SSS Similarity Criterion (Motivate) MCQs Quiz | Class 10
This quiz covers Class X Mathematics (Code 041), Unit IV: Geometry, focusing on the SSS Similarity Criterion (Motivate). It explores the concepts that when sides of two triangles are proportional, the triangles are similar, which in turn means their corresponding angles are equal. Test your understanding by attempting all 10 multiple-choice questions, then submit to check your score and download a detailed answer PDF for review.
Understanding SSS Similarity Criterion
The SSS (Side-Side-Side) similarity criterion is a fundamental concept in geometry that helps us determine if two triangles are similar based solely on the lengths of their sides. Similarity means that two figures have the same shape but not necessarily the same size. One triangle can be thought of as an enlarged or reduced version of the other.
Key Concepts of SSS Similarity
- Definition: Two triangles are similar if the ratios of their corresponding sides are equal. This means if we have two triangles, say ABC and DEF, and if AB/DE = BC/EF = AC/DF, then Triangle ABC is similar to Triangle DEF (denoted as Triangle ABC ~ Triangle DEF).
- Proportional Sides: The term “proportional” means that when you divide the length of a side from the first triangle by the length of its corresponding side in the second triangle, you get the same constant value for all three pairs of sides. This constant value is often called the ‘scale factor’.
- Consequence – Equal Angles: A crucial outcome of SSS similarity is that if two triangles are similar by the SSS criterion (i.e., their sides are proportional), then their corresponding angles must also be equal. For Triangle ABC ~ Triangle DEF, it implies that Angle A = Angle D, Angle B = Angle E, and Angle C = Angle F.
Example: Proportional Sides Leading to Similarity
Consider two triangles:
Triangle 1 (ABC):
- AB = 4 cm
- BC = 6 cm
- AC = 8 cm
Triangle 2 (DEF):
- DE = 2 cm
- EF = 3 cm
- DF = 4 cm
Let’s check the ratios of corresponding sides:
| Side Pair | Ratio | Value |
|---|---|---|
| AB/DE | 4/2 | 2 |
| BC/EF | 6/3 | 2 |
| AC/DF | 8/4 | 2 |
Since all ratios are equal to 2, the corresponding sides are proportional. Therefore, by the SSS Similarity Criterion, Triangle ABC ~ Triangle DEF. This also means that their corresponding angles are equal (e.g., Angle A = Angle D, Angle B = Angle E, Angle C = Angle F).
Quick Revision Points
- SSS Similarity: All three pairs of corresponding sides must be in the same ratio.
- Proportionality implies similarity.
- Similarity implies corresponding angles are equal.
- The constant ratio is the scale factor between the triangles.
Practice Questions
- Triangle XYZ has sides 7, 9, 11 units. Triangle PQR has sides 14, 18, 22 units. Are these triangles similar? If so, by which criterion?
- If two triangles are similar by SSS, and the ratio of their smallest sides is 1:2, what is the ratio of their largest sides?
- Triangle LMN has sides LM=5, MN=12, NL=13. Triangle STU has sides ST=10, TU=24, US=26. What can you say about the angles of Triangle LMN compared to Triangle STU?
- What is the necessary condition for two triangles to be similar using the SSS criterion?
- If Triangle ABC ~ Triangle XYZ and AB/XY = 3/4, then what is the value of BC/YZ?
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