Inaugurated by IN-SPACe
ISRO Registered Space Tutor
S3-SA2-0465
What is the SSS Similarity Criterion?
Grade Level:
Class 6
AI/ML, Data Science, Physics, Economics, Cryptography, Computer Science, Engineering
Definition
What is it?
The SSS (Side-Side-Side) Similarity Criterion states that if the corresponding sides of two triangles are proportional, then the triangles are similar. This means their shapes are the same, even if their sizes are different.
Simple Example
Quick Example
Imagine you have a small photo of your family and a larger, enlarged print of the exact same photo. The shapes of the people and objects in both photos are identical, but their sizes are different. This is like SSS Similarity – the sides of the larger photo are just a scaled-up version of the smaller photo's sides.
Worked Example
Step-by-Step
Let's check if Triangle ABC and Triangle PQR are similar using SSS Criterion.
Triangle ABC has sides AB = 3 cm, BC = 4 cm, CA = 5 cm.
Triangle PQR has sides PQ = 6 cm, QR = 8 cm, RP = 10 cm.
Step 1: Identify corresponding sides. AB corresponds to PQ, BC to QR, and CA to RP.
---
Step 2: Calculate the ratio of corresponding sides AB/PQ. Ratio = 3/6 = 1/2.
---
Step 3: Calculate the ratio of corresponding sides BC/QR. Ratio = 4/8 = 1/2.
---
Step 4: Calculate the ratio of corresponding sides CA/RP. Ratio = 5/10 = 1/2.
---
Step 5: Compare the ratios. All ratios are equal (1/2).
---
Step 6: Conclude based on SSS Criterion. Since all corresponding sides are proportional, Triangle ABC is similar to Triangle PQR.
Answer: Yes, Triangle ABC and Triangle PQR are similar by SSS Similarity Criterion.
Why It Matters
Understanding similarity helps engineers design models of bridges or buildings before constructing the real ones, ensuring they are stable. Data scientists use similar shapes to recognize patterns in images, like identifying different types of cars. This concept is vital for architects, game developers, and even in creating special effects in movies!
Common Mistakes
MISTAKE: Students confuse similarity with congruence. | CORRECTION: Similarity means same shape, different (or same) size. Congruence means same shape AND same size.
MISTAKE: Students don't match corresponding sides correctly. | CORRECTION: Always match the shortest side of one triangle with the shortest side of the other, the medium with medium, and the longest with longest, or match sides opposite corresponding angles.
MISTAKE: Students calculate ratios as big/small for some sides and small/big for others. | CORRECTION: Be consistent! If you start with (Triangle 1 side / Triangle 2 side), maintain that order for all three pairs of sides.
Practice Questions
Try It Yourself
QUESTION: Triangle XYZ has sides 2 cm, 3 cm, 4 cm. Triangle MNO has sides 4 cm, 6 cm, 8 cm. Are they similar by SSS? | ANSWER: Yes
QUESTION: Triangle DEF has sides DE=5, EF=7, FD=9. Triangle GHI has sides GH=10, HI=14, IG=16. Are they similar by SSS? Show your ratios. | ANSWER: No, because 9/16 is not equal to 5/10 or 7/14.
QUESTION: A small triangular park has sides 15m, 20m, 25m. A map of this park shows sides of 3cm, 4cm, 5cm. Is the map similar to the actual park? What is the scale factor (ratio of map side to park side)? | ANSWER: Yes, they are similar. Scale factor is 1/500 (or 0.002).
MCQ
Quick Quiz
Which of the following describes triangles that are similar by SSS criterion?
Their corresponding angles are equal.
Their corresponding sides are proportional.
They have the same size and shape.
Only two pairs of corresponding sides are proportional.
The Correct Answer Is:
B
The SSS Similarity Criterion specifically states that if the corresponding sides of two triangles are proportional, then the triangles are similar. Option A describes AA similarity, Option C describes congruence, and Option D is incorrect as all three pairs must be proportional.
Real World Connection
In the Real World
When architects design buildings in India, they first create small-scale models. These models are 'similar' to the actual building. They use the SSS principle to ensure all parts of the model are in correct proportion to the real building, helping them visualize and test designs efficiently, just like how ISRO scientists make small models of rockets.
Key Vocabulary
Key Terms
SIMILAR: Having the same shape but possibly different sizes | PROPORTIONAL: Having a constant ratio | CORRESPONDING SIDES: Sides that are in the same relative position in two different figures | RATIO: A comparison of two numbers by division
What's Next
What to Learn Next
Great job understanding SSS Similarity! Next, you should explore the 'SAS (Side-Angle-Side) Similarity Criterion' and 'AA (Angle-Angle) Similarity Criterion'. These build on your knowledge of proportionality and help you identify similar triangles in even more situations.
