- A12.5 cm
- B9 cm
- C8 cm
- D10 cm
Step-by-Step Solution
From Δ ~ Δ (∠ common, ∠ = ∠) we get , so and cm. 12.5 cm comes from pairing with instead of with — the wrong vertex correspondence; 9 cm adds and ; 10 cm copies .
Answer: C) 8 cm
In ΔXYZ, M lies on XY and N lies on XZ with ∠XNM = ∠XYZ. If XM = 5 cm, XN = 4 cm and XZ = 10 cm, find XY.
Class 10Triangles (Similarity)Geometry — Similarity
Key idea: Similarity vs congruence
**Congruent**: same shape AND same size. All corresponding parts equal.
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).
If two triangles are similar with scale factor :
- Corresponding sides differ by factor .
- Corresponding angles are equal (always, by definition).
- Areas differ by factor — critical fact, and a common test question.
**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).
**Similar**: same shape, possibly DIFFERENT size. Corresponding angles equal; corresponding sides PROPORTIONAL (in fixed ratio k).
If two triangles are similar with scale factor :
- Corresponding sides differ by factor .
- Corresponding angles are equal (always, by definition).
- Areas differ by factor — critical fact, and a common test question.
**Examples**:
- Equilateral triangles are ALL similar (same angles 60°-60°-60°).
- A photograph and its enlarged print are similar.
- Two right triangles sharing one acute angle are similar (AA).
Master this chapter in 30 minutes a day.
Don't just memorise the answer — build a daily practice habit.
Practice 5 Similar Questions Free →All Triangles (Similarity) practice questions
More Class 10 Triangles (Similarity) practice
In ΔABC right-angled at A, AD is the altitude to the hypotenuse BC. If BD = 5 cm and CD…In ΔABC, the bisector of ∠A meets BC at D. If AB = 7.5 cm, BD = 5 cm and DC = 6 cm, find…Two right-angled triangles are given. Which single extra fact is enough to guarantee…In ΔLMN, LM = 20 cm, MN = 21 cm and NL = 29 cm. A student says the right angle is at N,…ΔABC ~ ΔPQR with scale factor k = AB/PQ. Which of these quantities is NOT in the ratio k?