9. Proportional Segments Theorem - A line parallel to one side of a triangle that cuts the other two sides will divide them proportionally. This "slice-and-scale" trick is perfect for conquering parallel line problems! OnlineMathLearning: Proportional Segments
  10. Angle Bisector Theorem - An angle bisector splits the opposite side into segments proportional to the other two sides. This side‑splitting stunt comes in handy for solving sneaky bisector puzzles! OnlineMathLearning: Angle Bisector
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