Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Similar Figures Practice Quiz PDF

Practice similar figures with clear, guided answers

Difficulty: Moderate
Grade: Grade 8
Study OutcomesCheat Sheet
Paper art promoting Similar Figures Mastery quiz for middle to high school geometry students.

In similar figures, which property always holds true?
Corresponding angles are congruent.
Areas are always equal.
Perimeters are identical.
All sides are equal in length.
Similar figures always have congruent corresponding angles, even though their side lengths are not equal but proportional. This property distinguishes similarity from congruence.
What does the scale factor represent in similar figures?
The sum of corresponding angles.
The measure of a corresponding diagonal.
The ratio between any pair of corresponding sides.
The difference between the areas of the figures.
The scale factor is the constant ratio between any pair of corresponding sides of similar figures. It helps convert all dimensions from one figure to its similar counterpart.
Two rectangles are similar if their:
Diagonals are equal.
Length-to-width ratios are equal.
Perimeters are identical.
Areas are equal.
Rectangles are similar when their length-to-width ratios match, regardless of their actual dimensions. Equal area or perimeter is not required for similarity.
What is a key characteristic of the corresponding angles in similar figures?
They have measures that differ by a constant.
They are congruent.
They each sum to 180°.
They are supplementary.
A defining trait of similar figures is that each pair of corresponding angles is congruent. This ensures that the figures maintain the same overall shape.
A figure that has the same shape but not necessarily the same size is called:
Identical.
Scaled.
Similar.
Congruent.
When a figure maintains its shape but differs in size, it is regarded as similar. Congruent figures, by contrast, are identical in both shape and size.
Triangle ABC is similar to triangle DEF. If side AB measures 4 cm and side DE measures 8 cm, what is the scale factor from triangle ABC to triangle DEF?
2
8
1/2
4
The scale factor is determined by dividing the length of a side in triangle DEF by the corresponding side in triangle ABC, which is 8/4 = 2. This factor is applied to every pair of corresponding sides.
Two similar triangles have areas in the ratio 1:9. What is the ratio of their corresponding side lengths?
9:1
1:3
1:9
3:1
The area ratio of similar figures is the square of the ratio of their corresponding side lengths. Taking the square root of 1:9 gives a side length ratio of 1:3.
If two similar figures have a scale factor of k, what is the ratio of their perimeters?
k
k + 1
k²
1/k
Perimeter being a linear measure scales directly with the scale factor k. Thus, the ratio of the perimeters of similar figures is the same as the scale factor.
The sides of one triangle are 3, 4, and 5. A similar triangle has its shortest side of length 6. What is the length of the side corresponding to 5 in the similar triangle?
12
10
7
8
Determining the scale factor from the shortest sides gives 6/3 = 2. Multiplying the side of length 5 by this factor results in 5 x 2 = 10.
In two similar polygons, if the ratio of the perimeters is 4:7, what is the scale factor of their corresponding sides?
4:14
4:7
7:4
1:1
For similar figures, the ratio of the perimeters is identical to the ratio of any pair of corresponding sides. Therefore, the scale factor is 4:7.
Which statement accurately describes the relationship between similar triangles?
They have proportional angles.
They have equal corresponding angles and proportional corresponding sides.
They share the same area.
They have equal corresponding sides but different angles.
Similar triangles maintain equal corresponding angles and have sides that are proportional. This consistent proportionality allows for solving for unknown side lengths.
For two similar figures, if one side of the smaller figure is 5 cm and the corresponding side of the larger figure is 15 cm, what is the scale factor from the smaller to the larger figure?
1/3
15
3
5
The scale factor is found by dividing the corresponding side in the larger figure by that of the smaller one, yielding 15/5 = 3. This factor applies uniformly across all corresponding linear measurements.
The ratio of areas between two similar figures is 25:49. What is the ratio of their corresponding side lengths?
25:49
7:5
5:7
5:49
Since the area ratio is the square of the side length ratio, taking the square root of 25:49 results in 5:7. This demonstrates the quadratic relationship between side lengths and area in similar figures.
Triangle PQR is similar to triangle XYZ. If the ratio of corresponding sides is 2:3, what is the length of the side in triangle XYZ corresponding to a 10 cm side in triangle PQR?
12 cm
15 cm
20 cm
18 cm
With a side ratio of 2:3, each side from triangle PQR is scaled by a factor of 3/2 to produce the corresponding side in triangle XYZ. Multiplying 10 cm by 3/2 gives 15 cm.
A pair of similar quadrilaterals have corresponding side lengths in the ratio 3:5. If the area of the smaller quadrilateral is 27 square units, what is the area of the larger quadrilateral?
75 square units
135 square units
45 square units
90 square units
The area ratio is the square of the side length ratio, so (3/5)² becomes 9/25. Multiplying the area of the smaller quadrilateral by (25/9) gives 27 à - (25/9) = 75 square units.
Two similar solids have volumes in the ratio 1:27. What is the ratio of their corresponding linear dimensions?
1:27
1:9
1:3
3:1
The volume of similar solids scales with the cube of the linear dimensions. Since 27 is 3³, the ratio of the corresponding linear dimensions is 1:3.
Triangle ABC is similar to triangle DEF. If the altitude corresponding to a side in triangle ABC is 5 cm and the corresponding altitude in triangle DEF is 8 cm, what is the scale factor from triangle ABC to triangle DEF?
13/5
13/8
5/8
8/5
Altitudes in similar triangles are corresponding linear dimensions. The scale factor is the ratio of the altitudes, which is 8/5, and this factor applies uniformly to all corresponding sides.
Two similar figures have corresponding sides in the ratio 7:9. What is the ratio of their areas?
81:49
49:81
7:9
14:18
The area of similar figures scales as the square of the ratio of their corresponding sides. Squaring the ratio 7:9 gives 49:81, which is the area ratio.
If triangle LMN is similar to triangle RST and the sides of triangle LMN are 6, 8, and 10, which set of side lengths could represent triangle RST with a rational scale factor?
9, 12, 15
9, 10, 11
10, 12, 15
8, 10, 12
Multiplying the sides of triangle LMN by a scale factor of 1.5 (since 9/6 = 1.5) gives the sides 9, 12, and 15 for triangle RST. This maintains the proportional relationships required for similarity.
A pair of similar triangles have a corresponding side of 5 cm in the smaller triangle and 7 cm in the larger triangle. If the perimeter of the smaller triangle is 30 cm, what is the perimeter of the larger triangle?
50 cm
42 cm
56 cm
35 cm
The scale factor from the smaller triangle to the larger triangle is 7/5. Multiplying the smaller triangle's perimeter of 30 cm by 7/5 gives 42 cm as the perimeter of the larger triangle.
0
{"name":"In similar figures, which property always holds true?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"In similar figures, which property always holds true?, What does the scale factor represent in similar figures?, Two rectangles are similar if their:","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Identify similar figures within various geometric configurations.
  2. Apply proportional reasoning to calculate unknown side lengths.
  3. Analyze scale factors to determine relationships between corresponding dimensions.
  4. Evaluate and justify the steps used to solve similarity problems.
  5. Synthesize geometric concepts to boost problem-solving confidence for upcoming tests.

