- A5 cm
- B15 cm
- C11 cm
- D22 cm
Step-by-Step Solution
(AAS: common , right angles at and ), so by CPCT. , so cm.
Answer: C) 11 cm
In △ABC, AB = AC (tick marks). BE ⊥ AC and CF ⊥ AB are altitudes with CF = cm and BE = cm. Find the length of the orange altitude BE.
Class 9Triangles (Congruence)Geometry — Triangles
Key idea: Isosceles triangle properties
**Theorem**: Angles opposite equal sides of an isosceles triangle are equal.
In ΔABC if AB = AC, then ∠B = ∠C.
**Proof sketch**: Drop a median (or angle bisector) from A to BC, meeting at D.
- AB = AC (given), AD = AD (common), BD = DC (median).
- By SSS, ΔABD ≅ ΔACD.
- By CPCT, ∠B = ∠C. ✓
**Converse**: Sides opposite equal angles are equal. (∠B = ∠C → AB = AC.)
In ΔABC if AB = AC, then ∠B = ∠C.
**Proof sketch**: Drop a median (or angle bisector) from A to BC, meeting at D.
- AB = AC (given), AD = AD (common), BD = DC (median).
- By SSS, ΔABD ≅ ΔACD.
- By CPCT, ∠B = ∠C. ✓
**Converse**: Sides opposite equal angles are equal. (∠B = ∠C → AB = AC.)
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