Triangles:
The chapter 'Triangles' is typically carries a weightage of around eight marks in the board exam. It covers the concepts like 'Basic proportionality theorem, Similarity of triangles and Criteria for similarity of triangles.
Most possible variation of question types that we can expect in board exam as per previous year question paper are discussed below.
| Total marks 8 | |
| Variation 1 | Variation 2 |
Total marks = 8
|
Total marks = 8
|
- Basic proportionality theorem - theorem, finding missing term, checking for parallel lines.
- Similarity of triangles - checking similarity in triangles, finding missing terms
- Criteria for similarity of triangles - AAA, SSS, SAS similarity criterion.
| Important concept(Learning Outcomes) | Expected Question Type | Concept dealt with |
|
Basic proportionality theorem - finding missing terms,
checking for parallel lines
|
Sec A - MCQ, Sec B | Find the missing side |
| Basic proportionality theorem | Sec D | Prove the following |
|
Similarity of triangles - finding missing terms,
prove the conditions using similarity criterias
|
Sec A, Sec B Sec D |
Let us recall the concepts in Triangles:
1. Basic proportionality theorem or Thales theorem:
If a line is drawn parallel to one side of a triangle to intersect the other two sides in distinct points, the other two sides are divided in the same ratio.
2. Converse of Basic proportionality theorem:
If a line divides any two sides of a triangle in the same ratio, then the line is parallel to the third side.
3. Two triangles are similar; if
(i) Their corresponding angles are equal, and
(ii) Their corresponding sides are in the same ratio(or proportion).
4. AAA criteria: If in two triangles, corresponding angles are equal, then their corresponding sides are in the same ratio (or proportion) and hence the two triangles are similar.
5. SSS criteria: If in two triangles, sides of one triangle are proportional to (i.e., in the same ratio of ) the sides of the other triangle, then their corresponding angles are equal and hence the two triangles are similar.
6. SAS criteria: If one angle of a triangle is equal to one angle of the other triangle and the sides including these angles are proportional, then the two triangles are similar.