Similar Figures Worksheet with Answers PDF Cheat Sheet

  1. Understanding Similar Figures - Similar figures share the same shape but might come in all sizes, like tiny triangles next to towering ones! Their corresponding angles match exactly, and every side lines up in perfect proportion. This concept lays the groundwork for everything else in similarity studies. math.net
  2. Proportional Side Lengths - In similar figures, if you compare any side of one shape to its matching side on the other, you'll always get the same ratio. It's like having a secret code that unlocks their relationship. Mastering this idea helps you solve problems with confidence. GeeksforGeeks
  3. Congruent Corresponding Angles - No angle gets left behind - every angle in one figure has an equal twin in the other. Spotting these congruent angles is your first clue that two shapes are indeed similar. It's like matching puzzle pieces that fit perfectly every time. GeeksforGeeks
  4. Scale Factor - Think of scale factor as the magic multiplier that takes you from one figure to its twin. A scale factor of 3 means every side is three times longer, while 0.5 makes it half the size. This multiplier is your best friend when zooming shapes in or out! GeeksforGeeks
  5. Area Ratio - When similar shapes grow or shrink, their areas change by the square of the scale factor. Double the size, and you get four times the area - simple exponents at play! This squared relationship is perfect for quick calculations. BYJU'S
  6. Volume Ratio - In the 3D world, shapes follow an even cooler rule: volumes scale by the cube of the factor. Tripling the dimensions gives you a whopping 27× the volume! This cube law helps you visualize how real objects transform. BYJU'S
  7. Identifying Similar Polygons - To tag two polygons as similar detectives, verify both congruent angles and proportional sides. It's a two-step checklist to confirm you've got a match. Once you spot these clues, you've proven similarity like a geometry pro! Owlcation
  8. Dilation Transformation - Dilation stretches or shrinks figures from a center point, keeping their shape intact. Picture turning up the size dial or shrinking down with a magic lens. This transformation is your visual tool for exploring similarity on the coordinate plane. math.net
  9. Real-Life Applications - Architects, engineers, and cartographers rely on similarity to build scale models and accurate maps. From miniature prototypes to full-scale blueprints, proportional reasoning keeps designs on track. You're using these ideas every time you map out a room or sketch a building! Mathcation
  10. Practice with Worksheets - Drilling similarity problems with worksheets turns theory into habit. Each solved example strengthens your intuition and highlights areas for review. Keep practicing, and you'll handle any similarity challenge that comes your way! Mathcation
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker