NCERT Class 10 Maths • Chapter 6
Triangles Class 10 Worksheet with Online Quiz and Games
Practise similarity and proportional reasoning through 20 MCQs, 10 five-question revision sets and five extra questions with geometry diagrams.
Triangles Online Quiz for Class 10
Question 1 of 20 • Core reasoning • Answered 0/20
DE ∥ BC. If AD = 6, DB = 9 and AE = 8, find EC.
Triangles Online Games for Class 10
Each set has two easy questions, two average questions and one HOTS challenge.
1. BPT Segment Workshop
In every question, D lies on AB, E lies on AC and DE ∥ BC. Lengths are in cm.
AD = 5, DB = 7 and AE = 10. Find EC.
2. Corresponding-Side Navigator
Follow the vertex order rather than the orientation of the drawing.
△ABC ∼ △PQR. AB = 7, PQ = 14 and BC = 9. Find QR.
3. Converse of BPT Constructor
Choose the missing measure so DE becomes parallel to BC. D and E are interior points.
AD = 3, DB = 4 and AE = 9. Choose EC.
4. Nested Parallel-Line Lab
A,D,F,B lie in order on AB; A,E,G,C lie in order on AC. DE ∥ FG ∥ BC.
AD/AB = 13, AF/AB = 23 and BC = 24. Find DE and FG.
5. Build a Geometry Proof
Tap the reasoning cards in order. Use Undo to revise the argument.
Given DE ∥ BC, arrange the AA similarity argument.
Triangles HOTS Online Activities for Class 10
Explore algebraic lengths, shadows, trapeziums, ratio errors and counterexamples.
6. Algebraic Length Detective
DE ∥ BC in every question. Solve for x and check that the segments are positive.
AD = x, DB = 6, AE = 8 and EC = 12. Find x.
7. Shadow and Lamp Investigator
Use vertical objects and level ground. Sunlight questions assume the same light direction.
A 2 m staff casts a 3 m shadow. A tower casts a 21 m shadow. Find its height.
8. Trapezium Diagonal Lab
AB ∥ CD and diagonals AC and BD intersect at O. Use △AOB ∼ △COD.
AB = 6, CD = 15 and AO = 4. Find OC.
9. Repair the Ratio Error
Replace a misleading ratio with the correct part-to-part or corresponding-side relationship.
DE ∥ BC and AD : DB = 2 : 3. AE = 10. A student calls 15 the whole AC. Find the correct EC and AC.
10. Construct and Disprove
Choose valid lengths yourself. More than one answer can be accepted.
AD = 2 and DB = 3. Choose positive integer AE and EC so that DE ∥ BC.
Use positive integers from 1 to 20.
Triangles Class 10 Worksheet Guide
Use the existing worksheet download option on this page for written practice. This Triangles Class 10 worksheet adds diagram-based questions and interactive revision on similarity, the Basic Proportionality Theorem and its converse.
Start a geometry solution by recording the given information. Identify the triangles, establish the relevant angle equalities or side proportions and write the vertex correspondence before using a ratio.
For NCERT Class 10 Maths Chapter 6, BPT connects parallel lines with proportional side divisions. Its converse works in the other direction: proportional divisions establish parallelism. Check whether a question gives parallel lines or asks you to prove them.
The similarity sets practise AA, SSS and SAS reasoning. In SAS, the equal angle must be included between the two sides whose ratios are compared. A triangle’s appearance on the screen is not a reason for similarity.
The Triangles Class 10 HOTS activities include nested parallel lines, trapezium diagonals, shadow measurements and error analysis. Each set contains five questions so students can revisit the same skill with increasing reasoning demands.
These are original practice questions rather than questions labelled as previous year board questions. Use the separate Triangles notes and mind map for revision, then return to the worksheet to apply and justify each result.
BPT and Similar Triangles Formula Guide
For D on AB and E on AC, with DE ∥ BC:
ADDB = AEEC
Also, △ADE ∼ △ABC, so:
ADAB = AEAC = DEBC
Keep part-to-part ratios separate from part-to-whole ratios. Remember AB = AD + DB and AC = AE + EC.
- AA: two pairs of corresponding angles are equal.
- SSS: three pairs of corresponding sides are proportional.
- SAS: two side pairs are proportional and their included angles are equal.
Triangles Class 10 Extra Practice Questions
Mixed Triangles Revision
Five additional questions. Write the theorem and ratio before checking.
DE ∥ BC. AD = 8, DB = 12 and AE = 14. Find EC.
Triangles Revision Tips for Students
- Match vertices before matching sides.
- State the reason for every important angle equality.
- Check parallelism before applying BPT.
- Use the converse when proportional divisions are given.
- Distinguish a whole side from its remaining segment.
- Keep the direction of every corresponding-side ratio consistent.
- Check that algebraic lengths are positive.
- Use the stated measurements rather than estimating from a diagram.
Triangles Tips for Parent and Teacher
- Ask students to name the corresponding vertices before calculating.
- Compare BPT with its converse using the same diagram.
- Discuss why two proportional sides alone do not establish similarity.
- Ask for a written justification after the final HOTS question in each set.
Triangles Class 10 Worksheet FAQs
What is the Basic Proportionality Theorem?
A line parallel to one side of a triangle divides the other two sides in the same ratio. Apply it only after the required parallelism is established.
How is the converse of BPT different?
The converse starts with proportional side divisions and concludes that the joining line is parallel to the third side.
How do I match corresponding sides?
Use the similarity statement. In △ABC ∼ △PQR, A matches P, B matches Q and C matches R. Therefore AB matches PQ, BC matches QR and AC matches PR.
What is the difference between AA and SAS similarity?
AA uses two pairs of equal angles. SAS uses two proportional side pairs and equality of the angle included between those sides.
Are two proportional side pairs enough to establish similarity?
No. Additional information is required, such as equality of the included angles for SAS or proportionality of the third side pair for SSS.
Why is AD divided by DB different from AD divided by AB?
DB is only the remaining part of AB. Since AB = AD + DB, a part-to-part ratio is different from a part-to-whole ratio.
How do shadow problems use similar triangles?
Vertical objects on level ground form right triangles with their shadows. Under sunlight with the same direction, the corresponding acute angles agree, allowing AA similarity.
How are trapezium diagonals connected with similarity?
The parallel bases produce equal alternate angles, while the intersecting diagonals give equal vertically opposite angles. The resulting similar triangles give proportional diagonal segments.
Do similar triangles always have equal sides?
No. Their corresponding sides are proportional. Equal corresponding sides occur when the scale factor is 1.
Can students practise more questions within one activity?
Yes. Every revision set contains five questions. Previous Question and Next Question preserve entries while students move through the set.
Continue with the Triangles Online Quiz for Class 10
Complete a revision set, explain the theorem behind your answer and return to the online quiz to check your progress.
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