Madhyamik Mathematics Suggestion – Similarity focuses on selected questions from সদৃশ্যতা বা Similarity, Chapter 18. The chapter includes objective questions, True or False statements, fill-in-the-blanks, short-answer problems and 5-mark descriptive questions.
This rewritten guide presents the same source-supported question areas in a cleaner and more student-friendly format so that Class 10 students can use it for focused revision.
Similarity Chapter 18 – Important Question Areas
The suggested questions mainly test the basic ideas of similar triangles, proportional division, parallel lines, trapezium properties and relationships between corresponding sides and angles.
| Question Type | Marks | Main Focus |
|---|---|---|
| Multiple Choice Questions | 1 | Similarity and proportionality |
| True or False | 1 | Basic properties of similar figures |
| Fill in the Blanks | 1 | Definitions and standard properties |
| Short Answer | 2 | Reasoning and application |
| Long Answer | 5 | Geometrical proof |
Multiple Choice Questions | MCQ
Question 1
In ΔABC, BC is parallel to PQ. If AD = QC, AB = 12 cm and AQ = 2 cm, find the value of CQ.
Question 2
A line parallel to MN in ΔLMN meets LM and LN at P and O respectively. If PM = LQ, LP = 9 cm and QN = 4 cm, find PM.
Question 3
A line parallel to BC in ΔABC intersects AB and AC at P and Q respectively. If AP = 3.2 cm, AQ = 2.2 cm and QC = 2.2 cm, find the length of AB.
Question 4
A line parallel to BC in ΔABC intersects AB and AC at D and E respectively. If AD = x + 2, DB = 2x + 9, AE = x and EC = 2x + 3, find x.
Question 5
In trapezium ABCD, AD is parallel to BC. A line parallel to BC meets AB and DC at P and Q. If AP : PB = 2 : 1, determine DQ : QC.
True or False | সত্য অথবা মিথ্যা
These statements are useful for quickly revising the fundamental properties of similarity.
Fill in the Blanks | শূন্যস্থান পূরণ
Short Answer Questions | 2 Marks
Question 1 — Similar Triangles and Parallel Lines
If the given intersecting-line configuration forms similar triangles ΔACE and ΔBDE, show the parallel-line relationship indicated by the geometry.
From the similarity of ΔACE and ΔBDE, the corresponding angles are equal. Therefore, the relevant pairs of alternate angles are equal. Equal alternate angles establish a parallel relationship between the corresponding lines.
Question 2 — Rectangle and Square
Will a rectangle measuring 4 cm × 5 cm be similar to a square whose side is 3 cm. Give a reason.
No. Although the corresponding angles of both figures are right angles, their corresponding side ratios are not equal. Therefore, the rectangle and the square are not similar.
Question 3 — Comparing Two Passport-Size Photographs
Are a passport-size photograph taken ten years ago and a current passport-size photograph necessarily similar. Give a reason.
No. The two photographs may have the same stated size but their shapes may be different. Similarity depends on the preservation of shape and proportional dimensions, not merely on having the same nominal size.
Long Answer Questions | 5 Marks
Question 1 — Intersecting Chord and Diameter
A circle has AB as its diameter. PQ is a chord perpendicular to AB, and AB and PQ intersect at R. Prove that:
Proof
Question 2 — Perpendicular from a Point on a Circle
In a circle with centre O, AB is a diameter. From a point P on the circle, a perpendicular is drawn to AB and meets AB at N. Prove the corresponding product relationship given by the similarity of the two right triangles.
Proof
Important Similarity Concepts for Quick Revision
| Concept | Key Point |
|---|---|
| Similar Triangles | Corresponding angles are equal and corresponding sides are proportional. |
| Congruent Triangles | Congruent figures have the same shape and the same size. |
| Equilateral Triangles | All equilateral triangles are similar because their corresponding angles are equal. |
| Squares | All squares have the same shape, so they are similar. |
| Circles | All circles have the same shape, although their sizes may differ. |
| Parallel-Line Division | A line parallel to one side of a triangle produces proportional division of the other two sides. |
| Trapezium | A line parallel to the parallel sides divides the other two sides proportionally. |
How to Prepare Similarity Questions
Quick Revision Table
| Section | What to Revise | Priority |
|---|---|---|
| MCQ | Proportional division and similarity-based calculations | High |
| True or False | Difference between similarity and congruence | High |
| Fill in the Blanks | Standard similarity properties | High |
| Short Answer | Reasoning using angles, side ratios and shape | High |
| 5-Mark Problems | Similar triangles and geometrical proof | Very High |
Final Revision Note
For Madhyamik Mathematics Chapter 18 – Similarity, students should give special attention to proportional sides, corresponding angles, similar triangles and parallel-line constructions. The objective questions are useful for quick revision, while the descriptive problems require a proper sequence of geometrical reasoning.
Before writing a proof, identify the triangles involved, establish their similarity and then use the resulting proportional relationship. This approach makes the longer questions more systematic and easier to present in the examination.
Explore More Madhyamik Mathematics Resources
For broader Class 10 revision, you can also explore the Cademy Madhyamik suggestion resource covering Mathematics and other WBBSE subjects.
Explore Madhyamik Suggestion 2027 →